Abstracts - Dipartimento di Elettronica Applicata
Abstracts - Dipartimento di Elettronica Applicata
Abstracts - Dipartimento di Elettronica Applicata
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Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Fifth Italian Workshop on<br />
Metamaterials and Special Materials for<br />
Electromagnetic Applications and TLC<br />
&<br />
IV Italian Workshop “The Finite Element<br />
Method Applied to Electrical and Information<br />
Engineering”<br />
Rome 13-15 December, 2010<br />
<strong>Abstracts</strong><br />
Organized by “Roma Tre” University<br />
in cooperation with the University of Naples “Federico II”, the<br />
University of Sannio, the University of Salerno, and the Microwave<br />
Engineering Center for Space Applications (MECSA)<br />
1
Technical sponsors<br />
Gold sponsors<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Printed: Rome, Italy, December 2010<br />
2
Meta 2010 - Committees<br />
Chairmen<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
L. Vegni, “Roma Tre” University<br />
A. Toscano, “Roma Tre” University<br />
Scientific Committee<br />
F. Bilotti, “Roma Tre” University (chairman)<br />
G. Abbate, University of Naples "Federico II"<br />
A. Andreone, University of Naples "Federico II"<br />
F. Frezza, MECSA - "Sapienza" University of Rome<br />
V. Gal<strong>di</strong>, University of Sannio<br />
I.M. Pinto, University of Sannio<br />
A. Scaglione, University of Salerno<br />
G. Vecchi, Polytechnic of Turin, liaison with IEEE<br />
Local Committee<br />
M. Barbuto, “Roma Tre” University<br />
A. Monti, “Roma Tre” University<br />
D. Ramaccia, “Roma Tre” University<br />
3
FEM 2010 - Committees<br />
Chairmen<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
G. Schettini - Università "Roma Tre"<br />
A. Di Napoli - Università "Roma Tre"<br />
Scientific Committee<br />
S. Caorsi - Università <strong>di</strong> Pavia<br />
M. Feliziani - Università dell'Aquila<br />
G. Ghione - Politecnico <strong>di</strong> Torino<br />
R. Graglia - Politecnico <strong>di</strong> Torino<br />
G. Molinari - Università <strong>di</strong> Genova<br />
G. Pelosi - Università <strong>di</strong> Firenze<br />
G. Rubinacci - Università "Federico II" <strong>di</strong> Napoli<br />
Organizing Committee<br />
A. Salvini - Università "Roma Tre"<br />
A. Toscano - Università "Roma Tre"<br />
L. Pajewski - Università "Roma Tre"<br />
F. Riganti Fulginei - Università "Roma Tre"<br />
Secretary<br />
L. Di Palma - Università "Roma Tre"<br />
G. Pulcini - Università "Roma Tre"<br />
D. Ramaccia - Università "Roma Tre"<br />
G. Rossi - Università "Roma Tre"<br />
4
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Index<br />
Meta 2010 - Introduction 6<br />
Meta 2010 - Foreword 7<br />
FEM 2010 - Introduction 8<br />
FEM 2010 - Foreword 9<br />
Scientific Program<br />
Session MTM-1<br />
10<br />
Recent advances in Metamaterials and Photonic Quasi-Crystals<br />
Session MTM-2<br />
17<br />
Artificial electromagnetic materials: phenomenology and applications<br />
Session FEM-1<br />
20<br />
Magnetic device modeling<br />
Session FEM-2<br />
25<br />
Biome<strong>di</strong>cal applications and large scale problems<br />
Session MTM-3<br />
29<br />
Microwave metamaterial applications I<br />
Session MTM-4<br />
34<br />
Non-linear metamaterials<br />
Session FEM-3<br />
38<br />
Methods and solvers<br />
Session FEM-4<br />
43<br />
Design and applications<br />
Session MTM-5<br />
47<br />
Microwave metamaterial applications II<br />
Session MTM-6<br />
52<br />
Optical metamaterial applications<br />
Session MTM-7<br />
56<br />
Metamaterials theory and modeling 61<br />
Authors’ Index 67<br />
5
Meta 2010 - Introduction<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
The Fifth Italian Workshop on Metamaterials and Special Materials for<br />
Electromagnetic Applications and TLC continues the series of successful<br />
metamaterial meetings, following Florence (2003), Rome (2004, 2006), and Naples<br />
(2008). This year the event is jointly held with the IV Italian Workshop “The Finite<br />
Element Method Applied to Electrical and Information Engineering”. The workshop,<br />
hosted and organized by “Roma Tre” University in cooperation with “Federico II”<br />
University of Naples, Salerno University, Sannio University, and the Microwave<br />
Engineering Center for Space Applications (MECSA), takes place in the charming<br />
atmosphere of Rome during Christmas time.<br />
6
Meta 2010 Foreword<br />
La<strong>di</strong>es and Gentlemen,<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
welcome to the Fifth Workshop on Metamaterials and Special Materials for<br />
Electromagnetic Applications and TLC, held in Rome for the third time. As the<br />
chairmen of the workshop, we are very glad of welcoming all of you to this venue and<br />
to host these three exciting days of talks on metamaterials and special material<br />
applications in electromagnetics. This year the workshop is held jointly with the IV<br />
Italian Workshop “The Finite Element Method Applied to Electrical and Information<br />
Engineering”, that will be introduced in the afternoon by Profs. Giuseppe Schettini<br />
and Augusto Di Napoli.<br />
This workshop is aimed to present the recent research advances in the metamaterials<br />
and special materials area. It includes theoretical, numerical, and experimental<br />
contributions to the understan<strong>di</strong>ng of the behavior of several classes of metamaterials<br />
and to their potential applications in components, devices, and antennas at microwave<br />
up to optical frequencies. There is evidently a renewed interest around the scientific<br />
community in using and designing artificial structures to develop composite materials<br />
that mimic known material responses and that have new, physically realizable<br />
response functions that are not rea<strong>di</strong>ly available in nature. Starting from the word<br />
itself, meta-materials, it is evident how physicists, chemists and engineers involved in<br />
this field are investigating new possibilities for going beyond the limits that natural<br />
materials have in <strong>di</strong>fferent applications.<br />
This year the Scientific Committee, chaired by Prof. Filiberto Bilotti, has accepted 24<br />
abstracts, all of them from excellent research schools and with a very high quality<br />
level. This is a clear in<strong>di</strong>cation of the interest that metamaterials and special materials<br />
are raising at the moment in Italy. We are also very proud to have here three among<br />
the most internationally recognized scientists lea<strong>di</strong>ng the research on Metamaterials:<br />
Prof. Nikolay Zheludev from the University of Southampton, UK, Prof. Rick<br />
Ziolkowski from the University of Arizona, USA, and Prof. Silvio Hrabar from<br />
Zagreb University, Croatia. Thank you for being here and for having accepted our<br />
invitation.<br />
Finally, we would like to thank the IEEE Italy Section for technically supporting this<br />
event, Anosoft and CST for the financial support as Gold Sponsors, the members of<br />
the scientific and the organizing committees for the efforts they have spent for making<br />
this event possible, the Rector of “Roma Tre” University who gave us this beautiful<br />
room where we meet today, the authors of the papers for the high-level contributions<br />
they are going to present, and all of you for coming here in Rome to attend this event.<br />
We sincerely hope that you will enjoy your attendance to this workshop and to the<br />
social event we have organized. We will not steal more time to the sessions.<br />
Welcome to Rome!<br />
Lucio Vegni & Alessandro Toscano<br />
Chairmen of the Fifth Italian Workshop<br />
on Metamaterials and Special Materials for Electromagnetic Applications and TLC<br />
7
FEM 2010 - Introduction<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
The Fourth Italian Workshop on the Finite Element Method applied to Electrical and<br />
Information Engineering continues the series of successful meetings, following<br />
Cassino (2001), Genova (2004), and Rome (2007). This year, the vent is jointly held<br />
with the Fifth Italian Workshop on Metamaterials and Special Materials for<br />
Electromagnetic Applications and TLC. The workshop, hosted and organized by<br />
“Roma Tre” University takes place in the charming atmosphere of Rome during<br />
Christmas time.<br />
8
FEM 2010 Foreword<br />
La<strong>di</strong>es and Gentlemen,<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
welcome to the Fourth Italian Workshop on Finite Element Method applied to<br />
Electrical and Information Engineering, held in Rome for the second time. We are<br />
very glad of welcoming all of you to this event and have the occasion of <strong>di</strong>scussing<br />
about so exciting arguments on finite elements applied to electrical and information<br />
engineering during the workshop.<br />
This year the workshop is jointly held with Fifth Italian Workshop on Metamaterials<br />
and Special Materials for Electromagnetic Applications and TLC, that has the<br />
opening session in the morning.<br />
This workshop is aimed to present the recent research advances in the finite element<br />
method and its advanced applications. It includes numerical and experimental<br />
contributions to the comprehension of the behavior of several kinds of devices and to<br />
their applications as magnetic sensors, devices, electrical machines, antennas, and<br />
gui<strong>di</strong>ng components at microwave up to optical frequencies. The interest in studying<br />
new theoretical and numerical extensions of the method is renewing together with its<br />
application to an increasing number of <strong>di</strong>fferent and new fields. Among these we can<br />
cite magnetic modeling, biome<strong>di</strong>cal applications, microwave components,<br />
metamaterials, etc.<br />
This year the Scientific Committee has accepted 16 abstracts, all of them from<br />
excellent research schools and with a very high quality level. This is a clear in<strong>di</strong>cation<br />
of the interest that the finite element method is an active area of research in Italy. We<br />
are also very proud to have here one of the most internationally recognized scientists<br />
lea<strong>di</strong>ng the research on magnetic devices: Prof. Norio Takahashi from Okayama<br />
University, Japan. Thank you for being here and for having accepted our invitation.<br />
Finally, we would like to thank the IEEE Italy Section for technically supporting this<br />
event, Ansoft and CST for the financial support as Gold Sponsors, the members of the<br />
scientific and the organizing committees for the efforts they have spent for making<br />
this event possible, the Rector of “Roma Tre” University who gave us this beautiful<br />
room where we meet today, the authors of the papers for the high-level contributions<br />
they are going to present, and all of you for coming here in Rome to attend this event.<br />
We sincerely hope that you will enjoy your attendance to this workshop and to the<br />
social event we have organized. We will not steal more time to the sessions.<br />
Welcome to Rome!<br />
Augusto Di Napoli & Giuseppe Schettini<br />
Chairmen of the Fourth Italian Workshop<br />
on Finite Element Method applied to Electrical and Information Engineering<br />
9
08:30 – 09:20 Registration<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Scientific Program<br />
Monday 13 December 2010<br />
09:20 – 09:30 Opening Ceremony of Meta 2010<br />
Introduction of the Chairmen, L. Vegni and A. Toscano (“Roma<br />
Tre” University)<br />
09:30 – 10:50 Session MTM-1 – Recent advances in Metamaterials and<br />
Photonic Quasi-Crystals<br />
Chairperson: G. Schettini, “Roma Tre” University<br />
09:30-10:10<br />
Invited paper – N. Zheludev<br />
The road ahead for metamaterials: nonlinear, switchable and quantum<br />
metameterials<br />
10:10-10-30<br />
G. Strangi, A. De Luca, and R. Bartolino<br />
Gain induced optical transparency in meta-subunits<br />
10:30-10:50<br />
A. Ricciar<strong>di</strong>, I. Gallina, M. Pisco, S. Campopiano, G. Castal<strong>di</strong>, A. Cusano, and<br />
V. Gal<strong>di</strong><br />
Numerical and experimental stu<strong>di</strong>es on guided resonances in photonic<br />
quasicrystals<br />
10:50 – 11:20 Coffee break<br />
11:20 – 12:40 Session MTM-2 – Artificial electromagnetic materials:<br />
phenomenology and applications<br />
Chairperson: V. Gal<strong>di</strong>, University of Sannio<br />
11:20-11:40<br />
G. Parisi, D. Sammito, M. Natali, S. De Zuani, D. Garoli, and F. Romanato<br />
Parametrical analysis of metamaterials fishnet<br />
11:40-12:00<br />
E. Di Gennaro, T. Priya Rose, G. Zito, G. Abbate, and A. Andreone<br />
Effect of localized states on photonic quasicrystal waveguides<br />
10
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
12:00-12:20<br />
A.G. Chiariello, C. Forestiere, A. Maffucci, and G. Miano<br />
Scattering properties of carbon nanotube arrays<br />
12:20-12:40<br />
I. Gallina, G. Castal<strong>di</strong>, V. Gal<strong>di</strong>, A. Alù, and N. Engheta<br />
Image formation/<strong>di</strong>splacement and field tunneling in metamaterial<br />
transformation slabs<br />
12:40 – 13:50 Lunch<br />
13:50 – 14:00 Opening Ceremony of FEM 2010<br />
Introduction of the Chairmen, A. Di Napoli and G. Schettini (“Roma<br />
Tre” University)<br />
14:00 – 15:20 Session FEM-1 – Magnetic device modeling<br />
Chairperson: A. Salvini, “Roma Tre” University<br />
14:00-14:40<br />
Invited paper – N. Takahashi<br />
Application of ON/OFF method to new conceptual design of magnetic devices<br />
14:40-15:00<br />
C. Ragusa, B. Montrucchio, V. Giovara, F. Khan, O. Khan, M. Repetto, and B.<br />
Xie<br />
Implementation of a 3D micromagnetic code on a parallel and <strong>di</strong>stributed<br />
architecture<br />
15:00-15:20<br />
S. Coco, A. Laudani, F. Riganti Fulginei, A. Salvini<br />
Neural-FEM approach for the analysis of hysteretic materials in unbounded<br />
domain<br />
15:20 – 15:50 Coffee break<br />
15:50 – 16:50 Session FEM-2 – Biome<strong>di</strong>cal applications and large scale<br />
problems<br />
Chairperson: N. Takahashi, Okayama University<br />
15:50-16:10<br />
S. Coco and A. Laudani<br />
Finite Element model of charge transport across ionic channels<br />
11
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
16:10-16:30<br />
S. Tricarico, M. Goffredo, M. Schmid, S. Conforto, F. Bilotti, T. D’Alessio,<br />
and L. Vegni<br />
Transient model of the human upper limb under surface electrical stimulation<br />
16:30-16:50<br />
B. Bisceglia, F. De Terlizzi, A. Scaglione, NF. Tallarino<br />
Alterazione della elettroporazione in ortope<strong>di</strong>a. Simulazione del trattamento<br />
<strong>di</strong> masse tumorali<br />
16:50-17:10<br />
G. Rubinacci, A. Tamburrino, and S. Ventre<br />
Large scale computation for source integral equations<br />
12
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Tuesday 14 December 2010<br />
09:30 – 10:50 Session MTM-3 – Microwave metamaterial applications I<br />
Chairperson: L. Vegni, “Roma Tre” University<br />
9:30-10:10<br />
Invited paper – R. Ziolkowski<br />
Multi-functional, planar metamaterial-inspired near-field resonant parasitic<br />
antennas<br />
10:10-10:30<br />
E. Di Gennaro, I. Gallina, A. Andreone, G. Castal<strong>di</strong>, and V. Gal<strong>di</strong><br />
Cut-wire-induced enhanced transmission through sub-wavelength slits<br />
10:30-10:50<br />
D. Ramaccia, F. Bilotti, and A. Toscano<br />
Design formulas of High-Impedance Surfaces with circular patch arrays<br />
10:50 – 11:20 Coffee break<br />
11:20 – 12:40 Session MTM-4 – Non-linear metamaterials<br />
Chairperson: A. Andreone, University of Naples “Federico II”<br />
11:20-11:40<br />
A. Ciattoni, C. Rizza, and E. Palange<br />
Multistability at arbitrary low optical intensities through epsilon-near-zero<br />
nonlinear metamaterial<br />
11:40-12:00<br />
M. Centini, A. Benedetti, C. Sibilia, M. Bertolotti<br />
Optimized second harmonic generation in gold square rod chains<br />
12:00-12:20<br />
A. Massaro, F. Spano, R. Cingolani, and A. Athanassiou<br />
Tuning concept of PDMS nanocomposite material for optical fiber<br />
enhancement<br />
12:20-12:40<br />
N. Chikhi, E. Di Gennaro, A. Andreone, E. Esposito, I. Gallina, G. Castal<strong>di</strong>,<br />
and V. Gal<strong>di</strong><br />
Tunable metamaterials operating in the terahertz region<br />
12:40 – 14:00 Lunch<br />
13
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
14:00 – 15:00 Session FEM-3 – Methods and solvers<br />
Chairperson: F. Bilotti, “Roma Tre” University<br />
14:00-14:20<br />
G. Aiello, S. Alfonzetti, S. A. Rizzo, and N. Salerno<br />
A Comparison between Hybrid Methods: FEM-BEM versus FEM-DBCI<br />
14:20-14:40<br />
G. Borzì<br />
A comparison of <strong>di</strong>rect methods for the solution of finite element systems on<br />
shared memory computers<br />
14:40-15:00<br />
C. Molar<strong>di</strong>, E. Coscelli, F. Poli, A. Cucinotta, S. Selleri<br />
C-language-based 2D-optical mode solver<br />
15:00 – 15:20 Sponsor presentation<br />
15:20 – 15:50 Coffee break<br />
15:50 – 17:10 Session FEM-4 – Design and applications<br />
Chairperson: S. Selleri, University of Florence<br />
15:50-16:10<br />
S. Ceccuzzi, S. Meschino, F. Mirizzi, L. Pajewski, C. Ponti, and G. Schettini<br />
A FEM analysis of microwave components for oversized waveguides<br />
16:10-16:30<br />
U. d’Elia, G. Pelosi, S. Selleri, R. Taddei<br />
Finite Element design of CNT-based multilayer absorbers<br />
16:30-16:50<br />
S. Coco, A. Laudani, G. Pulcini, F. Riganti Fulginei, A. Salvini<br />
Optimization of multistage depressed collectors by using FEM and METEO<br />
16:50-17:10<br />
D. Ramaccia, F. Bilotti, and A. Toscano<br />
Parametric bandwidth analysis of an Artificial Magnetic Conductor surface<br />
20:00 – 23:00 Social Dinner at the restaurant “Al Biondo Tevere”<br />
14
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Wednesday 15 December 2010<br />
09:30 – 10:50 Session MTM-5 – Microwave metamaterial applications II<br />
Chairperson: R. Ziolkowski, University of Arizona<br />
09:30-10:10<br />
Invited paper – S. Hrabar<br />
Metamaterials based on non-Foster elements<br />
10:10-10:30<br />
L. Di Palma, F. Frezza, L. Pajewski, E. Piuzzi, C. Ponti, G. Rossi and G.<br />
Schettini<br />
Experimental investigations on woodpile EBG metamaterials<br />
10:30-10:50<br />
F. Bilotti, L. Di Palma, and L. Vegni<br />
Analytical model of connected bi-omega structures for enhanced microwave<br />
transmission<br />
10:50 – 11:20 Coffee break<br />
11:20 – 12:40 Session MTM-6 – Optical metamaterial applications<br />
Chairperson: F. Frezza, “Sapienza” University<br />
11:20-11:40<br />
A. Massaro, F. Spano, R. Cingolani, and A. Athanassiou<br />
Pillar type PDMS nanocomposite optical antenna for liquid detection systems<br />
11:40-12:00<br />
R. Marinelli and E. Palange<br />
Optical performances of micron-sized CMOS image sensors using metallic<br />
planar lenses<br />
12:00-12:20<br />
A. Benedetti, M. Centini, C. Sibilia, M. Bertolotti<br />
Second harmonic generation in gold nanoantennas<br />
12:20-12:40<br />
S. Tricarico, F. Bilotti, and L. Vegni<br />
Controlling optical forces on nanoparticles through metamaterials<br />
12:40 – 14:00 Lunch<br />
15
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
14:00 – 15:40 Session MTM-7 – Metamaterials theory and modeling<br />
Chairperson: S. Hrabar, University of Zagreb<br />
14:00-14:20<br />
P. Fernandes, M. Ottonello, and M. Raffetto<br />
Some comments on the solution of the linear algebraic systems defined by the<br />
finite element method when applied to electromagnetic problems involving<br />
bianisotropic me<strong>di</strong>a<br />
14:20-14:40 (withdrawn)<br />
G. Conte, G. Finocchio, A. Faba, A. Prattella, B. Azzerboni, E. Cardelli<br />
Double negative metamaterials based on ferromagnetic microwire: a<br />
numerical study<br />
14:20-14:40<br />
G. Ruffato and F. Romanato<br />
Near-field numerical analysis of Surface Plasmon Polariton propagation on<br />
metallic gratings<br />
14:40-15:00<br />
A. Massaro, D. Caratelli, A. Yarovoy, R. Cingolani, and A. Athanassiou<br />
Accurate circuit modeling for plasmon probe design<br />
15:00-15:20<br />
P. Zilio, D. Sammito, and F. Romanato<br />
Role of resonances of <strong>di</strong>gital plasmonic gratings in absorption profile<br />
remodulation<br />
16
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Session MTM-1<br />
Recent advances in Metamaterials and Photonic Quasi-Crystals<br />
Chairperson: G. Schettini, “Roma Tre” University<br />
09:30-10:10<br />
Invited paper – N. Zheludev<br />
The road ahead for metamaterials: nonlinear, switchable and quantum<br />
metameterials<br />
10:10-10-30<br />
G. Strangi, A. De Luca, and R. Bartolino<br />
Gain induced optical transparency in meta-subunits<br />
10:30-10:50<br />
A. Ricciar<strong>di</strong>, I. Gallina, M. Pisco, S. Campopiano, G. Castal<strong>di</strong>, A. Cusano, and<br />
V. Gal<strong>di</strong><br />
Numerical and experimental stu<strong>di</strong>es on guided resonances in photonic<br />
quasicrystals<br />
17
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Gain Induced Optical Transparency<br />
in Meta-Subunits<br />
Giuseppe Strangi, Antonio De Luca and Roberto Bartolino<br />
LICRYL (Liquid Crystals Laboratory, IPCF-CNR)<br />
Center of Excellence CEMIF.CAL and Department of Physics,<br />
University of Calabria 87036 Rende (CS), Italy –<br />
Giuseppe.Strangi@fis.unical.it<br />
This work is aimed to compensate absorptive losses in optical metamaterials<br />
based on gain functionalized core shell gold nanoparticles. In particular,<br />
resonant energy transfer from organic fluorescent molecules to noble metal<br />
nanoparticles properly designed to create reconfigurable optical metamaterials<br />
via self-assembling routes is reported. Multiple experimental investigations<br />
show that losses at optical frequencies, mainly due to plasmon-ra<strong>di</strong>ation field<br />
coupling, can be partly compensated. Resonant excitation energy transfer<br />
occurs via non-ra<strong>di</strong>ative process, by proper overlapping gain and plasmonic<br />
spectra and by optimizing size-ratios. The gain assistance of plasmonic<br />
elements through non-ra<strong>di</strong>ative processes is emphasized by Fluorescence<br />
quenching, enhanced Scattering Rayleigh, mitigation of ra<strong>di</strong>ation damping and<br />
related ra<strong>di</strong>ative and non-ra<strong>di</strong>ative effects.<br />
References:<br />
[1] M.I. Stockman , Nature Photonics, 2, 327, (2008)<br />
[2] Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, Phys. Rev. B 79, 241104 (2009).<br />
[3] G. Strangi, A. De Luca, S. Ravaine and R. Bartolino, submitted to Phys. Rev. Lett.<br />
18
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Numerical and Experimental Stu<strong>di</strong>es<br />
on Guided Resonances in Photonic Quasicrystals<br />
Armando Ricciar<strong>di</strong> (1) , Ilaria Gallina (2) , Marco Pisco (2) ,<br />
Stefania Campopiano (1) , Giuseppe Castal<strong>di</strong> (2) , Andrea Cusano (2) ,<br />
and Vincenzo Gal<strong>di</strong> (2)<br />
(1) University of Naples “Parthenope”, Department for Technologies<br />
Naples, Italy – E-mail: armando.ricciar<strong>di</strong>@uniparthenope.it,<br />
stefania.campopiano@uniparthenope.it<br />
(2) University of Sannio, Department of Engineering<br />
Benevento, Italy – E-mail: ilaria.gallina@unisannio.it, pisco@unisannio.it,<br />
castal<strong>di</strong>@unisannio.it, acusano@unisannio.it, vgal<strong>di</strong>@unisannio.it<br />
Guided resonances (GRs) [1] in photonic crystal (PC) slabs have been the<br />
subject of several recent stu<strong>di</strong>es. Such resonances can be observed in the<br />
transmittance/reflectance response of a plane-wave-excited PC slab as narrow<br />
Fano-like resonant line shapes superimposed on a smoothly varying<br />
background, and stem from the interference between the <strong>di</strong>rectly<br />
transmitted/reflected wave and the waves originating from the excited leaky<br />
modes.<br />
Here, we compactly review the salient results from a series of ongoing<br />
investigations [2-5] on GRs in aperio<strong>di</strong>cally-ordered “photonic quasicrystal”<br />
(PQC) slabs, intrinsically tied to the concept of “quasicrystal” in solid-state<br />
physics [6]. In particular, we show numerically [2] and experimentally [5]<br />
that, in spite of the seemingly necessary spatial perio<strong>di</strong>city, GRs could also be<br />
observed in PC slabs with quasiperio<strong>di</strong>c supercells based on the Ammann-<br />
Beenker (octagonal) tiling. Besides the phenomenological implications, our<br />
results endow with new perspectives and degrees of freedom in the defectengineering<br />
of GRs [3], and pave the way for new developments and<br />
applications (e.g., to sensing [4]).<br />
References<br />
[1] S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal<br />
slabs,” Phys. Rev. B, 65, 235112, 2002<br />
[2] A. Ricciar<strong>di</strong>, I. Gallina, S. Campopiano, G. Castal<strong>di</strong>, M. Pisco, V. Gal<strong>di</strong>, and A. Cusano,<br />
“Guided resonances in photonic quasicrystals,” Opt. Express, 17, 6335-6346, 2009.<br />
[3] I. Gallina, M. Pisco, A. Ricciar<strong>di</strong>, S. Campopiano, G. Castal<strong>di</strong>, A. Cusano, and V. Gal<strong>di</strong>,<br />
“Guided resonances in photonic crystals with point-defected aperio<strong>di</strong>cally-ordered<br />
supercells,”Opt. Express, 17, 19586-19598, 2009.<br />
[4] M. Pisco, A. Ricciar<strong>di</strong>, I. Gallina, G. Castal<strong>di</strong>, S. Campopiano, A. Cutolo, A. Cusano, and<br />
V. Gal<strong>di</strong>, “Tuning efficiency and sensitivity of guided resonances in photonic crystals and<br />
quasi-crystals: a comparative study,” Opt. Express, 18, 17280-17293, 2010<br />
[5] A. Ricciar<strong>di</strong>, M. Pisco, I. Gallina, S. Campopiano, V. Gal<strong>di</strong>, L. O’ Faolain, T. F. Krauss,<br />
and A. Cusano, “Experimental evidence of guided resonances in photonic crystals with<br />
aperio<strong>di</strong>cally-ordered supercells,” to be published in Opt. Lett., 2010<br />
[6] M. Senechal, Quasicrystals and Geometry, Cambridge University Press, Cambridge, UK,<br />
1995.<br />
19
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Session MTM-2<br />
Artificial electromagnetic materials: phenomenology and<br />
applications<br />
Chairperson: V. Gal<strong>di</strong>, University of Sannio<br />
11:20-11:40<br />
G. Parisi, D. Sammito, M. Natali, S. De Zuani, D. Garoli, and F. Romanato<br />
Parametrical analysis of metamaterials fishnet<br />
11:40-12:00<br />
E. Di Gennaro, T. Priya Rose, G. Zito, G. Abbate, and A. Andreone<br />
Effect of localized states on photonic quasicrystal waveguides<br />
12:00-12:20<br />
A.G. Chiariello, C. Forestiere, A. Maffucci, and G. Miano<br />
Scattering properties of carbon nanotube arrays<br />
12:20-12:40<br />
I. Gallina, G. Castal<strong>di</strong>, V. Gal<strong>di</strong>, A. Alù, and N. Engheta<br />
Image formation/<strong>di</strong>splacement and field tunneling in metamaterial<br />
transformation slabs<br />
20
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Parametrical analysis of metamaterials fish-net<br />
Giuseppe Parisi (1,2) , Davide Sammito (2,3) , Marco Natali (4) , Stefano De<br />
Zuani (1,2) , Denis Garoli (1,2,3) and Filippo Romanato (1,2,3)<br />
(1) University of Padova, Department of Physics<br />
Padova, Italy – E-mail: giuseppe.parisi@unipd.it<br />
(2) LaNN, Laboratory for Nanofabrication of Nanodevices<br />
Padova, Italy<br />
(3) IOM-TASC Natl. Lab. CNR-INFM, Trieste, Italy<br />
(4) CNR-ICIS, Padova, Italy<br />
Recently, the fabrication and optimization of nano-hole arrays in noble metal<br />
layers has attracted much attention both because of the interesting new physics<br />
associated with them and for their potential applications in nano-optics and<br />
biosensing [1,2]. Electric tuneability of the negative refractive index<br />
wavelength is theoretically foreseen to be possible by use of <strong>di</strong>electrics with<br />
electro-optical properties such as PZT. Here we report a design and a<br />
parametrical analysis of metamaterial fishnet in the optical spectral range [3].<br />
In particular a dependence analysis on the geometric features of the fishnet is<br />
carried out for both the magnetic and the electric resonance. We found out that<br />
a sharp negative resonance (electric in nature) is down-shifted to 200 nm by a<br />
stronger resonance (magnetic in origin). This split the bandwidth of negative<br />
refractive index in two frequency domains. For appropriately designed of<br />
squared hole-array structures, the frequency of the magnetic resonance<br />
coincides with a region of negative effective permittivity and a negative index<br />
of refraction is seen in the simulation. In figure 1 the simulated effective<br />
transmittance, reflectance and absorbance of the proposed structure are shown.<br />
We also show in figure 2 how the electric and magnetic resonance depend by<br />
the squared hole of the fishnet.<br />
Fig. 1. Simulated transmittance, reflectance<br />
and absorbance.<br />
21<br />
Fig. 2. Simulated dependence of negative<br />
refractive index on the hole size<br />
References<br />
[1] N.C.Lindquist , A. Lesuffleur, and H.Im Oh, Lab Chip, 9 (2009) 382 - 387.<br />
[2] J. Ji, G. O'Connel, D.J.D. Carter and D.N. Larson, . Anal. Chem., 80 (2008) 2491-2498<br />
[3] J. Valentine, S. Zhang, T.Zentgraf, E. Ulin-Avilal, D.A. Genov, G. Bartal, X. and Zhang,<br />
Nature 455 (2008) 367-379.
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Effect of Localized States on Photonic<br />
Quasicrystal Waveguides<br />
Emiliano Di Gennaro (1) , Priya Rose T. (1) , Gianluigi Zito (2) , Giancarlo<br />
Abbate (1) , and Antonello Andreone (1)<br />
(1) CNR-SPIN and University of Naples “Federico II,” Department of Physics<br />
Naples, Italy – E-mail: emiliano@na.infn.it, priyarose@na.infn.it,<br />
abbate@na.infn.it, andreone@unina.it<br />
(2) CNR-ICIB “E. Caianiello”,<br />
Pozzuoli (NA), Italy – E-mail: zito.gianluigi@libero.it<br />
In recent years, photonic quasicrystals have attracted enormous interest in the<br />
field of photonics of complex structured materials. The lack of translational<br />
symmetry into quasiperio<strong>di</strong>c and aperio<strong>di</strong>c crystals is compensated by longrange<br />
quasiperio<strong>di</strong>c translational order and high rotational symmetries not<br />
achievable by conventional perio<strong>di</strong>c crystals. Photonic Quasicrystals (PQCs)<br />
may possess large photonic bandgaps (PBGs) [1,2] with very interesting<br />
properties of light transmission, wave gui<strong>di</strong>ng and localization [3] that can be<br />
exploited in a wide variety of electro-optical and photonic applications.<br />
In this work we study the PBG properties of an octagonal interferential PQC.<br />
The 2D quasiperio<strong>di</strong>c pattern is obtained by placing ideal <strong>di</strong>electric cylinders<br />
(infinitely long) where the interference of 8 coherent light beams shows its<br />
local maxima [4]. In order to characterize the in-plane PBG properties of the<br />
abovementioned structure, we have designed and performed a series of<br />
experiments in the microwave regime (8-20 GHz). The sample under study<br />
consists of alumina cylindrical rods in air inserted in a parallel plate<br />
waveguide. Transmittance and field maps are obtained using an x-y robot and<br />
two <strong>di</strong>pole antennas connected to a two-port vectorial network analyzer<br />
(VNA) HP 8720C [5]. We focus on the response of a linear waveguide,<br />
whose transmittance can be controlled by tuning the <strong>di</strong>electric properties of<br />
the central post. Experimental results are compared and found in very good<br />
agreement with numerical simulations obtained by finite <strong>di</strong>fferences timedomain<br />
technique.<br />
References<br />
[1] M.E. Zoorob , M.D.B. Charlton, G.J. Parker, J.J. Baumberg, M.C. Netti, “Complete<br />
photonic bandgaps in twelve-fold symmetric quasicrystals” Nature 404, 740, 2000<br />
[2] Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional<br />
Photonic Quasicrystals” , Phys. Rev. Lett. 80, 956, 1998<br />
[3] S. S. M. Cheng, L. Li, C. T. Chan, and Z. Q. Zhang, "Defect and transmission properties<br />
of two-<strong>di</strong>mensional quasiperio<strong>di</strong>c photonic band-gap systems," Phys. Rev. B 59, 4091,<br />
1999<br />
[4] G. Zito, B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, and G. Abbate, "Two<strong>di</strong>mensional<br />
photonic quasicrystals by single beam computer-generated holography," Opt.<br />
Express 16, 5164, 2008<br />
[5] E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Gal<strong>di</strong>, G. Castal<strong>di</strong>, and<br />
V. Pierro, “Evidence of local effects in anomalous refraction and focusing properties of<br />
dodecagonal photonic quasicrystals,” Phys. Rev. B 77, 193104, 2008<br />
22
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Scattering Properties of Carbon Nanotube<br />
Arrays<br />
A. G. Chiariello (1) , C. Forestiere (2) , A. Maffucci (1) and G. Miano (2)<br />
(1) University of Cassino, Department DAEIMI, via Di Biasio 43, Cassino, 03043, Italy Email:<br />
chiariello@unicas.it, maffucci@unicas.it<br />
(2) University of Naples Federico II, Department of Electrical Engineering, via Clau<strong>di</strong>o 21,<br />
Naples, 80125, Italy E-mail: carlo.forestiere@unina.it, miano@unina.it<br />
Due to their unique electrical, thermal and mechanical properties, carbon nanotubes<br />
(CNTs) have been proposed for a wide range of nano-electronics applications [1],<br />
inclu<strong>di</strong>ng interconnects, packages, transistors, passive devices, antennas [2].<br />
Recently, carbon nanotubes have been also proposed as innovative scattering material<br />
[3-4], in the realization of absorbing materials in the aircraft industry, in view of<br />
replacing conventional materials, like polymeric sheets filled with magnetic or<br />
<strong>di</strong>electric loss materials, such as ferrite, permalloy.<br />
In this work we investigate the scattering properties of an array of finite-length<br />
single-wall carbon nanotubes (SWCNTs), up to terahertz frequencies. The problem is<br />
cast in terms of a Pocklington-like equation. The current density along the CNT is<br />
described by a quasi-classical transport model, recently proposed. The numerical<br />
solution is obtained by means of the Galerkin method. Case stu<strong>di</strong>es are carried out,<br />
either referred to isolated SWCNTs and array of SWCNTs, aimed at investigating the<br />
frequency behaviour of the scattered field.<br />
a) b)<br />
Figure 1 – (a) Scattered electric field for a 20µm-long CNT, with ra<strong>di</strong>us of 2.72nm at 300K,<br />
illuminated by a TEM plane wave impinging orthogonally. The scattered field has been<br />
evaluated at a <strong>di</strong>stance of 100 μm (b) Spatial <strong>di</strong>stributions of the current along the CNT at the<br />
frequencies<br />
References<br />
[1] R. H. Baughman, A.A. Zakhidov, W.A. de Heer., “Carbon nanotubes--the route toward<br />
applications ,” Science, 297(5582), 787-792, 2002<br />
[2] S. A Maksimenko, G. Ya. Slepyan, A. M. Nemilentsau, and M. V. Shuba, “Carbon<br />
nanotube antenna: Far-field, near-field and thermal-noise properties,” Physical Rev. E, 40,<br />
2360, 2008.<br />
[3] J. Hao and G.W. Hanson, “Electromagnetic scattering from finite-length metallic carbon<br />
nanotubes in the lower IR bands”, Physical Review B, 74, 035119, 2006.<br />
[4] A.G. Chiariello, C. Forestiere, A. Maffucci and G. Miano, “Scattering Properties of<br />
Carbon Nanotube Arrays,” in press on Intern. Journal of Microwave and Wireless<br />
Technologies<br />
23
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Image Formation/Displacement and Field<br />
Tunneling in Metamaterial Transformation Slabs<br />
Ilaria Gallina (1) , Giuseppe Castal<strong>di</strong> (1) , Vincenzo Gal<strong>di</strong> (1) ,<br />
Andrea Alù (2) , and Nader Engheta (3)<br />
(1) University of Sannio, Department of Engineering<br />
Benevento, Italy – E-mail: ilaria.gallina@unisannio.it,<br />
castal<strong>di</strong>@unisannio.it, vgal<strong>di</strong>@unisannio.it<br />
(2) The University of Texas at Austin, Department of Electrical and Computer<br />
Engineering, Austin, TX 78712, USA – E-mail: alu@mail.utexas.edu<br />
(3) University of Pennsylvania, Department of Electrical and Systems<br />
Engineering, Philadelphia, PA 19104, USA – E-mail: engheta@ee.upenn.edu<br />
Transformation optics has recently emerged as one of the most interesting and<br />
promising approaches to the synthesis of metamaterials for electromagneticfield<br />
manipulation (see, e.g., [1]).<br />
In this work, we review and summarize some recent results [2,3] on the<br />
electromagnetic properties of certain general classes of metamaterial slabs,<br />
inspired by transformation optics, that exploit their intrinsic anisotropy and<br />
inhomogeneity to achieve exotic material properties, within double-positive,<br />
double-negative or single-negative constitutive parameters. In particular, by<br />
means of analytical and numerical full-wave stu<strong>di</strong>es, we derive some<br />
con<strong>di</strong>tions for total transmission, which generalize some previous results in<br />
the literature, and explore the image <strong>di</strong>splacement/formation properties, of<br />
interest for applications such as anti-reflection radomes, anti-cloaking, and<br />
lensing/focusing.<br />
Our results confirm the broad breadth of transformation optics and its<br />
intriguing potentials as a general unifying approach to the design of<br />
application-oriented metamaterials. In particular, we systematically derive the<br />
con<strong>di</strong>tions for designs that do not require negative constitutive parameters, but<br />
that exploit the inherent anisotropy of the transformation slabs to achieve the<br />
required field-manipulation effects within the double-positive (possibly nonmagnetic)<br />
regime of operation.<br />
References<br />
[1] J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science,<br />
312, 1780-1782, 2006<br />
[2] I. Gallina, G. Castal<strong>di</strong>, V. Gal<strong>di</strong>, A. Alù, and N. Engheta, “General class of metamaterial<br />
transformation slabs,” Phys. Rev. B, 81, 125124, 2010<br />
[3] G. Castal<strong>di</strong>, I. Gallina, V. Gal<strong>di</strong>, A. Alù, and N. Engheta, “Transformation-optics<br />
generalization of tunnelling effects in bi-layers made of paired pseudo-epsilonnegative/mu-negative<br />
me<strong>di</strong>a,” to be published in J. Opt. (Special Issue on Transformation<br />
Optics), 2011<br />
24
Session FEM-1<br />
Magnetic device modeling<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Chairperson: A. Salvini, “Roma Tre” University<br />
14:00-14:40<br />
Invited paper – N. Takahashi<br />
Application of ON/OFF method to new conceptual design of magnetic devices<br />
14:40-15:00<br />
C. Ragusa, B. Montrucchio, V. Giovara, F. Khan, O. Khan, M. Repetto, and B.<br />
Xie<br />
Implementation of a 3D micromagnetic code on a parallel and <strong>di</strong>stributed<br />
architecture<br />
15:00-15:20<br />
S. Coco, A. Laudani, F. Riganti Fulginei, A. Salvini<br />
Neural-FEM approach for the analysis of hysteretic materials in unbounded<br />
domain<br />
25
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Application of ON/OFF Method to New<br />
Conceptual Design of Magnetic Devices<br />
Norio Takahashi<br />
Dept. Electrical and Electronic Eng., Okayama Univ. Tsushima, Okayama<br />
700-8530, Japan E-mail: norio@elec.okayama-u.ac.jp<br />
In the development of an electromagnetic device, the design based on the experience<br />
of designers is usually performed. Recently, various optimal design methods using<br />
electromagnetic field analysis are developed and applied to the design of actual<br />
magnetic devices. In those methods, we must imagine the outline of the optimal shape<br />
of the magnetic circuit, and the <strong>di</strong>mensions etc. are determined by the optimization<br />
software. Therefore, it may be <strong>di</strong>fficult to get a newly developed magnetic circuit<br />
which we could not imagine beforehand. If a topology optimization method which<br />
can determine the optimal topology by <strong>di</strong>stributing materials in a design domain is<br />
used, there is a possibility that a new magnetic circuit can be <strong>di</strong>scovered, because it is<br />
not necessary to set design variables in advance. In this paper, the ON/OFF method<br />
which can determine the optimal topology considering 3-D shape and the nonlinearity<br />
of magnetic material is examined. The effectiveness of the newly developed ON/OFF<br />
method is shown applying it to the design of various magnetic devices, such as<br />
magnetic head[1], shield[2], motor[3] etc. Fig.1 shows the obtained shape of high<br />
density magnetic head. A reasonable shape is obtained. Fig. 2 shows the optimal<br />
shape of IPM motor which produces a higher driving torque.<br />
References<br />
[1] K.Akiyama, D. Miyagi, N.Takahashi, “Design of CF-SPT Head Having Large Recor<strong>di</strong>ng Field<br />
and Small Stray Field Using 3-D ON/OFF Method”, IEEE Trans. on Magn., Vol. 42, No.10,<br />
pp.2431-2433, 2006.<br />
[2] N. Takahashi, S. Nakazaki, D. Miyagi: “ Examination of Optimal Design Method of<br />
Electromagnetic Shield Using ON/OFF Method”, IEEE Trans. on Magn., Vol. 45, no.3, pp.1546-<br />
1549, 2009.<br />
[3] N. Takahashi, T. Yamada, D. Miyagi: “Examination Optimal Design of IPM Motor Using ON/OFF<br />
Method ”, IEEE Trans. on Magn., Vol.46, No. 8, pp.3149-3152, 2010.<br />
26
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Implementation of a 3D Micromagnetic Code on a<br />
Parallel and Distributed Architecture<br />
Carlo Ragusa (1) , Bartolomeo Montrucchio (2) , Vittorio Giovara (2) ,<br />
Fiaz Khan (2) , Omar Khan (2) , Maurizio Repetto (1) (1, 3)<br />
, and Baochang Xie<br />
(1) Politecnico <strong>di</strong> Torino, Department of Electrical Engineering<br />
Torino, Italy – E-mail: carlo.ragusa@polito.it<br />
(2) Politecnico <strong>di</strong> Torino, Department of Control and Computer Engineering<br />
Torino, Italy – E-mail: bartolomeo.montrucchio@polito.it<br />
(3) Shanghai Jiaotong University (SJTU), Shanghai 200030,China<br />
We present the implementation of a full micromagnetic code developed on a low cost<br />
and low latency parallel and <strong>di</strong>stributed architecture based on OpenMP [1] and MPI<br />
over Infiniband [2]. Since the most time consuming part of a micromagnetic code is<br />
the magnetostatic field computation algorithm, many existing parallel<br />
implementations take advantage of Ethernet-based computer clusters [3]. Moreover,<br />
in recent years, the availability of low cost multi-core and<br />
multi-processor computers have enabled the parallelization of micromagnetic<br />
programs on shared memory computer systems [4]. In our approach we use a low<br />
latency Infiniband network coupled with a low cost multi processor, multi core<br />
cluster. The hardware architecture includes a 16 cores cluster composed by two<br />
double processor computers. The two computers are connected by means of<br />
Infiniband network cards that are <strong>di</strong>rectly connected together, without using a switch.<br />
The general implementation scheme is summed up in the following. As first, any<br />
standard sequential loop is parallelized to fully exploit all the eight cores<br />
each single machine can offer. By setting up proper shared/private variables lists, the<br />
loop is <strong>di</strong>vided among a given number of OpenMP threads and each carries out a<br />
portion of that iteration. Afterwards, the loop is split in two (n in the general<br />
case of a n nodes cluster) data sets, before executing OpenMP. Each part of the loop is<br />
submitted to a node of the cluster and separately executed. Eventually, at the end of<br />
the loop, data is exchanged back with MPI and merged so that the two (n) machines<br />
can continue working on complete arrays.<br />
References<br />
[1] R. Chandra, L. Dagum, D. Kohr, D. Maydan, J. McDonald, R. Menon, Parallel programming in<br />
OpenMP, Morgan Kaufmann Publishers, 2001<br />
[2] W. Gropp, E. Lusk, A. Skjellum, Using MPI - Portable parallel programming with the Message-<br />
Passing Interface, Scientific and Engineering computation series, The MIT Press, 1999<br />
[3] Y. Kanai, M. Saiki, K. Hirasawa, T. Tsukamomo, and K. Yoshida, IEEE Trans. on Magnetics, 44,<br />
1602, 2008<br />
[4] M.J. Donahue, “Parallelizing a micromagnetic program for use on multiprocessor shared memory<br />
computers” IEEE Trans. on Magnetics, 45, 3923-3925, 2009<br />
27
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Neural-FEM approach for the analysis of Hysteretic<br />
Materials in unbounded domain<br />
S. Coco (1) , A. Laudani (1) , A. Salvini (2) and F. Riganti Fulginei (2)<br />
(1) University of Catania, DIEES Catania, Italy – e-mail: alaudani@<strong>di</strong>ees.unict.it,<br />
coco@<strong>di</strong>ees.unict.it<br />
(2) Roma Tre University of, DEA<br />
Roma, Italy – e-mail: asalvini@uniroma3.it, riganti@uniroma3.it<br />
The Finite Element method has proved to be a powerful tool for the modeling of<br />
electromagnetic devices, thanks to the possibility of accurate representation of<br />
realistic geometry of the device. On the other hand, the modeling of magnetic material<br />
has also been the subject of many stu<strong>di</strong>ed, above all to take into account the hysteresis<br />
phenomenon and to model it in an efficient and accurate way. The possibility of using<br />
Neural Networks to model magnetic hysteresis has been verified in literature [1], and<br />
represents a good solution if a de<strong>di</strong>cated model for the training of the network is<br />
implemented.<br />
In this paper the authors present a Finite Element code for the analysis of magnetic<br />
problems in unbounded domains combined with a Neural Network (NN) approach for<br />
the characterization of magnetic hysteresis. In particular, the proposed NN is capable<br />
to perform the modelling of saturated and non-saturated, symmetric or asymmetric<br />
hysteresis loops. The use of this NN approach is advantageous for avoi<strong>di</strong>ng<br />
identification of hysteresis models and their inversion (if requested). Even if a number<br />
of measurements are requested, they are very simple and fast to perform (asymmetric<br />
saturated static loops). Thus, the present approach can be easily embedded into a set<br />
of field equations since it does not require a preliminary knowledge of the H (or B)<br />
waveform. In ad<strong>di</strong>tion, in order to treat boundlessness in the system of coupled<br />
equations used for solving the magnetic problem, we adopt an iterative scheme based<br />
on a fictitious boundary that encloses all the field sources and the hysteretic material<br />
regions with the aim to define a bounded domain. In this way the unbounded coupled<br />
problem solution is converted into the iterative solution of a sequence of bounded<br />
Dirichlet magnetic hysteresis problems. The boundary con<strong>di</strong>tions on the fictitious<br />
boundary are initially guessed and successively updated accor<strong>di</strong>ng to the solution<br />
obtained in the previous iteration step [3]. The main important advantage of this<br />
approach is its easy implementation starting from FEM codes for bounded domains.<br />
References<br />
[1] H.H. Saliah, D.A. Lowther, and B. Forghani, “A neural network model of magnetic hysteresis for<br />
computational magnetics,” IEEE Trans. on Magnetics, 33, 4146-4148, 1997<br />
[2] F.R. Fulginei and A. Salvini, “Softcomputing for the Identification of the Jiles–Atherton Model<br />
Parameters”, IEEE Trans. On Magnetics, 41, 1100-1108, 2005.<br />
[3] S. Coco and A. Laudani, “Iterative FE Solution of Unbounded Magneto-Thermal Problems”, Proc.<br />
of 10th IGTE Symposium on Numerical Field Calculation in Electrical Engineering, Graz, Austria,<br />
16-18 Sept, 2002.<br />
28
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Session FEM-2<br />
Biome<strong>di</strong>cal applications and large scale problems<br />
Chairperson: N. Takahashi, Okayama University<br />
15:50-16:10<br />
S. Coco and A. Laudani<br />
Finite Element model of charge transport across ionic channels<br />
16:10-16:30<br />
S. Tricarico, M. Goffredo, M. Schmid, S. Conforto, F. Bilotti, T. D’Alessio,<br />
and L. Vegni<br />
Transient model of the human upper limb under surface electrical stimulation<br />
16:30-16:50<br />
B. Bisceglia, F. De Terlizzi, A. Scaglione, NF. Tallarino<br />
Alterazione della elettroporazione in ortope<strong>di</strong>a. Simulazione del trattamento<br />
<strong>di</strong> masse tumorali<br />
16:50-17:10<br />
G. Rubinacci, A. Tamburrino, and S. Ventre<br />
Large scale computation for source integral equations<br />
29
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Finite Element model of charge transport across ionic<br />
channels<br />
S. Coco and A. Laudani<br />
(1) University of Catania, DIEES<br />
Catania, Italy – e-mail: alaudani@<strong>di</strong>ees.unict.it, coco@<strong>di</strong>ees.unict.it<br />
The exchange of signals between living cells takes place mainly through the cellular<br />
membrane, which represents a selective permeable barrier between the cell and<br />
extracellular environment. Among interesting substances, ions are of paramount<br />
importance, since activation of several critical signaling pathways and a number of<br />
cellular functions depend on ionic concentrations (especially Ca++ and K+). The flow<br />
of ions across cell membranes takes place through membrane channels, which are<br />
typical hydrophobic regions having a size of the order of few Å, where the membrane<br />
lipid bilayer exhibits ’openings’ [1]. The simulation of the mechanism of ion flow<br />
across ionic channels is a very complicated task, mainly for the lack of accurate<br />
descriptions of channel structure, the <strong>di</strong>fficulty of modeling the behaviour of the<br />
proteic chains constituting the channel walls, the very high number of atoms, the very<br />
short time scale of the involved dynamical phenomena, etc. Several attempts have<br />
been made to build coherent representations of ion flow across ionic channels, in<br />
accordance with experimental measurements. In literature the most investigated<br />
approaches are Molecular Dynamic (MD), Brownian Dynamic (BD), Langevin-<br />
Lorentz-Poisson (LLP) particle model, and Poisson-Nernst-Planck (PNP) [2-4].<br />
In this paper a 3-D Finite Element (FE) model of charge transport across ionic<br />
channel membrane is presented. The use of irregular FE mesh allows us to model the<br />
3-D channel geometry with a lower number of degree of freedom with respect to FD.<br />
The problem is solved by a FE <strong>di</strong>scretization and by an appositely developed iterative<br />
scheme. The model allows us to obtain an accurate description of ion flow across the<br />
cell membrane. The results are globally summarized by the computed I/V<br />
characteristic relationship, in which the ionic current flowing through the channel is<br />
shown as a function of the membrane voltage.<br />
References<br />
[1] B. Hille, Ionic Channels of Excitable Membranes, Sunderland, MA: Sinauer, 1992.<br />
[2] Salvatore Coco, Daniela S. M. Gazzo, Antonino Laudani, Giuseppe Pollicino, “3-D Finite Element<br />
Poisson-Nernst-Planck model for the analysis of ion transport across ionic channels”, IEEE trans.<br />
on Magnetics, 43, 1461-1464, 2007.<br />
[3] M. E. Oliveri, S. Coco, D. S. M. Gazzo, A. Laudani and G. Pollicino, “3-D FE particle based<br />
model of ion transport across ionic channels”, Scientific Computing in Electrical Engineering,<br />
Mathematics in Industry, Springer-Verlag, 9, 2006<br />
[4] S. Aboud, D. Marreiro, M.Saraniti, and R. Eisenberg, “A poisson p3m force field scheme for<br />
particle-based simulations of ionic liquids,” Journal of Computational Electronics, vol. 3, pp. 117–<br />
133, 2004.<br />
30
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Transient Model of the Human Upper Limb Under<br />
Surface Electrical Stimulation<br />
Simone Tricarico, Michela Goffredo, Maurizio Schmid, Silvia Conforto,<br />
Filiberto Bilotti, Tommaso D’Alessio, Lucio Vegni<br />
“Roma Tre” University, Department of Applied Electronics<br />
Rome, Italy – E-mail: stricarico@uniroma3.it<br />
In this contribution, we propose an accurate phantom model of the human upper limb<br />
based on the volume conductor approximation [1,2]. The model implements a<br />
simplified anatomical representation of the arm where the involved tissues are stacked<br />
in a multilayered cylindrical geometry (see Figure 1a). Each tissue has been<br />
characterized by proper electrical and geometrical properties. We applied the model to<br />
successfully derive the electromagnetic field <strong>di</strong>stribution induced inside the arm by<br />
the excitation of an array of electrodes fed by a generic current pattern (Figure 1b).<br />
We used, then, a finite integration based time domain commercial solver [3] to<br />
evaluate the passive electromagnetic response of the structure to the given<br />
stimulation. Following a classical two-step analysis [4], the model may thus<br />
effectively provide a set of reliable electric parameters, such as current density values,<br />
which can be used by active models to pre<strong>di</strong>ct nerve fibers behavior.<br />
b) b)<br />
Figure 1 – a) Cylindrical model of the human upper limb. b) magnitude of current density <strong>di</strong>stribution<br />
exited by an array of electrodes inside the arm at a given time instant.<br />
References<br />
[1] T.A. Kuiken, N.S. Stoykov, M. Popović, M. Lowery and A. Taflove, “Finite element modeling of<br />
electromagnetic signal propagation in a phantom arm,” IEEE Trans. Neural. Syst. Rehabil. Eng., 9,<br />
346–354, 2001<br />
[2] A. Kuhn, T. Keller, M. Lawrence and M. Morari, “A model for transcutaneous current stimulation:<br />
simulations and experiments,” Med. Biol. Eng. Comput., 47, 279–289, 2009<br />
[3] CST Design Stu<strong>di</strong>o TM 2009, www.cst.com<br />
[4] A. Kuhn and T. Keller, “A 3D transient model for transcutaneous functional electrical<br />
stimulation,” Proc. of 10th Annual Conference of the International FES Society, Montreal,<br />
Canada, July 2005<br />
31
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Alterazione della Elettroporazione in Ortope<strong>di</strong>a.<br />
Simulazione del Trattamento <strong>di</strong> Masse Tumorali<br />
B. Bisceglia (1) , F. De Terlizzi (2) , A. Scaglione (1) , NF. Tallarino (1)<br />
(1)<strong>Dipartimento</strong> <strong>di</strong> Ingegneria dell’Informazione e <strong>di</strong> Ingegneria Elettrica, Università<br />
<strong>di</strong> Salerno, Via Ponte Don Melillo, 84084 Fisciano, SA.<br />
bbisceglia@unisa.it, ascaglione@unisa.it, nftallarino@yahoo.it<br />
(2) Scientific Department, IGEA S.p.A.<br />
Via Parmenide 10/A, 41012 Carpi (Mo). f.deterlizzi@igeame<strong>di</strong>cal.com<br />
Vengono presentati alcuni risultati della ricerca (in progress) che vuole portare alla<br />
formulazione <strong>di</strong> un modello matematico per la descrizione della alterazione della<br />
elettroporazione. La simulazione implementata consente <strong>di</strong> acquisire informazioni<br />
sugli effetti della elettroporazione sul tessuto osseo. L’algoritmo fornisce la risposta<br />
del materiale biologico alla sollecitazione elettrica applicata. Da un punto <strong>di</strong> vista<br />
elettrico la valutazione del campo nei tessuti correla gli effetti terapeutici con le<br />
caratteristiche del campo (locale). In campo ortope<strong>di</strong>co è <strong>di</strong>ffuso l’impiego <strong>di</strong> tecniche<br />
che utilizzano la stimolazione elettrica per trattare fratture con campi elettrici e<br />
correnti <strong>di</strong> bassa intensità al fine <strong>di</strong> stimolarne il tasso <strong>di</strong> crescita e <strong>di</strong> riparazione. [1]<br />
L’elettroporazione è descritta come la formazione <strong>di</strong> pori (canali idrofili) all’interno<br />
della membrana cellulare per effetto dell’applicazione <strong>di</strong> impulsi elettrici, <strong>di</strong> opportuna<br />
durata ed intensità; ciò rende la membrana temporaneamente permeabile permettendo<br />
così il trasporto, altrimenti non consentito, <strong>di</strong> opportune molecole attraverso la<br />
membrana stessa. In alcuni casi si preferisce parlare <strong>di</strong> elettropermeabilizzazione. Nel<br />
caso <strong>di</strong> cellule tumorali si può produrre un incremento notevole della efficacia<br />
citotossica <strong>di</strong> alcuni farmaci chemioterapici. [2] In questo lavoro è stata utilizzata la<br />
stimolazione me<strong>di</strong>ante campo elettrico che consiste nell’applicare al target in esame<br />
una configurazione <strong>di</strong> elettro<strong>di</strong> inducendo nei tessuti un campo elettrico nominale E=<br />
1000 V/cm, alla frequenza <strong>di</strong> 5 KHz. I bersagli considerati sono tratti semplificati <strong>di</strong><br />
arto umano con presenza <strong>di</strong> massa tumorale: è stata fatta una modellizzazione<br />
numerica (utilizzando il co<strong>di</strong>ce <strong>di</strong> calcolo COMSOL� che impiega la tecnica agli<br />
elementi finiti) in approssimazione <strong>di</strong> quasi staticità date le <strong>di</strong>mensioni degli oggetti<br />
stu<strong>di</strong>ati rispetto alla lunghezza d’onda del segnale applicato. La modellizzazione degli<br />
oggetti è stata fatta in prima analisi considerando una geometria molto semplificata in<br />
cui i vari tessuti sono stati assunti (da un punto <strong>di</strong> vista <strong>di</strong>elettrico) omogenei, non<br />
<strong>di</strong>spersivi e lineari. La correlazione tra esposizione e processo <strong>di</strong> guarigione è un<br />
obiettivo non imme<strong>di</strong>atamente raggiungibile, i risultati ottenuti, la semplicità del<br />
modello, la conformità <strong>di</strong> tali risultati con dati sperimentali costituiscono al momento<br />
un buon supporto conoscitivo.<br />
References<br />
[1] B. Bisceglia, A. De Vita, and M. Sarti, “Numeric simulation of a therapeutic processing.<br />
Electrostimulation of bone rebuil<strong>di</strong>ng”, COMPEL: The International Journal for Computation and<br />
Mathematics in Electrical and Electronic Engineering, 27(6), 1249-1259,2008.<br />
[2] D. Miklavcic1, M. Snoj, A. Zupanic1, B. Kos, M. Cemazar, M. Kropivnik, M. Bracko, T. Pecnik,<br />
E. Gadzijev, and G. Sersa, “Towards treatment planning and treatment of deep-seated solid tumors<br />
by electrochemotherapy”, BioMe<strong>di</strong>cal Engineering OnLine, 9-10, 2010.<br />
32
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Large scale computation<br />
for source integral equations<br />
G. Rubinacci (1) , A. Tamburrino (2) and S. Ventre (2)<br />
(1) Università <strong>di</strong> Napoli Federico II, <strong>Dipartimento</strong> <strong>di</strong> Ingegneria Elettrica, v.<br />
Clau<strong>di</strong>o 21, Napoli, 80125, Italy, e-mail: rubinacci@unina.it<br />
(2) Università <strong>di</strong> Cassino, DAEIMI, v. G. Di Biasio 43, Cassino, 03043, Italy, email:<br />
tamburrino@unicas.it, ventre@unicas.it.<br />
The electromagnetic modeling of electromagnetic devices is an important<br />
issue in view of their design. This topic is particularly relevant in many<br />
important applications ranging from the design of large electrical turbogenerators<br />
to electrical transformers for specific applications and micro and<br />
nano-devices. As a matter of fact, nowadays, the complexity of three<strong>di</strong>mensional<br />
geometries, the presence of parts in motion, the nonlinear<br />
ferromagnetic material properties, require numerical models that can be ran on<br />
high performances computers such as those available in the frame of parallel<br />
architectures. Another critical field of application is the design of micro and<br />
nano electromagnetic devices like, for instance, arrays of resonant metallic<br />
nanoparticles for sensing applications. The mathematical models describing<br />
the behavior of their interaction is still classic and it is represented by fullwave<br />
Maxwell equations with proper constitutive relationships. However, as<br />
for an array of nanoparticles, the number of scatterers (and hence the elements<br />
of the mesh) easily saturate the limits of a serial computation.<br />
In this context, we will <strong>di</strong>scuss some results [1]-[4] of interest in the field of<br />
large scale computation based on source integral equations. The proposed<br />
numerical formulations use three-<strong>di</strong>mensional models of the electric<br />
(conduction and/or polarization) and magnetic sources in the presence of<br />
conductors and magnetic materials [5] or conductors and <strong>di</strong>electrics [2]. The<br />
fast and efficient resulting numerical codes are based on a recursive SVD<br />
sparsification of the main (fully populated) stiffness matrix combined with<br />
parallelization.<br />
References<br />
[1] R. Albanese et al., “Electromechanical Analysis of End Win<strong>di</strong>ngs in Turbo Generators”,<br />
proc. of the 14th International IGTE Symposium 2010, 19-22 September 2010, Graz<br />
(Austria).<br />
[2] L. Dal Negro, G. Miano, G. Rubinacci, A. Tamburrino, S. Ventre, "A fast computation<br />
method for the analysis of an array of metallic nanoparticles," IEEE Trans. on Magnetics,<br />
vol. 45, no. 3, pp. 1618-1621, March 2009.<br />
[3] G. Rubinacci, S. Ventre, F. Villone, Y. Liu. A fast technique applied to the analysis of<br />
Resistive Wall Modes with 3D conducting structures,. J. Comp. Phys., 228(5), p 1562-<br />
1572, 2009<br />
[4] G. Rubinacci, R. Fresa, S. Ventre, “An eddy current integral formulation on parallel<br />
computer systems”, International Journal for Numerical Methods in Engineering, vol. 62,<br />
n. 9, (2004).<br />
[5] R. Albanese, G. Rubinacci, “Finite element methods for the solution of 3D eddy current<br />
problems”, Advances in Imaging and Electron, vol. 102, (1990).<br />
33
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Session MTM-3<br />
Microwave metamaterial applications I<br />
Chairperson: L. Vegni, “Roma Tre” University<br />
9:30-10:10<br />
Invited paper – R. Ziolkowski<br />
Multi-functional, planar metamaterial-inspired near-field resonant parasitic<br />
antennas<br />
10:10-10:30<br />
E. Di Gennaro, I. Gallina, A. Andreone, G. Castal<strong>di</strong>, and V. Gal<strong>di</strong><br />
Cut-wire-induced enhanced transmission through sub-wavelength slits<br />
10:30-10:50<br />
D. Ramaccia, F. Bilotti, and A. Toscano<br />
Design formulas of High-Impedance Surfaces with circular patch arrays<br />
34
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Multi-functional, Planar Metamaterial-inspired Nearfield<br />
Resonant Parasitic Antennas<br />
Richard W. Ziolkowski, Peng Jin, and Chia-Ching Lin<br />
University of Arizona, Department of Electrical and Computer Engineering<br />
Tucson, AZ 85721, USA – E-mail: ziolkowski@ece.arizona.edu<br />
A variety of multi-frequency, linear (LP) and circularly (CP) polarized, metamaterialinspired,<br />
near-field resonant parasitic (NFRP) antennas have been developed and<br />
tested successfully [1]-[6]. While they are in general low-profile, electrically small<br />
antennas, the demand for conformal versions has led to the development of planar<br />
versions. Several planar designs, inclu<strong>di</strong>ng not only high efficiency, single and multifrequency,<br />
LP and CP examples, but also higher <strong>di</strong>rectivity electrically small antennas<br />
and their experimental validations will be described.<br />
Figu<br />
re 1 – Planar metamaterial-inspired NFRP GPS L1 and Global Star communication antenna. a) HFSS<br />
model, b) fabricated antenna that was tested by Galtronics, Tempe, AZ.<br />
References<br />
[1] P. Jin and R. W. Ziolkowski, “Metamaterial-inspired, electrically small, Huygens sources,” IEEE<br />
Antennas Wireless Propag. Lett., 9, 501-505, 2010.<br />
[2] C.-C. Lin, R. W. Ziolkowski, J. A. Nielsen, M. H. Tanielian, and C. L. Holloway, “An efficient,<br />
low profile, electrically small, VHF 3D magnetic EZ antenna,” Appl. Phys. Lett., 96, 104102,<br />
2010.<br />
[3] P. Jin and R. W. Ziolkowski, “Multiband extensions of the electrically small metamaterialengineered<br />
Z antenna,” IET Microwaves, Antennas & Propagation, 4, 1016–1025, 2010.<br />
[4] R. W. Ziolkowski, P. Jin, J. A. Nielsen, M. H. Tanielian, and C. L. Holloway, “Design and<br />
Experimental Verification of Z Antennas at UHF Frequencies,” IEEE Antennas Wireless Propag.<br />
Lett., 8, 1329-1333, 2009.<br />
[5] P. Jin and R. W. Ziolkowski, “Broadband, efficient, electrically small metamaterial-inspired<br />
antennas facilitated by active near-field resonant parasitic elements,” IEEE Trans. Antennas<br />
Propag., 58, 318-327, 2010.<br />
[6] P. Jin and R. W. Ziolkowski, “Low Q, electrically small, efficient near field resonant parasitic<br />
antennas,” IEEE Trans. Antennas Propag., 57, 2548-2563, 2009.<br />
35
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Cut-Wire-Induced Enhanced Transmission through<br />
Sub-Wavelength Slits<br />
Emiliano Di Gennaro (1) , Ilaria Gallina (2) , Antonello Andreone (1) ,<br />
Giuseppe Castal<strong>di</strong> (2) , and Vincenzo Gal<strong>di</strong> (1)<br />
(1) CNR-SPIN and University of Naples “Federico II,” Department of Physics<br />
Naples, Italy – E-mail: emiliano@na.infn.it, andreone@unina.it<br />
(2) University of Sannio, Department of Engineering<br />
Benevento, Italy – E-mail: ilaria.gallina@unisannio.it, castal<strong>di</strong>@unisannio.it,<br />
vgal<strong>di</strong>@unisannio.it<br />
The study of extraor<strong>di</strong>nary transmission phenomena through sub-wavelength<br />
apertures (holes, slits, grooves, etc.) has recently elicited a great attention from both<br />
theoretical and application viewpoints (see, e.g., [1] for a recent review).<br />
It has recently been shown [1] that substantial (nearly 800-fold) transmission<br />
enhancements of transverse-electric (TE) fields through sub-wavelength slits in a thin<br />
metallic screen can be obtained by placing a metallic cut-wire array (with the wires<br />
centered on the slits and parallel to them) on a thin <strong>di</strong>electric substrate at the side of<br />
the screen that is <strong>di</strong>rectly illuminated. Such phenomenon was shown to be attributable<br />
to the excitation of an electric (<strong>di</strong>pole-like) resonance in the cut wires, whose strong<br />
field localization near the input aperture of the slit allows effective coupling of the<br />
illuminating plane-wave with the evanescent spectrum, and thus its “squeezing”<br />
through the slits.<br />
Here, we report on some recent results which extend the above stu<strong>di</strong>es to the case of<br />
paired cut-wire arrays [2], and provide an experimental verification [3] of the<br />
phenomena. Experimental results, on printed-circuit-board prototypes operating at<br />
microwave frequencies, agree fairly well with numerical full-wave simulations [4].<br />
Besides the moderately higher transmission enhancement, by comparison with [1], the<br />
proposed scenario features a richer phenomenology, which involves both electric- and<br />
magnetic-type resonances, typical of cut-wire-pair structures, thereby endowing<br />
further degrees of freedom in the engineering of enhanced transmission (e.g., passband-type<br />
designs).<br />
References<br />
[1] F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through<br />
subwavelength apertures,” Rev. Mod. Phys., 82, 729-787, 2010<br />
[2] Y. Q. Ye and Y. Jin, “Enhanced transmission of transverse electric waves through subwavelength<br />
slits in a thin metallic film” Phys. Rev. E, 80, 036606, 2009<br />
[3] I. Gallina, G. Castal<strong>di</strong>, V. Gal<strong>di</strong>, E. Di Gennaro, and A. Andreone, “Paired cut-wire arrays for<br />
enhanced transmission of transverse-electric fields through subwavelength slits in a thin metallic<br />
screen,” IEEE Antennas Wireless Propagat. Lett., 9, 641-644, 2010<br />
[4] E. Di Gennaro, I. Gallina, A. Andreone, G. Castal<strong>di</strong>, and V. Gal<strong>di</strong>, “Experimental evidence of cutwire-induced<br />
enhanced transmission of transverse-electric fields through sub-wavelength slits in a<br />
thin metallic screen,” to be published in Opt. Express, 2010<br />
36
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Design formulas of High-Impedance Surfaces with<br />
circular patch arrays.<br />
D. Ramaccia, F. Bilotti and A. Toscano<br />
(1) University RomaTre, Department of Applied Electronics<br />
Rome, Italy – E-mail: davide.ramaccia@gmail.com<br />
Originally photonic band gap materials were introduced with the goal to control the<br />
optical properties of materials. Frequency Selective Surfaces (FSS) materials offer the<br />
same control for the electromagnetic properties of the materials at microwave<br />
frequencies. These perio<strong>di</strong>c metallic arrays are employed in the design of High<br />
Impedance Surfaces (HIS) [1], [2].<br />
A typical high–impedance surface with square patches, its equivalent circuit<br />
representation and the circular patch pattern are shown in Figure 1a, 1b and 1c,<br />
respectively.<br />
b) c)<br />
Figure 1: HIS a) typical structure with square patches. b) equivalent circuit model. c) circular patch<br />
array.<br />
It is well known that although the array with square and circular patches have the<br />
same perio<strong>di</strong>city D and the same separation d, the <strong>di</strong>fferent geometry of the elements<br />
causes a <strong>di</strong>fferent behavior in frequency. It is taken into account mo<strong>di</strong>fying the<br />
expression the separation gap d between two adjacent patches. The new parameter deq<br />
for circular patches is deq ��D�� d,<br />
where the coefficients � and � have been<br />
determined geometrically.<br />
The resonance frequency of the circuit in Figure 1b corresponds to the frequency<br />
when the structure present a 0 degree phase shift of the reflected wave. From the<br />
resonant circuit theory, it is �0 � 1 LC and consequently the gap d can mo<strong>di</strong>fy the<br />
resonant frequency of the structure. Fixing � 0 , the geometrical parameters of the<br />
structure can be used to define the bandwidth of operation.<br />
References<br />
[1] O. Luukkonen et al., "Simple and Accurate Model of Planar Grids and High–Impedance Surfaces<br />
Comprising Metal Strips or Patches," IEEE Trans. Antennas Propag., 56, 1624–1632, 2008.<br />
[2] D. Sievenpiper et al., "High-Impedance Electromagnetic Surfaces with a Forbidden Frequency<br />
Band," IEEE Transaction Microwave Theory Tech., 47, 1999.<br />
37<br />
a)
Session MTM-4<br />
Non-linear metamaterials<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Chairperson: A. Andreone, University of Naples “Federico II”<br />
11:20-11:40<br />
A. Ciattoni, C. Rizza, and E. Palange<br />
Multistability at arbitrary low optical intensities through epsilon-near-zero<br />
nonlinear metamaterial<br />
11:40-12:00<br />
M. Centini, A. Benedetti, C. Sibilia, M. Bertolotti<br />
Optimized second harmonic generation in gold square rod chains<br />
12:00-12:20<br />
A. Massaro, F. Spano, R. Cingolani, and A. Athanassiou<br />
Tuning concept of PDMS nanocomposite material for optical fiber<br />
enhancement<br />
12:20-12:40<br />
N. Chikhi, E. Di Gennaro, A. Andreone, E. Esposito, I. Gallina, G. Castal<strong>di</strong>,<br />
and V. Gal<strong>di</strong><br />
Tunable metamaterials operating in the terahertz region<br />
38
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Multistability at arbitrary low optical intensities<br />
through epsilon-near-zero nonlinear metamaterial<br />
Alessandro Ciattoni (1) , Carlo Rizza (2) and Elia Palange (2)<br />
(1) Consiglio Nazionale delle Ricerche, CNR-SPIN 67100 L'Aquila, Italy<br />
E-mail: alessandro.ciattoni@aquila.infn.it<br />
(2) Electrical Engineering Department, University of L'Aquila, 67100 Zona Industriale<br />
<strong>di</strong> Pile (L'Aquila), Italy<br />
We show that a nonlinear metal-<strong>di</strong>electric layered slab of subwavelength thickness<br />
and very small average <strong>di</strong>electric permittivity <strong>di</strong>splays optical multistable behavior at<br />
arbitrary low optical intensities. This is due to the fact that, in the presence of the<br />
small linear permittivity, one of the multiple electromagnetic slab states exists no<br />
matter how small is the transmitted optical intensity. We prove that multiple states at<br />
ultra-low optical intensities can be reached only by simultaneously operating on the<br />
incident optical intensity and incidence angle.<br />
b)<br />
a)<br />
Figure 1 – a) Transmissivity at two <strong>di</strong>fferent incidence angles and surface of allowed electromagnetic<br />
states. b) Geometry of the metal-<strong>di</strong>electric layered slab together with overall slab transmissivity and<br />
parameter space region (shaded region) where multistability occurs. Note that multistable states exist<br />
no matter how small is the incident optical intensity.<br />
References<br />
[1] A. Ciattoni, C. Rizza and E. Palange, “Multistability at arbitrary low optical intensities in a metal<strong>di</strong>electric<br />
layered structure”, submitted for publication on Physical Review Letters.<br />
arXiv:1009.4053v1<br />
39
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Optimized second harmonic generation in gold<br />
square rod chains<br />
Marco Centini, Alessio Benedetti, Concita Sibilia, Mario Bertolotti<br />
<strong>Dipartimento</strong> <strong>di</strong> Scienze <strong>di</strong> Base e Applicate per l'Ingegneria- Sez Fisica. Sapienza<br />
Università <strong>di</strong> Roma. Via A. Scarpa 16 00161 Roma – Italy<br />
E-mail: marco.centini@uniroma1.it<br />
Thanks to the development of nanotechnologies and nanoscience, nonlinear properties<br />
of metallic nanostructures have been deeply investigated both theoretically and<br />
experimentally in the last years. SHG enhancement from nanoantennas and nano<strong>di</strong>mers<br />
has been observed both in near and far fields[1,2]. In a recent work we stu<strong>di</strong>ed<br />
SHG in gold nanowires pointing out the possibility to tailor the properties of the<br />
generated signal by proper design of the system [3]. The same method developed in<br />
[3] has been used to investigate SHG by a chain of gold rods. Here we report the<br />
results of our calculations by considering, as an example, a chain made of five gold<br />
rods (figure 1a). We show that strong field localizations are obtained in the region<br />
between the rods resulting from interference of localized surface plasmons when the<br />
fundamental field is tuned on a coupled resonance (figure 1a). This effect provides a<br />
more efficient coupling of the pump energy to plasmon modes and is responsible of<br />
the enhancement of second harmonic generated signal (figure 1b).<br />
40<br />
150<br />
210<br />
120<br />
240<br />
90<br />
270<br />
3e-018<br />
2e-018<br />
1e-018<br />
4e-018<br />
180 0<br />
c) b)<br />
Figure 1: (a) modulus of the magnetic field H normalized with respect to the amplitude of the incident<br />
field. Fundamental field wavelength is 770 nm, rod sections are 120x120 nm2 and gaps between rods<br />
are 15 nm. (b) polar plot of the nonlinear <strong>di</strong>fferential scattering cross section for the generated second<br />
harmonic field. Typical values of the nonlinear scattering cross section by a gold flat surface at the<br />
same wavelength are of the order of 10 -20 cm 2 /W.<br />
References<br />
[1] B. K. Canfield et al., Nano Letters, 7, 5, 1251-1255 (2007)<br />
[2] T. Hanke et al., Phys. Rev. Lett. 103, 257404 (2009).<br />
[3] A. Benedetti et al., JOSA B 27, 3, 408-416 (2010)).<br />
60<br />
300<br />
30<br />
330
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Tuning Concept of PDMS Nanocomposite Material<br />
for Optical Fiber Enhancement<br />
Alessandro Massaro (1) , Fabrizio Spano (1) , Roberto Cingolani (2) , and Athanassia<br />
Athanassiou (1),(3)<br />
(1) Italian Institute of Technology IIT, Center of Biomolecular Nanotechnologies<br />
Arnesano (Le), Italy – E-mail: alessandro.massaro@iit.it<br />
(2) Italian Institute of Technology IIT- Genova- Italy.<br />
(3) National Nanotechnology Laboratory, CNR Institute of Nanoscience Lecce, IT<br />
In this work we propose a new design approach of nanocomposite material design by<br />
means of tuning of concentration of micro-nanoparticles in a polymeric material. The<br />
method is based on the control of the optical enhancement by changing the gold<br />
concentration (in<strong>di</strong>cated by the volume filling factor �). We consider as material the<br />
Poly<strong>di</strong>methylsiloxane (PDMS) polymer film due to its ability to generate gold<br />
nanoparticles starting from gold precursors by chemical reduction [1]-[3]. A key<br />
parameter used for the design is the scattering efficiency. Figure 1 (a) shows the<br />
calculated scattering efficiency for <strong>di</strong>fferent gold concentration ����and Fig. 2<br />
(b)�in<strong>di</strong>cates an application useful for probe detection systems (light enhancement), of<br />
an optical fiber embedded in the PDMS-Au. The peaks of Fig. 1 (a) in<strong>di</strong>cate the<br />
working wavelength of the optical fiber.<br />
1 (a) (b)<br />
Q scatt.<br />
0<br />
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4<br />
�[�m]<br />
�<br />
������<br />
������<br />
������<br />
41<br />
Optical fiber<br />
embedde<strong>di</strong>n<br />
PDMS‐Au<br />
nanocomposite<br />
Figure 1 – a) PDMS-Au scattering efficiency versus the working wavelength for <strong>di</strong>fferent gold<br />
micro/nanoparticles concentration ��in PDMS material. b) Enhanced light of an optical fiber end<br />
embedded in PDMS-Au nanocomposite material.<br />
References<br />
[1] Q. Zhang, J. J. Xu, Y. Liu, and H. Y. Cuen, “In-situ synthesis of poly(<strong>di</strong>methylsiloxane)- gold<br />
nanoparticles composite filmsand its application in microflui<strong>di</strong>c system,” Lab on chip, 8, 352-357,<br />
2008.<br />
[2] C. E. Hoppe, C. Ridriguez-Abreu, M. Lazzari, M. A. Lopez-Quintela, and C. Solans, “One-pot<br />
preparation of gold-elastomer nanocomposites using PDMS- graft – PEO copolymer micelles as<br />
nanoreactors ,” Phys. Stat. Sol. (a), 205, 1455-1459, 2008.<br />
[3] A. Goyal, A. Kumar, P. K. Patra, S. Mahendra, S. Tabatabaei, P. J. J. Alvarez, G. Jhon, and P. M.<br />
Ajayan, “In situ synthesis of metal nanoparticles embedded free stan<strong>di</strong>ng multifunctional PDMS<br />
films,” Macromol. Rapid Commun., 30, 1116-1122, 2009.
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Tunable metamaterials operating<br />
in the terahertz region<br />
Nassim Chikhi (1) , , Emiliano Di Gennaro (1) , Antonello Andreone (1) , Emanuela<br />
Esposito (2) , Ilaria Gallina (3) , Giuseppe Castal<strong>di</strong> (3) , and Vincenzo Gal<strong>di</strong> (3)<br />
(1)<br />
CNR-SPIN and University of Naples “Federico II,” Department of Physics<br />
Naples, Italy – E-mail: chikhi@na.infn.it, emiliano@na.infn.it, andreone@unina.it<br />
(2)<br />
CNR-ICIB “E. Caianiello”,<br />
Pozzuoli (Na), Naples, Italy – E-mail: e.esposito@cib.na.cnr.it<br />
(3)<br />
University of Sannio, Department of Engineering<br />
Benevento, Italy – E-mail: ilaria.gallina@unisannio.it, castal<strong>di</strong>@unisannio.it,<br />
vgal<strong>di</strong>@unisannio.it<br />
During the last two decades, substantial progress has been achieved in the<br />
development of terahertz (THz) science and technology. However, there are several<br />
restrictions which limit the development of fruitful applications within the full THz<br />
frequency region. One of the main constraints is the lack of appropriate responses, at<br />
those frequencies, from many naturally existing materials. This problem can be solved<br />
using artificially structured electromagnetic materials (“metamaterials”), typically<br />
comprised of perio<strong>di</strong>c arrays of sub-wavelength metallic resonating inclusions.<br />
Different strategies have been explored in order to achieve tunability in the resonating<br />
inclusions within various ranges of frequencies, from microwaves to the THz region,<br />
inclu<strong>di</strong>ng the use of <strong>di</strong>fferent kinds of capacitors, microelectromechanical systems<br />
(MEMS) or liquid crystals [1-3]. The geometry that we considered here is based on<br />
the concept of split ring resonator (SRR) [4, 5]. A comprehensive numerical study<br />
based on full-wave simulations (via CST Microwave Stu<strong>di</strong>o ) has been carried out<br />
in order to characterize the device response in the required frequency region. The<br />
proposed tuning mechanism is based on the use of a liquid crystal (LC).<br />
References<br />
[1] S. Gevorgian, and A. Vorobiev, “Tunable metamaterials based on ferroelectric varactors”,<br />
Procee<strong>di</strong>ngs of the 37 th European Microwave Conference, 2007 EuMA, Munich, Germany.<br />
[2] T. Hand and S. Cummer, “Characterization of tunable metamaterial elements using MEMS<br />
switches”, IEEE Antennas Wireless Propag. Lett. 6, 401 (2007).<br />
[3] J. A. Bossard, et al., “Tunable frequency selective surfaces and negative-zero-positive index<br />
metamaterials based on liquid crystals”, IEEE Trans. Antennas Propag. 56, 1308 (2008).<br />
[4] H. Chen, et al., ”Experimental demonstration of frequency-agile terahertz metamaterials”, Nature<br />
Phot. 2, 295 (2008).<br />
[5] K. Ay<strong>di</strong>n, and E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial<br />
components”, J. Appl. Phys. 101, 024911 (2007).<br />
[6] F. Zhang, L. Kang, Q. Zhao, J. Zhou, X. Zhao, and D. Lippens, ”Magnetically tunable left handed<br />
metamaterials by liquid crystal orientation”, Optics Express 17, 4360 (2009).<br />
42
Session FEM-3<br />
Methods and solvers<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Chairperson: F. Bilotti, “Roma Tre” University<br />
14:00-14:20<br />
G. Aiello, S. Alfonzetti, S. A. Rizzo, and N. Salerno<br />
A Comparison between Hybrid Methods: FEM-BEM versus FEM-DBCI<br />
14:20-14:40<br />
G. Borzì<br />
A comparison of <strong>di</strong>rect methods for the solution of finite element systems on<br />
shared memory computers<br />
14:40-15:00<br />
C. Molar<strong>di</strong>, E. Coscelli, F. Poli, A. Cucinotta, S. Selleri<br />
C-language-based 2D-optical mode solver<br />
43
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
A Comparison between Hybrid Methods:<br />
FEM-BEM versus FEM-DBCI<br />
G. Aiello, S. Alfonzetti, S. A. Rizzo, and N. Salerno<br />
Università <strong>di</strong> Catania, <strong>Dipartimento</strong> <strong>di</strong> Ingegneria Elettrica, <strong>Elettronica</strong> e dei Sistemi<br />
(DIEES), Catania, Italy – E-mail: alfo@<strong>di</strong>ees.unict.it<br />
In the literature several methods have been devised to enable the Finite Element<br />
Method (FEM) to solve static and quasi-static electromagnetic field problems in openboundary<br />
domains. Among these there are the hybrid FEM/BEM (Boundary Element<br />
Method) method [1], and the hybrid FEM-DBCI (Dirichlet Boundary Con<strong>di</strong>tion<br />
Iteration) method proposed by the authors [2]. This paper compares these two hybrid<br />
methods by referring to simple electrostatic field problems.<br />
Consider an electrostatic system made of voltaged conductors, <strong>di</strong>electric objects and<br />
charge <strong>di</strong>stributions embedded in air. In the FEM-BEM method a truncation boundary<br />
�F enclosing the system is introduced. On �F an unknown Neumann con<strong>di</strong>tion<br />
�r�v/�n=q is assumed. The FEM-BEM leads to the global system [1]:<br />
� A A F 0 � � v � �b<br />
0 �<br />
� t<br />
� � �<br />
�<br />
� �<br />
�<br />
A F A FF C<br />
� �<br />
v F � �<br />
0<br />
�<br />
(1)<br />
��<br />
0 H � G��<br />
��<br />
q ��<br />
��<br />
0 �<br />
F �<br />
where: v and vF are the vectors of the unknown values of the potential v in the nodes<br />
inside the domain and on �F, respectively, A, AF and AFF are sparse matrices of<br />
coefficients, b0 is the known term vector due to the conductor potentials and sources,<br />
C is a sparse matrix of coefficients, and qF is the vector of the unknown values of q,<br />
evaluated in nodes other than those of v [1].<br />
In the FEM-DBCI method a Dirichlet boundary con<strong>di</strong>tion is assumed on �F. The<br />
global system is [2]:<br />
� A A F � � v � �b0<br />
�<br />
� � � � � � � (2)<br />
��<br />
G'<br />
H'<br />
� �v<br />
F � � 0 �<br />
Comparing the two methods the following considerations can be made. First, by<br />
analyzing the <strong>di</strong>mensions of the various matrices, it can be shown that FEM-DBCI<br />
requires less memory than FEM-BEM. Moreover, the greater complexity of (1) with<br />
respect to (2) makes FEM-BEM more time-consuming than FEM-DBCI.<br />
From the point of view of accuracy, it can be noted that in FEM-DBCI a numerical<br />
derivative of the potential is performed on the integration curve, whereas this is not<br />
necessary in FEM-BEM. FEM-BEM can therefore be expected to give more accurate<br />
results than FEM-DBCI.<br />
These considerations have been verified by means of a set of examples, exhibiting analytical<br />
solutions.<br />
References<br />
[1] S. Alfonzetti, N. Salerno, “A non-standard family of boundary elements for the hybrid FEM-BEM<br />
method,” IEEE Trans. Magn., 45, 1312-1315, 2009.<br />
[2] G. Aiello, S. Alfonzetti, “Charge iteration: a procedure for the finite-element computation of<br />
unbounded electrical fields,” Int. J. Num. Meth. Engng, 37, 4147-4166, 1994.<br />
44
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
A Comparison of Direct Methods for the Solution<br />
of Finite Element Systems on Shared Memory<br />
Computers<br />
Giuseppe Borzì<br />
University of Messina, Department of Civil Engineering<br />
Messina, Italy – E-mail: gborzi@ieee.org<br />
The numerical solution of electromagnetic problems by means of the finite element<br />
method involves the construction of a linear algebraic system and its solution. When<br />
the order of the system is very high, the solution is achieved by means of iterative<br />
solvers such as those of the Lanczos family [1], Multigrid [2] or Algebraic Multigrid<br />
[3]. The convergence characteristics of iterative solvers are not well understood,<br />
except for a few special cases, like Symmetric Positive Definite matrices for Lanczos<br />
based solvers. Moreover, for complex linear systems the convergence theory is even<br />
less understood than for real linear systems. So, for small and me<strong>di</strong>um size linear<br />
systems, <strong>di</strong>rect solvers for sparse matrices can be more suitable. Unlike iterative<br />
solvers, <strong>di</strong>rect ones can be used as ‘black boxes’, that is to say, the user does not need<br />
to give parameters such as the<br />
convergence tolerance, or precon<strong>di</strong>tioning parameters. Most of these parameters are<br />
chosen heuristically, and an unwise choice may lead wrong results or a breakdown of<br />
the iteration. The downside of <strong>di</strong>rect methods is their higher memory and CPU usage<br />
when compared with iterative solvers, but with the commercial availability of multi<br />
core/threaded CPUs with huge memory this is no more a serious drawback. In this<br />
paper, some public available <strong>di</strong>rect solvers for sparse matrices, such as those included<br />
in the suitesparse package [4], superlu and superlu_mt [5-6] and spooles [7] are<br />
compared on some test matrices resulting from the finite element <strong>di</strong>scretization of<br />
electromagnetic problems.<br />
References<br />
[1] G. H. Golub and C. F. van Loan, Matrix Computations, 3rd Ed., The John Hopkins University<br />
Press, Baltimore, USA, 1996<br />
[2] W. L. Briggs, A Multigrid Tutorial, SIAM Books, Philadelphia, USA, 1987<br />
[3] K. Stueben, “Algebraic multigrid (AMG): An introduction with applications,” GMD -<br />
Forschungszentrum Informationstechnik GmbH, Tech. Rep. 53, Sankt Augustin, Germany, Mar.<br />
1999<br />
[4] T. A. Davis, Direct Methods for Sparse Linear Systems, SIAM Books, Philadelphia, USA, 2006<br />
[5] J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. S. Li, and J W. H. Liu, “A supernodal approach to<br />
sparse partial pivoting,” SIAM J. Matrix Analysis and Applications, 20, 720-755, 1999<br />
[6] J. W. Demmel, J. R. Gilbert, and X. S. Li, “An Asynchronous Parallel Supernodal Algorithm for<br />
Sparse Gaussian Elimination,” SIAM J. Matrix Analysis and Applications, 20, 915-952, 1999<br />
[7] C. Ashcraft, and R. Grimes, “SPOOLES: An object-oriented sparse matrix library,” Procee<strong>di</strong>ngs of<br />
the Ninth SIAM Conference on Parallel Processing, San Antonio, Texas, USA, March 22-24,<br />
1999.<br />
45
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
C-Language-Based 2D-Optical Mode Solver<br />
C. Molar<strong>di</strong>, E. Coscelli, F. Poli, A. Cucinotta, S. Selleri<br />
Information Engineering Department, University of Parma, I-43124 Parma, Italy<br />
stefano.selleri@unipr.it<br />
Finite Element Method (FEM), based on edge elements, approach to the modal analysis of modern<br />
optical structures leads to a generalized eigenvalue problem, that involves several resolutions of a<br />
linear equations system in order to span a basis of the Krylov subspace, in which we find<br />
eigensolutions. The matrix of this system is large, sparse, symmetric and not positive definite, so we<br />
can <strong>di</strong>scard every iterative method for resolution. The only way to proceed is to perform a sparse<br />
factorization, that carries on the well known numerical problem called fill-in. A good factorization<br />
algorithm that preserves fill-in small is strongly required; despite this, the memory space to store<br />
matrix factors increases largely with the increase of mesh points, so a wise use of memory is the prime<br />
requisite. Fortran coded modal solver currently used in the department, suffers from an oversized use of<br />
memory space, so a new solver has been developed using the C programming language that offers an<br />
easy, powerful and dynamic memory allocation approach, furthermore, modern C compilers can<br />
generate highly optimized code and give programmers the possibility to include Fortran subroutines. In<br />
the new solver, the handling of memory and the framework algorithms are written in C, creating an<br />
efficient interface to Arpack subroutines to calculate the eigensolutions. In order to show the goodness<br />
of the work, for simulation an ytterbium doped large mode area PCF rod-type fiber with double<br />
clad<strong>di</strong>ng has been considered, searching for Fundamental Mode (FM) and Higher Order Mode (HOM)<br />
on various wavelenghts using a mesh with 89135 points. The new C modal solver results are compared<br />
with the old solver solutions. As shown in the table results fit. Then the number of mesh points has<br />
been gradually increased, comparing execution time and memory space needed by both solvers, on a<br />
32-bit Intel Pentium4 2.80 GHz 2 GByte of RAM with a Linux operating system installed. C solver<br />
gains in speed using significantly less memory space as shown in Fig. 1(a) and (b) respectively. This<br />
give the abilities to simulate with a higher number of points, up to 360000 as reported in Fig. 1(c).<br />
Figure 1 – (a) Speed and (b) memory comparisons between C solver and Fortran solver. (c) Memory required by C solver.<br />
References<br />
[1] J. Jin, The Finite Element Method in Electromagnetics, (John Wiley & Sons Inc. 1993).<br />
[2] Z. Bai, J. Demmel, J. Dongarra, A. Rhue, H. van der Vorst, “Templates for the Solution of Algebraic Eigenvalue Problems:<br />
a Practical Guide”, (Draft 1999).<br />
[3] W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, Third<br />
E<strong>di</strong>tion, (Cambridge University Press 2007).<br />
[4] S. Selleri, L. Vincetti, A. Cucinotta, M. Zoboli “Complex FEM modal solver of optical waveguides with PML boundary<br />
con<strong>di</strong>tions”, Optical and Quantum Electronics 33: 359, 2001<br />
46
Session FEM-4<br />
Design and applications<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Chairperson: S. Selleri, University of Florence<br />
15:50-16:10<br />
S. Ceccuzzi, S. Meschino, F. Mirizzi, L. Pajewski, C. Ponti, and G. Schettini<br />
A FEM analysis of microwave components for oversized waveguides<br />
16:10-16:30<br />
U. d’Elia, G. Pelosi, S. Selleri, R. Taddei<br />
Finite Element design of CNT-based multilayer absorbers<br />
16:30-16:50<br />
S. Coco, A. Laudani, G. Pulcini, F. Riganti Fulginei, A. Salvini<br />
Optimization of multistage depressed collectors by using FEM and METEO<br />
16:50-17:10<br />
D. Ramaccia, F. Bilotti, and A. Toscano<br />
Parametric bandwidth analysis of an Artificial Magnetic Conductor surface<br />
47
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
A FEM Analysis of<br />
Microwave Components for Oversized Waveguides<br />
Silvio Ceccuzzi (1) , Simone Meschino (2) , F. Mirizzi (1) , L. Pajewski (2) , C. Ponti (2) ,<br />
and G. Schettini (2)<br />
(1) Associazione EURATOM-ENEA sulla Fusione, C.R. Frascati, P.O.Box 65, 00044<br />
Frascati (Rome), Italy – E-mail: mirizzi@frascati.enea.it<br />
(2) Roma Tre University, Department of Applied Electronics,<br />
Rome, Italy – E-mail: s.meschino@unroma3.it<br />
The present work has been developed within the frame of the EFDA task “HCD-08-<br />
03-01: LH4IT, EU contribution to the ITER LHCD Development Plan”<br />
The use of rectangular oversized waveguides in the Main Transmission Lines (MTLs)<br />
of the Lower Hybrid Current Drive (LHCD) system of ITER, requires to investigate<br />
the problem of bends [1, 2]. In this context, the principal specifications that<br />
characterize the design of the bends are: a) to minimize the reflection of the<br />
fundamental TE10 mode; b) to maximize the transmission of the fundamental TE10<br />
mode; c) to minimize the coupling between the TE10 mode and other spurious modes<br />
that propagate at 5 GHz.<br />
This paper presents an overview about the bend options, and it compares the<br />
performances of several curved frameworks analyzed by using the Finite Element<br />
Method (FEM) commercial software, HFSS ® .<br />
Simple circular trajectory curves are considered, varying the ben<strong>di</strong>ng ra<strong>di</strong>us. The<br />
design of such curves is quite simple but not much flexible, being the ben<strong>di</strong>ng ra<strong>di</strong>us<br />
the only parameter. More design flexibility can be achieved using a Mitre Bend<br />
structure. It is of great interest to study this type of bends in terms of coupling, to<br />
check the possible advantages.<br />
Finally an innovative mo<strong>di</strong>fied Mitre-Bend-trapezoidal-elements solution is proposed.<br />
In particular, a preliminary performances comparison among those <strong>di</strong>fferent<br />
alternatives is presented.<br />
References<br />
[1] A. A. San Blas, B. Gimeno, V. E. Boria, H. Esteban, S. Cogollos e A. Coves, “A<br />
Rigorous and efficient full-wave analysis of uniform bends in rectangular waveguide<br />
under arbitrary incidence”, IEEE Trans. Microwave Theory Tech., 51, 397-405, 2003.<br />
[2] L. Lewin, D. C. Chang, and E. F. Kuester, Electromagnetic Waves and Curved<br />
Structures, London, U.K.: Peregrinus, 1977.<br />
[3] S. Ceccuzi, S. Meschino, F. Mirizzi, L. Pajewski, S. Schettini, et al., “Bends in Oversized<br />
Rectangular Waveguide,” Proc. of the 26 th Fusion Technology Symp., P1-045, Porto, Portugal,<br />
Sept. 27- Oct. 1, 2010.<br />
48
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Finite Element Design of<br />
CNT-based Multilayer Absorbers<br />
Ugo d’Elia (1) , Giuseppe Pelosi (2) , Stefano Selleri (2) , Ruggero Taddei (2)<br />
(1) MBDA Italia, via Tiburtina km. 12,400, 00131<br />
Roma, Italy – E-mail: ugo.delia@mbda.it<br />
(2) University of Florence, Electronics and Telecommunications Department<br />
Via C. Lombroso 6/17 – 50134<br />
Florence, Italy E-mail: [giuseppe.pelosi, stefano.selleri, ruggero.taddei]@unifi.it<br />
Absorbing materials are of relevant industrial interest both for radar cloaking and<br />
anechoic chambers. For the former problem, lightweight, compact, durable materials<br />
adequate to be layered on the vehicle hull are at a premium.<br />
In the radar cloaking context frequency selective surfaces (FSS) comprising regular<br />
lattices of lossy elements are an interesting possibility. FSS elements constituted of<br />
conductive rings loaded with lumped resistors are a possibility investigated in<br />
literature [1], yet they are <strong>di</strong>fficult to manufacture; an FSS exploiting ring resonators<br />
with inherent high losses would be more interesting. To this aim, in this contribution,<br />
a very recently developed carbon nanotubes paper-like material is exploited [2]. This<br />
material exhibits relatively high losses and consequently - for the frequencies at which<br />
the rings resonates - a very high absorption.<br />
A design for multi-layer absorbers based on this FSS is here stu<strong>di</strong>ed. The FSS if<br />
analyzed via finite element (FE) analysis over a single perio<strong>di</strong>c cell by exploiting<br />
Floquet theory [3]. Analyses are carried out for <strong>di</strong>fferent polarization and <strong>di</strong>fferent<br />
values of the incident plane wave angle over a single layer FSS. A genetic algorithm<br />
(GA) based optimization is then performed to design multiple layer FSS satisfying<br />
specific set of bandwidths and absorption requirements.<br />
Design is finally validated via full wave FEM simulations.<br />
References<br />
[1] B.A. Munk, P. Munk, J. Pryor, “On designing Jaumann and circuit analog absorbers (CA<br />
absorbers) for oblique angle of incidence,” IEEE Trans. Antennas Propag., 55, 186–193, 2007.<br />
[2] L. Wang, R. Zhou, H. Xin, “Microwave (8-50GHz Characterization of Multiwalled Carbon<br />
Nanotube Papers Using Rectangular Waveguides,” IEEE Trans. Microwave Theory Tech., 56,<br />
499-506, 2008.<br />
[3] G. Pelosi, R. Coccioli, S. Selleri, Quick Finite Elements for Electromagnetic Waves, 2nd E<strong>di</strong>tion,<br />
Artech House, London (UK), 2009.<br />
49
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Optimization of Multistage Depressed Collectors by<br />
using FEM and METEO<br />
Salvatore Coco (1) , Antonino Laudani (1) , Giuseppe Pulcini (2) , Francesco Riganti<br />
Fulginei (2) , Alessandro Salvini (2)<br />
(1) University of Catania, DIEES Catania, Italy – e-mail: alaudani@<strong>di</strong>ees.unict.it<br />
(2) Roma Tre University, Department of Applied Electronics - Roma, Italy<br />
Specialized 3-D simulators are required by TWT multistage depressed collector<br />
(MDC) designers to help them to analyze and test new and arbitrarily shaped<br />
geometries for high efficiency TWTs. To perform such a task a Finite Element (FE)<br />
approach can be pursued, since it allows a very flexible meshing and gives the<br />
possibility of using irregular meshes to fit properly the MDC’s geometry; in such a<br />
way complex geometries can be accurately simulated [1]. Unfortunately, the use of<br />
optimization techniques in the design process of these devices is rarely used [2],<br />
because of the high number of parameters and the high computational cost of<br />
efficiency evaluation (the fitness function). In this paper the authors present the<br />
application of a novel metaheuristics technique called METEO (Metric-Topologicalevolutionary-Optimization)<br />
[3], to optimize the performance of multistage collectors,<br />
simulated by means of Finite element collector and electron gun simulator<br />
COLLGUN [4]. METEO [3] is a hybrid algorithm composed by three <strong>di</strong>fferent<br />
heuristics: FSO (Flock of Starlings Optimization) [5], PSO (Particle Swarm<br />
Optimization), and BCA (Bacterial Chemotaxis Algorithm); it performs the<br />
optimization using both the topological as the metric rules. In fact the mentioned<br />
heuristics own a <strong>di</strong>fferent performance taken alone, in particular FSO presents a high<br />
degree of exploration, and a good capability to escape from local minima, whilst PSO,<br />
and BCA own a good proprieties of convergence. Besides, they offer a natural parallel<br />
implementation that allows spee<strong>di</strong>ng up the whole process of optimization. This<br />
characteristic can be useful exploited in order to obtain the desired target with an<br />
acceptable computational cost.<br />
References<br />
[1] S. Coco, F. Emma, A. Laudani, S. Pulvirenti, M. Sergi, “COCA: A Novel 3-D FE Simulator for<br />
the Design of TWTs Multistage Collectors”, IEEE trans. on electron devices, 48 , 24-31, 2001.<br />
[2] T. K. Ghosh, R.G. Carter, “Optimization of Multistage Depressed Collectors”, IEEE trans. on<br />
electron devices, 54 , 2031-2039, 2007.<br />
[3] G. Pulcini, F. Riganti Fulginei, A. Salvini, “Metric-Topological-Evolutionary Optimization”,<br />
OIPE2010 Procee<strong>di</strong>ngs, Sofia - Bulgaria, Sept. 14-18 2010, pp. 3-4.<br />
[4] S. Coco, S. Corsaro, A. Laudani, G. Pollicino, R. Dionisio, and R. Martorana, “COLLGUN: A 3D<br />
FE simulator for the design of TWT's electron guns and multistage collectors”, Scientific<br />
Computing in Electrical Engineering, Mathematics in Industry, Springer-Verlag, 9, 175-180, 2006<br />
[5] F. R. Fulginei, A. Salvini, “Model identification by the Flock-of-Starlings Optimization”, Int.<br />
Journal of applied Electromagnetics and Mechanics, vol. 30, n. 3-4, pp. 321-331, 2009.<br />
50
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Parametric bandwidth analysis of an<br />
Artificial Magnetic Conductor surface<br />
D. Ramaccia, F. Bilotti and A.Toscano<br />
University RomaTre, Department of Applied Electronics<br />
Rome, Italy – E-mail: davide.ramaccia@gmail.com<br />
In this contribution we show a possible application of Finite Integral Technique for<br />
the parametric analysis of the bandwidth of an Artificial Magnetic Conductor (AMC)<br />
made by a perio<strong>di</strong>c array of metallic patches on a <strong>di</strong>electric grounded substrate. As is<br />
well know, these structures mimic the perfect magnetic conductor con<strong>di</strong>tion in a small<br />
frequency range [1-3].<br />
A typical AMC surface with square patches, its equivalent circuit representation are<br />
shown in Figure 1a and 1b respectively.<br />
a) b)<br />
Figure 1: HIS a) typical structure with square patches. b) equivalent circuit model.<br />
Consider an incident electromagnetic wave normally. If the surface is made by a<br />
Perfect electric conductor, the wave is reflected back with a 180 degree phase shift, so<br />
it is opposite in phase with respect to the incident one. If the surface is made by an<br />
AMC, the reflected wave is in phase with respect to the incident one. As mentioned<br />
before, this particular behavior is only in a small frequency range that is defined as the<br />
range within the phase shift is inside the interval [-90°;+90°].<br />
The geometric and electrical parameters of the structure allow us to mo<strong>di</strong>fy the values<br />
of the lumped elements and consequently the bandwidth of the structure as show in<br />
Fig. 2.<br />
Figure 2: Increased Bandwidth around 20 GHz for a AMC with perio<strong>di</strong>city D=7mm and substrate<br />
permittivity ε = 3 .<br />
References<br />
[1] O. Luukkonen et al., "Simple and Accurate Model of Planar Grids and High–Impedance Surfaces Comprising<br />
Metal Strips or Patches," IEEE Trans. Antennas Propag., 56, 1624–1632, 2008.<br />
[2] D. Sievenpiper et al., "High-Impedance Electromagnetic Surfaces with a Forbidden Frequency Band," IEEE<br />
Transaction Microwave Theory Tech., 47, 1999.<br />
[3] F.Costa et al., “On the Bandwidth of High-Impedance Frequency Selective Surfaces,” IEEE Antennas and<br />
Prop. Lett., 8, 2009.<br />
51
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Session MTM-5<br />
Microwave metamaterial applications II<br />
Chairperson: R. Ziolkowski, University of Arizona<br />
09:30-10:10<br />
Invited paper – S. Hrabar<br />
Metamaterials based on non-Foster elements<br />
10:10-10:30<br />
L. Di Palma, F. Frezza, L. Pajewski, E. Piuzzi, C. Ponti, G. Rossi and G.<br />
Schettini<br />
Experimental investigations on woodpile EBG metamaterials<br />
10:30-10:50<br />
F. Bilotti, L. Di Palma, and L. Vegni<br />
Analytical model of connected bi-omega structures for enhanced microwave<br />
transmission<br />
52
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Metamaterials based on Non-Foster Elements<br />
Silvio Hrabar (1) , Igor Krois (1) , Ivan Bonic (1) , and Aleksandar Kiricenko (1)<br />
(1) University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb,<br />
Croatia– E-mail:Silvio.Hrabar@fer.hr<br />
It is well known that any passive metamaterial must satisfy basic <strong>di</strong>spersion<br />
constraints:<br />
� ����( �)<br />
� ��<br />
� � 0 , � �� � �(<br />
�)<br />
� ��<br />
� �0.<br />
(1)<br />
This fundamental issue is a cause of inherent narrowband behavior of all<br />
metamaterials (SNG, DNG, SNZ, DNZ). In [1], a possibility of going around the<br />
basic <strong>di</strong>spersion constrains by the use of non-Foster active elements such as negative<br />
capacitors and negative inductors, was pre<strong>di</strong>cted theoretically. Very recent<br />
experimental stu<strong>di</strong>es [2,3] showed that is indeed possible to build active (almost)<br />
<strong>di</strong>spersionless ENZ and MNZ metamaterials. Here, the basic physics of non-Foster<br />
metamaterials will be reviewed and several illustrative examples of practical<br />
prototypes developed at University of Zagreb will be presented. These include a 2D<br />
ENZ unit cell for broadband 2D electromagnetic cloak (Fig. 1) and a broadband ENZ<br />
RF transmission line with superluminal phase and group velocities (Fig. 2). Finally,<br />
currently investigated novel concepts of matched ‘EM nihility’ and frequency<br />
independent active transmission lines will be highlighted.<br />
C 2+<br />
C 1-<br />
��� �<br />
NIC circuit located on the<br />
ground plane<br />
microstrip line<br />
via hole to negative C<br />
a substrate<br />
Effective<br />
permittivity<br />
Fig. 1: (After [2]), Upper: 2D active ENZ<br />
unit cell, Lower: Microstrip realization<br />
References<br />
[1] S. Tretyakov, ‘Meta-materials with wideband negative permittivity and permeability’,<br />
Microwave and Optical Technology Lett., Vol. 31, No. 3, pp. 163-165, November 2001<br />
[2] S. Hrabar, I. Koris, A. Kiricenko, ‘Towards Active Dispersionless ENZ Metamaterial for<br />
Cloaking Applications’ , Metamaterials, Vol. 4 No. 2-3, pp. 89-97. August-September 2010<br />
[3] S. Hrabar, I. Krois, I.Bonic, A Kiricenko, ‘Experimental Investigation of Active Broadband ENZ<br />
Transmission line’, Proc. on ‘Metamaterial Congress 2010, p.p 63-65, Karlsruhe, September 2010<br />
53<br />
Z 0<br />
�x=����<br />
CNE<br />
Realistic<br />
Realistic CNE<br />
Realistic CNE<br />
C<br />
�x=����<br />
C<br />
�x=����<br />
2.0<br />
1.9<br />
1.8<br />
1.7<br />
1.6<br />
1.5 active ENZ off<br />
1.4<br />
1.3<br />
1.2<br />
1.1<br />
1.0<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
m10<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0.0<br />
m11 active ENZ on<br />
0 5 10 15 20 25 30 35 40 45 50<br />
freq, MHz<br />
Fig. 2: (After [3]) Upper : RF active ENZ<br />
transmission line, Lower: Measurement results<br />
C
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Experimental investigations on<br />
woodpile EBG metamaterials<br />
Luca Di Palma (1) , Fabrizio Frezza (2) , Lara Pajewski (1) , Emanuele Piuzzi (2) ,<br />
Cristina Ponti (1) , Giorgia Rossi (1) , and Giuseppe Schettini (1)<br />
(1) Roma Tre University, Department of Applied Electronics<br />
Rome, Italy – E-mail: g.schettini@uniroma3.it<br />
(2) Sapienza University, Department of Information Engineering,<br />
Electronics, and Telecommunications<br />
Rome, Italy – E-mail: fabrizio.frezza@uniroma1.it<br />
Electromagnetic Band.Gap (EBG) materials are a class of artificial materials made by<br />
a perio<strong>di</strong>c arrangement of <strong>di</strong>electric and/or metallic unit cells, which allow to control<br />
the propagation of electromagnetic waves along certain <strong>di</strong>rections, depen<strong>di</strong>ng on the<br />
perio<strong>di</strong>city [1]. They can be employed to design a novel class of planar antennas, with<br />
properties of enhanced <strong>di</strong>rectivity [2]-[5].<br />
In this work, a three-<strong>di</strong>mensional EBG with woodpile unit cell is presented, that has<br />
been implemented into two alumina prototypes. Experimental measurements have<br />
given a full characterization of the frequency selectivity through the structure,<br />
especially when employed as a cavity resonator, with two identical mirrors separated<br />
by an air-gap. For this particular layout, the effect of the field polarization, and of the<br />
gap length, on the frequency response, has been deeply investigated. The main result<br />
is the existence of transmission peaks when the air-gap is a multiple of the<br />
wavelength, which, as far as symmetric cavities are concerned, may be applied to the<br />
design of resonator antennas. Starting from a microstrip patch, a new compound<br />
ra<strong>di</strong>ator has been built, placing the ground plane of the basic ra<strong>di</strong>ator in the symmetry<br />
plane of the EBG resonator, and removing its lower part. Many antenna layouts can<br />
be implemented, accor<strong>di</strong>ng to the woodpile orientation, and the <strong>di</strong>stance between the<br />
ground plane and the woodpile superstrate. Compared to the basic ra<strong>di</strong>ator, the<br />
woodpile-covered antenna has narrow beam-width, and reduced side-lobe level, and a<br />
gain enhancement up to 10 dB has been measured on several antenna layouts.<br />
References<br />
[1] J. D. Joannopoulos et al., Photonic Crystals: Mol<strong>di</strong>ng the Flow of Light, Princeton University<br />
Press, Princeton NJ 2008.<br />
[2] F. Yang and Y. Rahmat-Samii, Electromagnetic Band Gap Structures in Antenna Engineering,<br />
Cambridge University Press, New York 2009.<br />
[3] Y. J. Lee, J. Jeo, R. Mittra, and T. S. Bird, “Application of Electromagnetic Bandgap (EBG)<br />
superstrates with controllable defects for a class of patch antennas as spatial angular filters,” IEEE<br />
Trans. Ant. Propag., 53, 224-235, 2005.<br />
[4] A. R. Weily, L. Horvath, K. P. Esselle, B. C. Sanders, and T. S. Bird, “A planar resonator antenna<br />
based on a woodpile EBG material,” IEEE Trans. Ant. Propag. 53, 216-223, 2005.<br />
[5] F. Frezza, L. Pajewski, E. Piuzzi, C. Ponti, and G. Schettini, Analysis and experimental<br />
characterization of an alumina woodpile-covered planar antenna,” Proc. 40th European<br />
Microwave Conference 2009, 200-203, Paris, France, Sept. 28-30 2010.<br />
54
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Analytical Model of Connected Bi-Omega<br />
Structures for Enhanced Microwave<br />
Transmission<br />
Filiberto Bilotti, Luca Di Palma, and Lucio Vegni<br />
“Roma Tre” University, Department of Applied Electronics<br />
Rome, Italy – E-mail: bilotti@uniroma3.it<br />
In this contribution, we present a new analytical model of two connected biomega<br />
particles (Figure 1a). Exploiting the analytical models of chiral and<br />
planar omega particles [1-2] and the equivalent circuit of the bi-helix particle<br />
[3], we have developed a new analytical model for the isolated bi-omega<br />
particle (i.e. a single omega particle backed by its reversed replica). Assuming<br />
the particle electrically small, the proposed analytical model is given in terms<br />
of a proper lumped element equivalent circuit. Then, we have extended the<br />
model to the case of two connected bi-omega particles, by considering the<br />
relevant coupling terms. Since this structure is symmetric, it does support two<br />
fundamental modes, characterized by an even and an odd electric field<br />
<strong>di</strong>stribution, respectively. The analytical model, in fact, pre<strong>di</strong>cts two <strong>di</strong>fferent<br />
resonant frequencies related to the two modes of operation. Such a result is<br />
confirmed also by proper full-wave numerical simulations (Figure 1b). The<br />
proposed analytical model has been successfully used to design compact<br />
devices to obtain extraor<strong>di</strong>nary transmission through sub-wavelength apertures<br />
in metallic waveguides. This result opens the door to the design of a new class<br />
of microwave components (filters, impedance matching devices, mode<br />
converters, cavity resonators, miniaturized probes and ra<strong>di</strong>ating systems, etc.),<br />
some of which will be shown at the conference.<br />
55<br />
Magnetic field amplitude [A/m]<br />
25<br />
20<br />
15<br />
10<br />
5<br />
“even” mode<br />
“odd” mode<br />
0<br />
0 1 2 3 4 5<br />
Frequency [GHz]<br />
d) b)<br />
Figure 1 – a) Sketch of two connected bi-omega particles and b) its typical resonant behavior.<br />
References<br />
[1] S.A. Tretyakov, et al. “Analytical Antenna Model for Chiral Scatterers: Comparison with<br />
Numerical and Experimental Data,” IEEE Trans. Antennas Propagat., 44, 1006-1014,<br />
1996.<br />
[2] C.R. Simovski, S.A. Tretyakov, A.A. Sochava, “Antenna Model for Conductive Omega<br />
Particles,” J. Elettromag. Waves Applicat., 11, 1509-1530, 1997.<br />
[3] A.N. Lagarkova, et al. “Resonance Properties of Bi-helix Me<strong>di</strong>a at Microwaves,”<br />
Electromagnetics, 17, 213-237, 1997.
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Session MTM-6<br />
Optical metamaterial applications<br />
Chairman: F. Frezza, “Sapienza” University<br />
11:20-11:40<br />
A. Massaro, F. Spano, R. Cingolani, and A. Athanassiou<br />
Pillar type PDMS nanocomposite optical antenna for liquid detection<br />
systems<br />
11:40-12:00<br />
R. Marinelli and E. Palange<br />
Optical performances of micron-sized CMOS image sensors using<br />
metallic planar lenses<br />
12:00-12:20<br />
A. Benedetti, M. Centini, C. Sibilia, M. Bertolotti<br />
Second harmonic generation in gold nanoantennas<br />
12:20-12:40<br />
S. Tricarico, F. Bilotti, and L. Vegni<br />
Controlling optical forces on nanoparticles through metamaterials<br />
56
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Pillar Type PDMS Nanocomposite Optical<br />
Antenna for Liquid Detection Systems<br />
Alessandro Massaro (1) , Fabrizio Spano (1) , Roberto Cingolani (2) , and<br />
Athanassia Athanassiou (1),(3)<br />
(1) Italian Institute of Technology IIT, Center of Biomolecular<br />
Nanotechnologies<br />
Arnesano (Le), Italy – E-mail: alessandro.massaro@iit.it<br />
(2) Italian Institute of Technology IIT- Genova, Italy.<br />
(3) National Nanotechnology Laboratory, Institute of Nanoscience of CNR of<br />
Lecce – Italy<br />
In this work we propose a new pillar sensor device suitable for detection of<br />
liquid’s permittivity. Due to the ability to generate gold nanoparticles starting<br />
from gold precursors by chemical reduction [1], poly<strong>di</strong>methylsiloxane<br />
(PDMS) polymer is used. A pillar type layout is chosen in order to collect and<br />
ra<strong>di</strong>ate the signal in an optical fiber probe. The ra<strong>di</strong>ated signal is enhanced by<br />
the light scattering of the gold micro/nano particles and allows to perform an<br />
high detection sensitivity during the deposition of an ethanol droplet on the<br />
sensor: as shown in Fig. 1 (a) a reduction of the transmitted light intensity is<br />
observed when the ethanol is detected. The detection corresponds to a<br />
variation of the <strong>di</strong>electric contrast dn due to the presence of ethanol. In Fig. 1<br />
(b) is reported the experimental setup used for the measurements. The sensor<br />
is also able to measure the evaporation effect of the ethanol droplet.<br />
Optical ra<strong>di</strong>ated intensity [a.u.]<br />
2200<br />
2000<br />
1800<br />
1600<br />
1400<br />
1200<br />
1000<br />
800<br />
600<br />
Broad<br />
lamp<br />
source<br />
Multimode<br />
optical fiber<br />
400<br />
800 900 1000 1100 1200 1300 1400<br />
�[nm]<br />
OMA<br />
Multimode<br />
(a) optical fiber<br />
(b)<br />
PDMS-Au pillar<br />
PDMS-Au pillar+ ethanol<br />
dn<br />
57<br />
Optical fiber<br />
probe<br />
Optical fiber<br />
source<br />
Pillar type<br />
sensor<br />
Figure 1 – a) PDMS-Au pillar type sensor and detection of ethanol as reduction of the optical<br />
transmitted intensity. Inset below: image of the fabricated PDMS-Au prototype with the<br />
height of a single pillar of 1.5 mm, the <strong>di</strong>ameter of 1 mm and the side of the square layout of<br />
2.5 mm. Inset above: schematic <strong>di</strong>agram of the used experimental setup. b) Experimental<br />
setup.<br />
References<br />
[1] Q. Zhang, J. J. Xu, Y. Liu, and H. Y. Cuen, “In-situ synthesis of poly(<strong>di</strong>methylsiloxane)-<br />
gold nanoparticles composite filmsand its application in microflui<strong>di</strong>c system,” Lab on<br />
chip, 8, 352-357, 2008.
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Optical performances of micron-sized CMOS<br />
image sensors using metallic planar lenses<br />
Rino Marinelli and Elia Palange<br />
Università degli Stu<strong>di</strong> dell’Aquila, <strong>Dipartimento</strong> <strong>di</strong> Ingegneria Elettrica e<br />
dell’Informazione<br />
L’Aquila, Italy – E-mail: rino.marinelli@univaq.it<br />
CMOS image sensors equipped with metallic planar lenses have been<br />
designed and simulated by CST Microwave Stu<strong>di</strong>o. The increase of the spatial<br />
resolution of CMOS image sensors implies the reduction of their pixel<br />
<strong>di</strong>mensions. It has been demonstrated that for pixel size smaller than 1.4 μm,<br />
<strong>di</strong>ffraction effects become so significant to prevent the microlens from acting<br />
as a focusing element [1]. The research of <strong>di</strong>fferent focusing components is, at<br />
present, a challenge for a further size reduction of the image sensor pixel.<br />
Recently, planar lenses based on aperio<strong>di</strong>c nanoslit arrays on metal films<br />
allowed subwavelength focusing [2]. In this communication, we will report on<br />
the design and simulation of micron-sized planar lenses simply formed by<br />
circular holes in a metallic layer. We will show that the proposed <strong>di</strong>ffracting<br />
lenses with a lightpipe integrated in each pixel [3], make them suitable to<br />
replace the conventional microlenses in the CMOS image sensors and are<br />
compatible with their fabrication process.<br />
In Fig. 1 we show the CMOS image sensor model used for the simulations, the<br />
resulting pattern focusing and light confinement at �=633 nm and, finally, the<br />
normalized optical and cross-talk efficiency versus the pixel size.<br />
a) b) c)<br />
Figure 1 – a) The model of a 1.75 µm single pixel: gold layer is holed, 1.1µm in <strong>di</strong>ameter. b)<br />
The z-component of the Poyting vector at λ=633 nm. c) Normalized optical and cross-talk<br />
efficiency calculated for 4 pixel model versus pixel size at 1.75-1.4-1.2-1 µm.<br />
References<br />
[1] Y. Huo, C. C. Fesenmaier, and P. B. Catrysse, “Microlens performance limits in sub-2μm<br />
pixel CMOS image sensor”, Opt. Express, 18, 5861-5872, 2010.<br />
[2] L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S.<br />
Fan, “Planar lenses based on nanoscale slit arrays in a metal film”, Nanoletters, 9, 235-<br />
238, 2009.<br />
[3] C. C. Fesenmaier, Y. Huo and P. B. Catrysse, “Optical confinement methods for<br />
continued scaling of CMOS image sensor pixels”, Opt. Express, 16, 20457-20470, 2008.<br />
58
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Second Harmonic Generation in Gold<br />
Nanoantennas<br />
Alessio Benedetti, Marco Centini, Concita Sibilia, Mario Bertolotti<br />
<strong>Dipartimento</strong> <strong>di</strong> Scienze <strong>di</strong> Base e Applicate per l'Ingegneria- Sez Fisica.<br />
Sapienza Università <strong>di</strong> Roma. Via A. Scarpa 16 00161 Roma – Italy<br />
E-mail: concita.sibilia@uniroma1.it<br />
The second order nonlinear response from flat metal screens has been widely<br />
investigated, both theoretically and experimentally, from the late 1960s–1980s<br />
[1]. The last few years witnessed renewed interest in the study of nonlinear<br />
second order properties of metal/<strong>di</strong>electric composites thanks to the<br />
development of nanotechnologies and nanoscience. In this work we study the<br />
enhancement of SHG due to the interaction between two 3D metallic wires<br />
with sections of arbitrary shape, focusing on the effect of the surface<br />
morphology and defects. We also analyze the possibility of tailoring the<br />
emission pattern. Numerical calculations have been performed applying a<br />
Green's tensor method [2,3]. The SHG as a function of the wires cross section<br />
size is investigated in both the near and far field regimes. An accurate study of<br />
the effects related to the nonlinear surface contribution for the SHG process,<br />
and of the mo<strong>di</strong>fication of the nonlinear scattering cross section (NLSCS) due<br />
to surface roughness in realistic samples has been performed. Figure 1a shows<br />
the sample description: we note that the shape can be arbitrarily mo<strong>di</strong>fied to<br />
take into account for surface roughness and for <strong>di</strong>screpancies from perfect<br />
rectangular shape. In Figure 1b we plot the NLSCS for a gold nanoantenna<br />
calculated when a pump field consisting of a plane wave at 800 nm, polarized<br />
along the long axis <strong>di</strong>rection of the rods is considered.<br />
e) b)<br />
Figure 1: a)Sample which takes into account the imperfections and roughnesses of the metal<br />
surface. b) 3D Nonlinear SH-Scattering Cross Section for a gold nanoantenna (λ=400nm).<br />
References<br />
[1] J. E. Sipe and G. I. Stegeman, V. M. Agranovich and D. L. Mills, eds. (North-Holland,<br />
1982).<br />
[2] M. Paulus and O. J. F. Martin, J. Opt. Soc. Am. A 18, 854–861 (2001).<br />
[3] A. Benedetti et al., JOSA B 27, 3, 408-416 (2010)).<br />
59
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Controlling Optical Forces on Nanoparticles<br />
through Metamaterials<br />
Simone Tricarico, Filiberto Bilotti and Lucio Vegni<br />
University “Roma Tre”, Department of Applied Electronics<br />
Rome, Italy – E-mail: stricarico@uniroma3.it<br />
In this contribution, we propose a theoretical analysis showing how<br />
metamaterials conformal covers surroun<strong>di</strong>ng a given nanoscatterer may be<br />
effectively used not only to design cloaking devices [1,2], but also to<br />
synthesize shells able to control acting optical forces [3]. Here, we extend the<br />
scattering cancellation approach in order to derive the proper con<strong>di</strong>tions under<br />
which plasmonic me<strong>di</strong>a or metamaterials can be used to manipulate optical<br />
forces exerted by the illuminating ra<strong>di</strong>ation on a Rayleigh particle. In the long<br />
wavelength limit, in fact, such kind of forces are <strong>di</strong>rectly related to the<br />
amplitude of the object electric polarizability. Since scattering cancellation<br />
technique relies in suppressing the scattered field by nullifying the<br />
polarizability of the overall object, we may exploit the inherently <strong>di</strong>spersive<br />
behavior metamaterials to design a suitable cover able to govern optical forces<br />
(see Figure 1).<br />
x<br />
�0<br />
y �0<br />
2<br />
E0<br />
f) b)<br />
Figure 1 – a) Gra<strong>di</strong>ent force field <strong>di</strong>stribution for a bare <strong>di</strong>electric spherical particle placed in<br />
the interference region of two orthogonal stan<strong>di</strong>ng waves with zero phase shift. b) Gra<strong>di</strong>ent<br />
force field <strong>di</strong>stribution in the same configuration for a <strong>di</strong>electric spherical covered by a<br />
metamaterial shell. At the working frequency (zero crossing of the electric polarizability) the<br />
gra<strong>di</strong>ent force is minimized.<br />
References<br />
[1] A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial<br />
coatings,” Phys. Rev. E, 72, 016623, 2005<br />
[2] S. Tricarico, F. Bilotti, and L. Vegni, “Reduction of optical forces exerted on nanoparticles<br />
covered by scattering cancellation based plasmonic cloaks,” Phys. Rev. B, 82,<br />
045109, 2010<br />
[2] S. Tricarico, F. Bilotti, A. Alù, and L. Vegni, “Plasmonic Cloaking for Irregular Objects<br />
with Anisotropic Scattering Properties,” Phys. Rev. E, 81, 026602, 2010<br />
60<br />
x<br />
�0<br />
y �0<br />
2<br />
E0
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Session MTM-7<br />
Metamaterials theory and modeling<br />
Chairperson: S. Hrabar, University of Zagreb<br />
14:00-14:20<br />
P. Fernandes, M. Ottonello, and M. Raffetto<br />
Some comments on the solution of the linear algebraic systems defined<br />
by the finite element method when applied to electromagnetic problems<br />
involving bianisotropic me<strong>di</strong>a<br />
14:20-14:40 (withdrawn)<br />
G. Conte, G. Finocchio, A. Faba, A. Prattella, B. Azzerboni, E.<br />
Cardelli<br />
Double negative metamaterials based on ferromagnetic microwire: a<br />
numerical study<br />
14:20-14:40<br />
G. Ruffato and F. Romanato<br />
Near-field numerical analysis of Surface Plasmon Polariton<br />
propagation on metallic gratings<br />
14:40-15:00<br />
A. Massaro, D. Caratelli, A. Yarovoy, R. Cingolani, and A.<br />
Athanassiou<br />
Accurate circuit modeling for plasmon probe design<br />
15:00-15:20<br />
P. Zilio, D. Sammito, and F. Romanato<br />
Role of resonances of <strong>di</strong>gital plasmonic gratings in absorption profile<br />
remodulation<br />
61
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Some comments on the solution of the linear<br />
algebraic systems defined by the finite element<br />
method when applied to electromagnetic<br />
problems involving bianisotropic me<strong>di</strong>a<br />
Paolo Fernandes (1) , Marina Ottonello (2) and Mirco Raffetto (2)<br />
(1) Istituto <strong>di</strong> Matematica <strong>Applicata</strong> e Tecnologie Informatiche del<br />
Consiglio Nazionale Delle Ricerche,<br />
Via De Marini 6, I 16149 Genoa, Italy – E-mail: fernandes@ge.imati.cnr.it<br />
(2) Department of Biophysical and Electronic Engineering,<br />
University of Genoa, Via Opera Pia 11a,<br />
I 16145, Genoa, Italy – E-mail: ottonello@<strong>di</strong>be.unige.it,<br />
raffetto@<strong>di</strong>be.unige.it<br />
It is well known that the finite element (FE) method, when applied to the<br />
solution of time-harmonic electromagnetic boundary value problems involving<br />
linear me<strong>di</strong>a, requires the solution of linear algebraic systems of equations<br />
characterized by very sparse matrices [1]. For this task <strong>di</strong>fferent techniques of<br />
solution can be considered: <strong>di</strong>rect solvers and iterative solvers [1]. Usually<br />
iterative solvers [2] work very well and are used worldwide in FE simulations<br />
of electromagnetic boundary value problems. Many types of iterative solvers<br />
have been developed [2] and, among these, some solvers like the conjugate<br />
gra<strong>di</strong>ent [1], [2], the biconjugate gra<strong>di</strong>ent [1], [2] and the Conjugate<br />
Orthogonal Conjugate Gra<strong>di</strong>ent [3], which have received a particular attention<br />
in the research community working on the FE method, assume some kind of<br />
symmetry of the FE matrices.<br />
When the time-harmonic electromagnetic boundary value problem of interest<br />
involves innovative and linear me<strong>di</strong>a, like the so-called bianisotropic materials<br />
[4], [5], the usual symmetry of the FE matrices can be lost and for the most<br />
widely used algebraic iterative algorithms convergence is not guaranteed<br />
anymore. This is the reason why in [6] the authors considered the me<strong>di</strong>um<br />
analyzed in [5] setting a parameter to zero, so reducing the bianisotropic<br />
me<strong>di</strong>um to a biisotropic one. In this contribution we analyze what can be done<br />
to overcome this <strong>di</strong>fficulty.<br />
References<br />
[1] J. Jin, The finite element method in electromagnetics, John Wiley & Sons, 1993.<br />
[2] R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R.<br />
Pozo, C. Romine and H. Van der Vorst, Templates for the Solution of Linear Systems:<br />
Buil<strong>di</strong>ng Blocks for Iterative Methods, 2nd E<strong>di</strong>tion, SIAM, 1994.<br />
[3] H. A. van der Vorst and J. B. M. Melissen, “A Petrov-Galerkin type method for solving<br />
Ax=b, where A is symmetric complex,” IEEE Trans. Magnetics, vol. 26, pp. 706-708,<br />
1990.<br />
[4] J. A. Kong, Theory of Electromagnetic Waves, Wiley, 1975.<br />
[5] S. Maruyama and M. Koshiba, “A vector finite element formulation for general<br />
bianisotropic waveguides,” IEEE Transactions on Magnetics, vol. 33, pp. 1528- 1531,<br />
1997.<br />
[6] P. Fernandes and M. Raffetto, “Well posedness and finite element approximability of<br />
time-harmonic electromagnetic boundary value problems involving bianisotropic<br />
materials and metamaterials, Mathematical Models and Methods in Applied Sciences,<br />
vol. 19, pp. 2299-2335, December 2009.<br />
62
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Double negative metamaterials based on<br />
ferromagnetic microwire: a numerical study<br />
G. Conte (1) , G. Finocchio (1) , A. Faba (2)(3) , A. Prattella (1) , B. Azzerboni (1) , E.<br />
Cardelli (2)(3)<br />
(1) University of Messina, Department of Matter Physics and Electronic<br />
Engineering - Messina, Italy<br />
(2) University of Perugia, Polo Scientifico e Didattico <strong>di</strong> Terni,<br />
Terni, Italy<br />
(3) University of Perugia, Department of Industrial Engineering<br />
Perugia, Italy<br />
The double negative (DNG) properties of metamaterials based on array of<br />
ferromagnetic thin wires in the RF spectrum have recently been highlighted<br />
[1,2]. This fact is interesting due the possibility to control the DNG with a<br />
magnetic field applied to the wires (control of the ferromagnetic resonance<br />
frequency).<br />
This work consists of a systematic study of the electric properties of a perio<strong>di</strong>c<br />
array of this kind of me<strong>di</strong>a in order to determine how it is influenced the DNG<br />
effect. The negative electric permittivity can be tuned by acting on the<br />
geometric parameters a and r as suggested by Pendry et al [3].<br />
The FTDT method was employed to analyze 1D and 2D array with size of 3x1<br />
and 3x2 in waveguide environment (8÷12 GHz - WR-90 waveguide). The<br />
wires composed by CoSiB have a ra<strong>di</strong>us of 2 μm. The performance of the<br />
samples are expressed in terms of scattering parameters S11 and S21 and<br />
normal absorbed power (Pabs=1-|S11| 2 -|S21| 2 ) and calculated for three values of<br />
dc magnetic field (parallel to the wires). For both arrays, the performances are<br />
enhanced when the a (<strong>di</strong>stance between the wires) is increased up to a critical<br />
value (about 5 mm). For larger value the scattering phenomenon is not<br />
negligible. Our computations show the DNG effect is visible only when the<br />
ra<strong>di</strong>us of the wire is comparable with the skin length. We also see that the<br />
transmission of the signal in the DNG region roughly decrease in the double<br />
layer case, in the case with a third layer the DNG effects became almost<br />
negligible.<br />
References<br />
[1] J. Carbonell, et al, “Double negative metamaterials based on ferromagnetic microwires,”<br />
Phys. Rev. B 81, 024401, 2010.<br />
[2] H. García-Miquel, J. Carbonell, V. E. Boria and J. Sánchez-Dehesa, “Experimental<br />
evidence of left handed transmission through arrays of ferromagnetic microwires,” Appl-<br />
Phys. Lett. 94, 054103, 2009<br />
[3] J. B. Pendry, J. A. Holden, J. D. Robbins, and J. W. Stewart, “Low frequency plasmons in<br />
thin-wire structures,” J. Phys. Condensed Matter, vol. 10, pp. 4785–4809, 1998<br />
[4] N. Engheta and R. W. Ziolkowski, “Metamaterials. Physics and Engineering<br />
Explorations,” Wiley Inter-Science, IEEE Press, Piscataway, NJ, 2006<br />
63
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Near-field numerical analysis of Surface Plasmon<br />
Polariton propagation on metallic gratings<br />
Gianluca Ruffato (1,2)* and Filippo Romanato (1,2,3)**<br />
(1) University of Padova, Department of Physics ‘G.Galilei’ Via Marzolo 8, 35131 Padova,<br />
Italy<br />
(2) LaNN Laboratory for Nanofabrication of Nanodevices, Corso Stati Uniti 4, 35127 Padova<br />
Italy<br />
(3) CNR-INFM IOM National Laboratory S.S. 14 Km 163.5, 34012 Basovizza Italy<br />
*E-mail:gianluca.ruffato@unipd.it **E-mail: romanato@tasc.infm.it<br />
Sinusoidal 1D metallic gratings are shown to efficiently couple the<br />
propagation of Surface Plasmon Polaritons (SPPs). Numerical simulations<br />
were performed in order to analyze the SPP excitation and propagation on<br />
these metallic gratings in the conical mounting. C-Method 1 was implemented<br />
to design the best grating profile and material choice so to optimize SPP<br />
coupling and optical response for applications in the bio-sensing field 2 . In<br />
recent papers we experimentally demonstrated benefits in sensitivity 3 and<br />
polarization phenomenology 4 that are originated by azimuthal rotation.<br />
Numerical simulations confirm these experimental results and complete the<br />
analysis with a study of SPP near-field on metallic surface: electromagnetic<br />
field intensity and polarization, out-of-scattering plane SPP propagation,<br />
multiple SPP excitation. The code allows describing the full optical behavior<br />
of this plasmonic grating also when coated with <strong>di</strong>electric multi-layer that can<br />
be used as special substrates for sensing purposes.<br />
g) b)<br />
Figure 1 – a) Reflectivity <strong>di</strong>ps for angular scan at azimuth �=40° and illuminating wavelength<br />
�=700nm for <strong>di</strong>fferent incident polarization. Sinusoidal bimetallic Ag(37nm)-Au(7nm) grating<br />
on silicon substrate: period 500nm, amplitude 25nm. b) H-field z-component of excited SPPs<br />
on the grating surface xy and reconstruction of wavevector resonance sum kSPP = k|| - G, where<br />
k|| is the on-plane incident light momentum, G is grating momentum.<br />
References<br />
[1] J.Chandezon, M.T.Dupuis, G.Cornet J. Opt. Soc. Am. 72, 839-846, 1982<br />
[2] J. Homola, Chemical Reviews 108, 462-493, 2008<br />
[3] F. Romanato, K. H. Lee, H. K. Kang, G. Ruffato and C. C. Wong, Optics Express, 17,<br />
12145, 2009<br />
[4] F. Romanato, K. H. Lee, G. Ruffato, and C. C. Wong, Appl. Phys. Lett. 96, 111103, 2010<br />
64
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Accurate Circuit Modeling for Plasmon Probe<br />
Design<br />
Alessandro Massaro (1) , Diego Caratelli (2) , Alexander Yarovoy (2) , Roberto<br />
Cingolani (3) , and Athanassia Athanassiou (1),(4)<br />
(1) Italian Institute of Technology IIT, Center of Biomolecular<br />
Nanotechnologies<br />
Arnesano (Le), Italy – E-mail: alessandro.massaro@iit.it<br />
(2) IRCTR, Delft University of Technology, Mekelveg 4, Delft, The Netherlands<br />
(3) Italian Institute of Technology IIT- Genova- Italy.<br />
(4) National Nanotechnology Laboratory, Institute of Nanoscience of CNR of<br />
Lecce<br />
- Italy<br />
An accurate transmission line model for metallic plasmon probe design is<br />
proposed. The new approach is based on the simultaneous transverse<br />
resonance <strong>di</strong>ffraction (STRD) [1] method which allows to evaluate the near<br />
field generated by a metallic wedge excited by surface plasmon wave. The<br />
generic model considers a metallic wedge in <strong>di</strong>fferent <strong>di</strong>electric materials as<br />
illustrated in Fig. 1 (a). By means of the resonance con<strong>di</strong>tion of the equivalent<br />
transmission line circuit of Fig. 1 (b) [1] we evaluate the singularity v of the<br />
electromagnetic field. This singularity is implemented in a multipole<br />
expansion of the Green’s function by provi<strong>di</strong>ng the near field ra<strong>di</strong>ation pattern<br />
of Fig. 1 (c). The proposed approach is used for the design of metallic probes<br />
detecting variation of permittivity.<br />
(a) (b) (c)<br />
��� ��� i+1<br />
��� ��� i<br />
�� i+1<br />
�� i+1<br />
�� i�� i��<br />
��� ��� 2<br />
�� ��<br />
�� N<br />
�� 2<br />
�� ��<br />
�<br />
��� ��� N-1<br />
�� 2<br />
�� ��<br />
�� N<br />
�� N<br />
�� �� 1<br />
1<br />
��� ��� 1<br />
��� ���<br />
Conductor<br />
��� ��� N<br />
�� ��<br />
��� ���<br />
N<br />
��� N<br />
����<br />
65<br />
�� ��<br />
� ���<br />
2 2<br />
��� 2<br />
�� ��<br />
��� ���� ���� Figure 1 – a) Metallic wedge in <strong>di</strong>electric materials. b) Transmission line circuit for a generic<br />
metallic wedge profile. c) STRD near field ra<strong>di</strong>ation pattern for a gold metallic wedge with<br />
�=�/4 working at �0 =1 �m.<br />
References<br />
[1] A. Massaro, L. Pierantoni, R. Cingolani, and T. Rozzi, “A new analytical model of<br />
<strong>di</strong>ffraction by 3D-<strong>di</strong>electric corners,” IEEE Trans. on Antennas Propagat., 57, 2323-2330,<br />
2009.<br />
��� ���
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Role of Resonances of Digital Plasmonic<br />
Gratings in Absorption Profile Remodulation<br />
Pierfrancesco Zilio (1,2) , Davide Sammito (2,3) and Filippo Romanato (1,2,3)<br />
(1) University of Padova, Department of Physics<br />
Padova, Italy – E-mail: pierfrancesco.zilio@pd.infn.it<br />
(2) LaNN - Laboratory of Nanofabriaction of Nanodevices- viale Stati Uniti 4.<br />
35200 Padova, Italy.<br />
(2) IOM-CNR- S.S. 14 km 163.5- Basovizza Trieste<br />
Padova, Italy – E-mail: filippo.romanato@venetonanotech.it<br />
This work investigates the potentialities of 1D subwavelength <strong>di</strong>gital metallic<br />
gratings to modulate the EM field absorption profile in the silicon substrate<br />
underneath. Two well known optical properties of such structures are<br />
particularly attractive for this purpose: Surface Plasmon Polaritons (SPP) and<br />
the Extraor<strong>di</strong>nary Optical Transmission (EOT) [1].<br />
We focused on the optical response of the system to a normally impinging<br />
1000nm-monochromatic TM-polarized wave, varying systematically both<br />
period (d) and thickness (h) of the grating. The ratio between slit width and<br />
period is kept constant to 0.1. The full EM fields <strong>di</strong>stribution has been<br />
computed using COMSOL Multiphysics software which implements a finite<br />
elements analysis. For each configuration (h,d) we calculated transmittance<br />
and absorptance within <strong>di</strong>fferent depths in silicon. We also computed the<br />
effective absorption profile of light as a function of depth in silicon. The same<br />
results have been computed using also a semi-analytical model based on the<br />
decomposition of the fields in Bloch-Floquet modes in air and silicon and in<br />
waveguide modes within the slits [2].<br />
a) b)<br />
Figure 1 – a) Transmittance map as a function of period and thickness of the grating. Solid<br />
lines represent pre<strong>di</strong>ctions of the analytic model. b) Grating configurations showing<br />
respectively Extraor<strong>di</strong>nary Optical Transmission (left) and Surface Plasmon Polaritons (right).<br />
References<br />
[1] F.J. Garcia-Vidal, L.M. Martin-Moreno, T.W. Ebbesen, L. Kuipers, “Light passing<br />
through subwavelength apertures”, Rev. Mod. Phys. , 82, pp. 729-787 (2010).<br />
[2] P. Zilio, D. Sammito, G. Zacco and F. Romanato, “Absorption profile modulation by<br />
means of 1D <strong>di</strong>gital plasmonic gratings”, Optics Express, 18, pp. 19558-19565 (2010).<br />
66
Author Index<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Abbate, G., MTM-2<br />
Aiello, G., FEM-3<br />
Alfonzetti, S., FEM-3<br />
Alù, A., MTM-2<br />
Andreone, A., MTM-2, MTM-3; MTM-4<br />
Athanassiou, A., MTM-4, MTM-6, MTM-7<br />
Azzerboni, B., MTM-7<br />
Bartolino, R., MTM-1<br />
Benedetti, A., MTM-4, MTM-6<br />
Bertolotti, M., MTM-4, MTM-6<br />
Bilotti, F., FEM-2, MTM-3, FEM-4, MTM-5, MTM-6<br />
Bisceglia, B., FEM-2<br />
Bonis, I., MTM-5<br />
Borzì, G., FEM-3<br />
Campopiano, S., MTM-1<br />
Caratelli, D., MTM-7<br />
Cardelli, E., MTM-7<br />
Castal<strong>di</strong>, G., MTM-1, MTM-2, MTM-3, MTM-4<br />
Ceccuzzi, S., FEM-4<br />
Centini, M., MTM-4, MTM-6<br />
Chiariello, AG., MTM-2<br />
Chikhi, N., MTM-4<br />
Ciattoni, A., MTM-4<br />
Cingolani, R., MTM-4, MTM-6, MTM-7<br />
Coco, S., FEM-1, FEM-2, FEM-4<br />
Conforto, S., FEM-2<br />
Conte, G., MTM-7<br />
Coscelli, E., FEM-3<br />
Cucinotta, A., FEM-3<br />
Cusano, A., MTM-1<br />
D’Alessio, T., FEM-2<br />
d’Elia, U., FEM-4<br />
De Luca, A., MTM-1<br />
De Terlizzi, F., FEM-2<br />
De Zuani, S., MTM-2<br />
Di Gennaro, E., MTM-2, MTM-3, MTM-4<br />
Di Palma, L., MTM-5, MTM-5<br />
Engheta, N., MTM-2<br />
Esposito, E., MTM-4<br />
Faba, A., MTM-7<br />
Fernandes, P., MTM-7<br />
Finocchio, G., MTM-7<br />
Forestiere, C., MTM-2<br />
Frezza, F., MTM-5<br />
Gal<strong>di</strong>, V., MTM-1, MTM-2, MTM-3, MTM-4<br />
Gallina, I., MTM-1, MTM-2, MTM-3, MTM-4<br />
Garoli, D., MTM-2<br />
Giovara, V., FEM-1<br />
67
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Goffredo, M., FEM-2<br />
Hrabar, S., MTM-5<br />
Jin, P., MTM-3<br />
Khan, F., FEM-1<br />
Khan, O., FEM-1<br />
Kiricenko, A., MTM-5<br />
Kronis, I., MTM-5<br />
Laudani, A., FEM-1, FEM-2, FEM-4<br />
Lin, C.C., MTM-3<br />
Maffucci, A., MTM-2<br />
Marinelli, R., MTM-6<br />
Massaro, A., MTM-4, MTM-6, MTM-7<br />
Meschino, S., FEM-4<br />
Miano, G., MTM-2<br />
Mirizzi, F., FEM-4<br />
Molar<strong>di</strong>, C., FEM-3<br />
Montrucchio., B,FEM-1<br />
Natali, M., MTM-2<br />
Ottonello, M., MTM-7<br />
Pajewski, L., FEM-4, MTM-5<br />
Palange, E., MTM-4, MTM-6<br />
Parisi, G., MTM-2<br />
Pelosi, G., FEM-4<br />
Pisco, M., MTM-1<br />
Piuzzi, E., MTM-5<br />
Poli, F., FEM-3<br />
Ponti, C., FEM-4, MTM-5<br />
Prattella., A,MTM-7<br />
Priya Rose., T,MTM-2<br />
Pulcini, G., FEM-4<br />
Raffetto, M., MTM-7<br />
Ragusa, C., FEM-1<br />
Ramaccia, D., MTM-3, FEM-4<br />
Repetto, M., FEM-1<br />
Ricciar<strong>di</strong>, A., MTM-1<br />
Riganti Fulginei, F., FEM-1, FEM-4<br />
Rizza, C., MTM-4<br />
Rizzo, S., FEM-3<br />
Romanato, F., MTM-2, MTM-7, MTM-7<br />
Rossi, G., MTM-5<br />
Rubinacci, G., FEM-2<br />
Ruffato, G., MTM-7<br />
Salerno, N., FEM-3<br />
Salvini, A., FEM-1, FEM-4<br />
Sammito, D., MTM-2, MTM-7<br />
Scaglione, A., FEM-2<br />
Schettini, G., FEM-4, MTM-5<br />
Schmid, M., FEM-2<br />
Selleri, S., FEM-3<br />
Selleri, S., FEM-4<br />
68
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
Sibilia, C., MTM-4, MTM-6<br />
Spano, F., MTM-4, MTM-6<br />
Strangi, G., MTM-1<br />
Taddei, R., FEM-4<br />
Takahashi, N., FEM-1<br />
Tallarino, NF., FEM-2<br />
Tamburrino, A., FEM-2<br />
Toscano, A., MTM-3, FEM-4<br />
Tricarico, S., FEM-2, MTM-6<br />
Vegni, L., FEM-2, MTM-5, MTM-6<br />
Ventre, S., FEM-2<br />
Xie, B., FEM-1<br />
Yarovoy, A., MTM-7<br />
Zheludev,N., MTM-1<br />
Zilio, P., MTM-7<br />
Ziolkowski, R., MTM-3<br />
Zito, G., MTM-2<br />
69
Notes<br />
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010<br />
70
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