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edited by Fabio Della Sala | Stefania D’Agostino

H A N D B O O K O F
MOLECULAR
PLASMONICS

H A N D B O O K O F
MOLECULAR
PLASMONICS
edited by Fabio Della Sala and Stefania D’Agostino

Published by
Pan Stanford Publishing Pte. Ltd.
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Handbook of Molecular Plasmonics
Copyright c○ 2013 Pan Stanford Publishing Pte. Ltd.
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ISBN 978-981-4303-20-0 (Hardcover)
ISBN 978-981-4303-21-7 (eBook)
PrintedintheUSA

Contents
Preface
Acknowledgment
xiii
xvii
1 Foundations of Molecular Plasmonics 1
F. Della Sala
1.1 Electromagnetic Waves 2
1.1.1 Propagation in a Homogeneous Medium 5
1.1.1.1 Poynting vector 7
1.1.2 Reflection and Transmission at an Interface 9
1.1.2.1 Normal incidence 13
1.1.3 Current and Charges as Sources of Fields 14
1.1.3.1 Green’s function 15
1.2 Dielectric Function of Metals 17
1.2.1 The Drude Model 17
1.2.2 Noble Metals 22
1.2.3 Linear Response Theory 23
1.3 Delocalized Surface Plasmon Resonances 27
1.3.1 The Surface Plasmon-Polariton Wavevector 30
1.3.1.1 Propagation length 32
1.3.1.2 Field-penetration depths 33
1.4 Localized Surface Plasmon Resonances 33
1.4.1 Nanosphere in the Quasi-Static Approximation 35
1.5 Dipole Radiation 41
1.5.1 Radiation Pattern 45
1.5.2 Dissipated Power 46
1.5.3 Classical Approach 47
1.6 Scattering Theory 50
1.6.1 Scattering Cross-Section 52
1.6.2 Optical Theorem 54

vi
Contents
1.6.3 Rayleigh Scattering by a Nanosphere 55
1.6.4 Radiative Damping 57
1.6.5 Mie Scattering 58
1.7 Dipole Radiation in Scattering Environments 60
1.7.1 Forced Damped Oscillator 61
1.7.2 Purcell’s Effect 62
1.7.3 Fluorescence Lifetime and Quantum Yield 64
1.7.4 Fluorescence Emission Near a Metal
Surface 66
1.7.5 Fluorescence Emission Near a Metal
Nanosphere 72
1.7.5.1 The Gersten-Nitzan model 75
1.7.5.2 The Carminati model 76
PART I
THEORY AND COMPUTATIONAL METHODS
2 Computational Approaches for Plasmonics 83
M. A. Yurkin
2.1 Introduction 83
2.2 Overview of Different Methods 84
2.2.1 Finite Scatterers in Homogeneous Medium 84
2.2.2 Periodic Scatterers 86
2.2.3 Scatterers Near an Infinite Plane Surface 87
2.3 Electric Permittivity 88
2.4 Theory of the DDA 90
2.4.1 General Framework 90
2.4.2 Numerical Scheme 95
2.4.2.1 Iterative methods to solve the linear
system 95
2.4.2.2 Block-Toeplitz structure and FFT
acceleration 99
2.4.2.3 Orientation averaging and repeated
calculations 102
2.4.3 Existing Formulations 104
2.4.3.1 Interaction term 104
2.4.3.2 Polarizability prescription 106
2.4.3.3 Calculating measurable quantities 110
2.4.3.4 Decreasing shape errors 112

Contents
vii
2.5 Practical Aspects of DDA Simulations 113
2.5.1 General Applicability 113
2.5.2 System Requirements 114
2.5.3 Free Parameters 115
2.5.4 Available Codes 117
2.6 Accuracy of the DDA 119
3 Size and Shape Dependence of Localized Surface Plasmon
Resonances 137
S. D’Agostino
3.1 Introduction 138
3.2 Size Dependence 139
3.2.1 Small Nanoparticles and Surface Damping 139
3.2.2 Large Nanoparticles and Higher-Order Modes 140
3.3 Shape Dependence 144
3.3.1 Radially Symmetric Nanoparticles 144
3.3.1.1 Ellipsoids and spheroids 144
3.3.1.2 Cylinders and disks 146
3.3.2 Prisms and Finite-Number Facets
Nanoparticles 148
3.3.2.1 Cubes 148
3.3.2.2 Triangular prisms 150
3.3.3 Polyhedral Nanoparticles 152
3.3.3.1 Truncated cubes 152
3.3.3.2 Rounded, regular and marks
decahedral nanoparticles 153
3.3.4 Multi-Tips Objects 156
3.3.4.1 Stars 156
3.3.4.2 Urchins-like nanoparticles 157
3.3.5 Void Nanoparticles 161
3.3.5.1 Nanoshells 161
3.3.5.2 Void cubes 164
3.4 Conclusions 165
4 Computational Molecular Photophysics 175
E. Fabiano
4.1 Introduction 175
4.2 Electronic Excitations 177

viii
Contents
4.2.1 Electronic Absorption Spectrum 180
4.2.2 Vibrational Contributions 182
4.3 Photophysics 184
4.3.1 Semiclassical Description of Internal
Conversion and Inter-System Crossing 187
4.4 Computational Methods for Excited States 190
4.4.1 Configuration Interaction 194
4.4.2 Time-Dependent Density Functional
Theory 196
4.4.3 Linear Response TD-DFT 200
5 Metal–Molecule Electrodynamic Coupling 213
S. Corni
5.1 Introduction 213
5.2 The Quasi-Static Limit 217
5.3 The Point-Dipole Model of the Molecule, and the
Classical Metal Nanoparticle 219
5.3.1 Light Absorption 220
5.3.2 Light Emission 225
5.3.3 Light Scattering 234
5.3.4 The Dielectric Function of the Classical Metal
Nanoparticle 237
5.4 Toward an ab initio Molecular Plasmonics 243
5.4.1 Coupling the ab-initio Description of the
Molecule with a Continuous Metal 243
5.4.2 Fully ab initio Description of the
Molecule–Metal Nanoparticle Systems 246
PART II
APPLICATIONS AND EXPERIMENTAL ASPECTS
6 Near-Fields in Assembled Plasmonic Nanostructures 261
P. K. Jain and C. Deeb
6.1 Introduction 262
6.2 Optical Properties of Metal Nanoparticles 262
6.2.1 Nanoplasmonic Field Enhancement 265
6.2.2 Tunability of the LSPR and Near-Field 266
6.3 Optical Properties of Coupled Nanoparticles 268
6.3.1 Nanoparticle Assemblies 268

Contents
ix
6.3.1.1 LSPR response of assemblies 268
6.3.1.2 Field enhancement 268
6.3.1.3 Plasmonic wave-guiding 269
6.3.2 Polarization Dependence of Coupling in a
Dimer 269
6.3.3 Dipolar-Coupling Model 271
6.3.4 Analogy to Exciton Coupling in Molecular
Aggregates 273
6.3.5 Bonding and Anti-Bonding of Plasmons 275
6.4 Spatial Profile of the Near-Field 277
6.4.1 Distance-Dependence of the Near-Field 278
6.4.2 Size-Scaling of Near-Field Decay 278
6.4.3 Direct Mapping of the Near-Field 280
6.5 Applications of Near-Field Coupling Concepts 283
6.5.1 Plasmon Ruler 283
6.5.2 Metal Nanoshells 284
6.5.3 Coupling in Larger Arrays 285
6.5.4 Molecular Sensing 285
6.6 Future Outlook 286
7 Noble Metal Nanostructure Enhancement of Fluorescence 295
R. J. Phaneuf
7.1 Introduction 295
7.2 Nanostructure Size, Shape and Spacing Dependence 298
7.3 Role of Substrate 302
7.4 Standing Wave Surface Plasmons 306
7.5 Spacer Layer Effect 312
8 Surface-Enhanced Raman Scattering 321
M. Sun
8.1 Introduction 322
8.2 Electromagnetic Mechanism and Numerical Methods 323
8.3 Chemical Mechanism and Visualization Method of
Charge Transfer 329
8.4 Synthesis and Experiment on SERS 333
8.5 Remote-Excitation SERS 339
8.6 Conclusions 346

x
Contents
9 Parabolic Mirror–Assisted Gap-Mode Optical
Ultramicroscopy 355
D. Zhang and A. J. Meixner
9.1 Introduction 355
9.2 Principles 356
9.2.1 Instrumentation 359
9.2.1.1 Optics layout 359
9.2.2 PM Optics 361
9.2.3 Tip-Sample Distance Control and Image
Recording 365
9.3 Different Types of Gap-Modes 367
9.3.1 Gap-Mode of Metallic System 367
9.3.1.1 Au tip and Au substrate 367
9.3.1.2 Au tip and monolayer adsorbates/Au
substrate 372
9.3.1.3 Au tip and single molecule/Au
substrate 377
9.3.2 Gap-Mode of Metal-Organic Semiconductor
System 379
9.3.2.1 Au tip and diindenoperylene molecule 379
9.3.2.2 Au tip and organic solar cell blends 379
9.3.2.3 Gap-mode of metal-inorganic
semiconductor system 381
9.4 Conclusion 387
10 Wet-Chemical Synthesis Techniques for Colloidal Plasmonic
Nanostructures Assisted by Convective or Microwave
Dielectric Heating 395
L. Carbone
10.1 Introduction 395
10.1.1 Wet-Chemical Synthesis: Basic Principles 397
10.1.1.1 Hybrid nanoarchitecture
formation 401
10.2 Synthesis under Conventional Convective Heating 402
10.2.1 Hard-Templated Growth 402
10.2.2 Precipitation-Promoted Growth 403
10.2.3 Electrochemical and Shape-Controlled
Growth 405

Contents
xi
10.2.4 Photochemical and Shape-Controlled
Growth 408
10.2.5 Galvanic Displacement-Mediated Growth 409
10.2.6 Seed-Promoted Growth 416
10.2.6.1 Homogeneous nucleation 417
10.2.6.2 Heterogeneous nucleation 421
10.3 Synthesis under Microwave Dielectric Heating 425
10.3.1 Basic Principles of Microwave-Promoted
Growth 425
10.3.2 Mono-Metallic Nanostructures 429
10.3.3 Bi-Metallic Hetero-Nanostructures 434
10.4 Conclusions 440
Index 463

Preface
The term molecular plasmonics refers to a rapidly growing interdisciplinary
science which aims at investigating the coupling,
at the nanoscale level, between emitting molecules and metallic
nanostructures. Collective oscillations of the conduction electrons,
named surface plasmons, can strongly enhance the electromagnetic
field around metallic nanoparticles and nano-patterned surfaces:
the optical responses (absorption, fluorescence, lifetime, and Raman
scattering) of molecules close to the metal are thus strongly
modified.
Despite these effects have been known since the seventies, it is
only with the recent progress in the synthesis and fabrication of
nanosystems as well as innovations in the characterization procedures
and spectroscopies that interest in molecular plasmonics has
been boosted. Surface-enhanced Raman spectroscopy (SERS), localized
surface plasmon resonance (LSPR) spectroscopy, and metalenhanced
fluorescence (MEF) find large applications in biology, to
realize plasmonic biosensors or to detect molecular-binding events,
as well as in medicine, for molecular-specific imaging, detection,
and photothermal therapy of cancer. Surface plasmons and MEF
are also widely used in organic opto-electronics, photonics, and
energy-conversion applications. In addition, different theoretical
approaches and modeling tools have been developed in recent years
to describe both organic molecules and metal nanoparticles as
well as their interactions, with increased accuracy and efficiency.
Molecular plasmonics thus has great interdisciplinary appeal,
attracting researchers from fields as diverse as telecommunication
engineering (as emitting molecules behave like electromagnetic
antennas), inorganic chemistry (to synthesize metal nanoparticles),
quantum mechanics (to describe optical properties of molecules and

xiv
Preface
metals), nano-photonics (to manipulate light at a length scale below
the diffraction limit), and optical microscopy (to measure the nearfield
around metallic objects).
Handbook of Molecular Plasmonics is intended for a broad
readership and contains both high-level specialized chapters and
introductory chapters as well as theoretical and experimental
reviews. The main idea underlying this project is to create a useful
feedback between theory and experiments, giving a theoretical
reference to experimentalists and, at the same time, new inputs to
theoreticians for further developments.
This handbook is organized in 10 chapters that reflect the
current status of this evolving scientific field, discuss the most recent
developments, and identify the directions of future research.
Chapter 1 introduces the basic foundations of molecular plasmonics.
It is a self-contained chapter, starting with Maxwell’s
equations and concluding with the derivation of the radiative
and non-radiative decay rates of emitting molecules near metal
surfaces and nanoparticles. After this introductory chapter, the
handbook is subdivided in two parts: the first one describes the
computational and theoretical methods of interest in molecular
plasmonics, while the second is entirely dedicated to the most
relevant applications and experimental techniques. Both parts
contain precious contributions from international experts to ensure
a plurality of points of view.
Part I, Theory and Computational Methods, opens with a chapter
by M. A. Yurkin (Russia) who describes in detail the Discrete
Dipole Approximation (DDA) approach, which is an efficient method
to study the absorption and scattering of metal nanoparticles of
arbitrary shapes. This chapter will serve as an important reference
for theoreticians to model metal nanoparticles. Chapter 3 reports
DDA results for nanoparticles of different sizes and shapes. This
systematic analysis, inspired by recent literature, should represent
an important reference for both experimentalists and theoreticians
to verify and compare the absorption and scattering spectra
of different nanoparticles. While these first two chapters are
completely dedicated to metal nanoparticles, Chapter 4 introduces
the discussion about the molecular counterpart. In this chapter
E. Fabiano (Italy) sheds light on the optical and photophysical

Preface
xv
properties of organic molecules as well as theoretical methods of
quantum mechanics. The interaction between metals and organic
molecules is then analyzed in detail in Chapter 5 by Stefano Corni
(Italy). This chapter represents the synthesis of the concepts of all
previous chapters.
Part II, Applications and Experimental Aspects, starts with
a chapter by P. K. Jain (Illinois) and C. Deeb (Illinois). They
describe the coupling between two plasmonic nanostructures and
concepts and applications of the optical near-field. This chapter
serves as a link between theory and experiments. In Chapter
7, R. J. Phaneuf (Maryland) discusses recent results on MEF.
Both localized and delocalized surface plasmon resonances are
presented, including comparison between theory and experiments.
Chapter 8 is dedicated to SERS, and M. Sun (China) gives special
emphasis to theoretical calculations of charge-transfer effects and to
experimental results on remote SERS excitation, a treatment which
should be useful for both theoreticians and experimentalists. In
Chapter 9, D. Zhang and A. J. Meixner (Germany) describe nearfield
microscopy and the techniques based on the parabolic mirror
confocal microscope. Different types of gap modes are discussed and
relevant experimental images and results are presented. The last
chapter is devoted to the colloidal synthesis of metal nanoparticles.
L. Carbone (Italy) presents a complete review on different synthetic
approaches, ranging from convective to microwave heating. This
chapter should prove very useful not only to chemists but also
to readers from other backgrounds as a reference for all types of
nanoparticles that can be realized experimentally.
It has been a great pleasure to work with all these leading
scientists of this field, and we thank all of them for their support.
We hope this handbook proves to be a helpful reference manual
and a useful tool for both students and experts in this field, and we
encourage readers to give their valuable comments/suggestions so
that the book can be improved further.
Fabio Della Sala
Stefania D’Agostino
Summer 2013

Acknowledgment
We would like to thank all our collegues of the National Nanotechnology
Laboratory who have collaborated with us in the field of
molecular plasmonics.
F. D. S. thanks his wife Erika for her constant support and for
proofreading the book.
S. D. thanks the Photonics and Nanostructures group of the
Physics Department of Pavia for the precious friendship and support
received during the period of the project.