WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

12. P.I. Borel, A. Harpøth, L.H. Frandsen, M. Kristensen, P. Shi, J.S. Jensen and O. Sigmund, “Topology
Optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996–2001 (2004),
http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996.
13. A. Lavrinenko, P.I. Borel, L.H. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen and T. Niemi,
“Comprehensive FDTD Modelling of Photonic Crystal Waveguide Components,” Opt. Express 12, 234-248
(2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234.
14. P.I. Borel, L. H. Frandsen, M. Thorhauge, A. Harpøth, Y. X. Zhuang, M. Kristensen, and H. M. H. Chong,
“Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE
polarized light.” Opt. Express 11, 1757-1762 (2003),
http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757.
15. A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, M. Agio, “Photonic-crystal ultrashort
bends with improved transmission and low reflection at 1.55 µm,” Appl. Phys.Lett. 80, 547-549 (2002).
16. E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, J. D. Joannopoulos, “Quantitative analysis of bending
efficiency in photonic-crystal waveguide bends at λ = 1.55 µm wavelengths,” Opt. Lett. 26, 286-288 (2001).
17. M. P. Bendsøe and O. Sigmund, Topology optimization — Theory, Methods and Applications (Springer-Verlag,
2003).
18. K. Svanberg, “The method of moving asymptotes: a new method for structural optimization,” Int. J. Numer.
Meth. Engng. 24, 359-373 (1987).
19. J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization:
Low-loss waveguide bends,” Appl. Phys. Lett. 84, 2022-2024 (2004).
20. O. Sigmund and J. S. Jensen, “Systematic design of phononic band gap materials and structures by topology
optimization,” Phil. Trans. R. Soc. Lond. A 361, 1001-1019 (2003).
21. J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: A high bandwidth low loss
T-junction waveguide,” J. Opt. Soc. Am. B, accepted (2004).
22. R. L. Espinola, R. U. Ahmad, F. Pizzuto, M. J. Steel, R. M. Osgood, Jr., ”A study of high-index contrast 90°
waveguide bend structures,” Opt. Express 8, 517-528 (2001),
http://www.opticsexpress.org/abstract.cfm? URI=OPEX-8-9-517.
1. Introduction
Modulating the refractive index profile periodically in an optical material can create photonic
bandgaps (PBGs) wherein no optical modes can exist [1-3]. Such structures are often referred
to as photonic crystals (PhCs) and have attracted a lot of attention as they potentially allow
ultra-compact photonic integrated circuits (PICs) to be realized [4-6]. Planar PhC structures
are often defined as triangular arrangements of low dielectric pillars in a high dielectric
material. This configuration gives rise to a large PBG for the transverse-electric (TE)
polarization [7, 8]. Defects in the PhC can introduce modes in the PBG. In this way, photonic
crystal waveguides (PhCWs) can be formed by locally breaking the periodicity along a
specific direction of the PhC lattice. Due to the triangular lattice configuration, such PhCWs
are naturally bent in steps of 60°, thus, making the 60° PhCW bend a key component in PhCbased
PICs.
In the field of planar photonic crystals, research has within the last decade mostly relied on
an Edisonian design approach combining physical arguments and experimental/numerical
verifications [9, 10]. Further optimizations have typically been done in an iterative trial-anderror
procedure to improve a chosen performance measure of the PhC component. Such an
approach is very time-consuming and does not guarantee optimal solutions. Recently, Smajic
et al. [11] have shown that sensitivity analyses can be assistive in choosing the critical PhC
rods/holes to be altered. A different approach was suggested in our previous work [12], in
which we used an inverse design strategy called topology optimization to optimize the
performance of a PhCW containing two consecutive 120° bends. This design method offers an
effective and robust optimization of the photonic crystal structure irrespectively of the device
under consideration. Here, we apply the topology optimization method to the much more
important and commonly used PhCW 60° bend and demonstrate an experimental 1-dB
transmission bandwidth of more than 200nm. Experimental transmission spectra are compared
to spectra obtained from 3D finite-difference-time-domain (FDTD) calculations [13] and good
agreement is found.
#5520 - $15.00 US Received 19 October 2004; revised 12 November 2004; accepted 15 November 2004
(C) 2004 OSA 29 November 2004 / Vol. 12, No. 24 / OPTICS EXPRESS 5917