光子在其波長尺度下的週期性排列晶體中，存在著光子晶體能隙，此種晶體稱之為光子晶體。由於在光子晶體能隙俱有隔絕光波傳遞的效果，可以用來調制光波的傳播進而設計各式光學元件。本文提出並分析可調式二維光子晶體結構，其結構由圓柱形的介電彈性體所組成。為了設計可主動控制的光子晶體元件，將局部介電彈性體圓柱置換為空心圓柱致動器，由於介電彈性體致動器會因外加電場的作用而產生幾何尺寸上的變化，在光子晶體耦合器的耦合區中置放空心圓柱型的致動器，藉由外加電場的改變可以用來控制耦合長度。除此之外，利用光子晶體光波導和共振腔的組合來設計一光塞取濾波器，在波導的通道中引入一褶式耦合器的設計來增進濾波器的傳輸效率。經由時域耦合理論的分析得到高傳輸效率濾波器的參數設定，以時域有限差分法的電磁場模擬結果印證所設計光學元件的可行性。

Photonic crystals which possess the photonic bandgap due to their periodic structures have attracted intensive interests in sciences and technologies. Analogous to electrons in solids, photons with some specific energy are forbidden within the photonic bandgap. Making use of the photonic bandgap based confinement and waveguiding, ultra-small resonators formed by introducing point-defects into perfect photonic crystals as well as extremely narrow waveguides consisting of line-defects. In this paper, we proposed a tunable directional coupler based on a two dimensional photonic crystal made of dielectric elastomer rods embedded in air background. The coupling length of the photonic crystal coupler depends on the voltage applied between the electrodes are analyzed by the plane wave expansion method. Besides, we proposed a three-port channel drop filter with a folded directional coupler in a two dimensional photonic crystal. The folded directional coupler is to work as a frequency-dependent mirror for enhancement of the drop efficiency. The frequency response of the channel drop filter has been derived by the couple-mode theory and the highly efficient drop conditions have been discussed. Numerical simulations obtained by the finite-difference time-domain method confirmed the feasibility of the optical devices proposed.

[1] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Physical Review Letters, Vol.58, pp.2059-2062 (1987).
[2] S. John, “Strong Localization of photons in certain disordered dielectric superlattices,” Physical Review Letters, Vol.58, pp.2486-2489 (1987).
[3] E. Yablonovitch and T. J. Gmitter, “Photonic band structure: The face-centered-cubic case,” Physical Review Letters, Vol.63, pp.1950-1953 (1989).
[4] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the flow of light, Princeton University Press, Princeton, New Jersey (1995).
[5] S.G. Johnson, and J. D. Joannopoulos, “Designing synthetic optical media: photonic crystals,” Acta Materialia, Vol.51, pp.5823-5835 (2003).
[6] J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science, Vol.282, pp.1476-1478 (1998).
[7] K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Physical Review Letters, Vol.65, 3152-3155 (1990).
[8] K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Physical Review Letters, Vol.65, pp.2646-2649 (1990).
[9] Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Physical Review Letters, Vol.65, pp.2650-2653 (1990).
[10] E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Physical Review Letters, Vol.67, pp.2295-2298 (1991).
[11] M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, “Two-dimesional photonic band structures,” Optics Communications, Vol.80, pp.199-204 (1991).
[12] M. Plihal, and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Physical Review B, Vol.44, pp.8565–8571 (1991).
[13] H. S. S z er, J. W. Haus and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Physical Review B, Vol.45, pp.13962-13972(1992).
[14] P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Computing Physics Communications, Vol.85, pp.306-322 (1995).
[15] A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method. ( Norwood, MA: Artech House, 1995).
[16] X. Wang, X. G. Zhang, Q. Yu, B. N. Harmon, “Multiple-scattering theory for electromagnetic waves,” Physical Review B, Vol.47, pp.4161–4167 (1993).
[17] J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Physical Review Letters, Vol.69, pp.2772-2775 (1992).
[18] R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap material,” Physical Review B, Vol.48, pp.8434-8437 (1993).
[19] K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas and M. Sigalas, “Photonic band gaps in three dimensions: New layer-by-layer periodic structures,” Solid State Communications, Vol.89, pp.413-416 (1994).
[20] J. C. Knight, T. A. Birks, P. St. J. Russell and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Optics Letters, Vol.21, pp.1547-1549 (1996).
[21] P. R. Villeneuve, S. Fan and J. D. Joannopoulos, “Microcavities in photonic crystals: Mode symmetry, tenability, and coupling efficiency,” Physical Review B, Vol.54, pp.7837-7842 (1996).
[22] S. Foteinopoulou and C. M. Soukoulis, “Theoretical investigation of one-dimsional cavities in two-dimensional photonic crystals,” IEEE Journal of Quantum Electronics, Vol.38, pp.844-849 (2002).
[23] S.-H. Kim and Y.-H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE Journal of Quantum Electronics, Vol.39, pp.1081-1085 (2003).
[24] R. Moussa, L. Salomon, F. de Fornel and H. Aourag, “Numerical study on localized defect modes in two-dimensional lattices: A high Q-resonant cavity,” Physica B, Vol.338, pp.97-102 (2003).
[25] D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen and L. A. Kolodziejski, “One-dimensional photonic bandgap microcavities for strong optical confinement in GaAs and GaAs/AlxOy semiconductor waveguides,” Journal of Lightwave Technology, Vol.17, pp.2152-2160 (1999).
[26] O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” Journal of Optics A: Pure and Applied Optics, Vol.3, pp.S161-S170 (2001).
[27] K. Inoshita and T. Baba, “Fabrication of GaInAsP/InP photonic crystal lasers by ICP etching and control of resonant mode in point and line composite defects,” IEEE Journal of Selected Topics in Quantum Electronics, Vol.9, pp.1347-1354 (2003).
[28] A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Physical Review Letters, Vol.77, pp.3787-3790 (1996).
[29] S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental Demonstration of Guiding and Bending of Electromagnetic Waves in a Photonic Crystal,” Science, Vol.282, pp.274-276 (1998).
[30] K. Sakoda, T. Ueta and K. Ohtaka, “Numerical analysis of eigenmodes localized at line defects in photonic lattices,” Physical Review B, Vol.56, pp.14905-14908 (1997).
[31] T. Sondergaard and K. H. Dridi, “Energy flow in photonic crystal waveguides,” Physical Review B, Vol.61, pp.15688-15696 (2000).
[32] J. Yonekura, M. Ikeda, and T. Baba, “Analysis of finite 2-D photonic crystals and lightwave devices using the scattering matrix method,” Journal of Lightwave Technology, Vol.17, pp.1500-1508 (1999).
[33] S. Fan, S. G. Johnson, J. D. Joannopoulos, and C. Manolatou and H. A. Haus, “Waveguide branches in photonic crystals,” Journal of the Optical Society of America B, Vol.18, pp.162-165 (2001).
[34] G. R. Hadley, “Out-of-plane losses of line-defect photonic crystal waveguides,” IEEE Photonics Technology Letters, Vol.14, pp.642-644 (2002).
[35] T. Uusitupa, K. Kärkkäinen and K. Nikoskinen, “Studying 120º PBG waveguide bend using FDTD,” Microwave and Optical Technology Letters, Vol.39, pp.326-333 (2003).
[36] P. I. Borel, A. Harpoth, L. H. Frandsen and M. Kristensen, “Topology optimization and fabrication of photonic crystal structures,” Optics Express, Vol.12, pp.1996-2001 (2004).
[37] A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Physical Review B, Vol.62, pp.4488-4492 (2000).
[38] M. Koshiba, Y. Tsuji and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” Journal of Lightwave Technology, Vol.18, pp.102-110 (2000).
[39] M. Koshiba, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” Journal of Lightwave Technology, Vol.19, pp.1970-1975 (2001).
[40] S. Boscolo, M. Midrio and C. G. Someda, “Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides,” IEEE Journal of Quantum Electronics, Vol.38, pp.47-53 (2002).
[41] S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. P. Pearsall and D. Nedeljkovic, “Coupling between photonic crystal waveguides,” IEEE Journal of Quantum Electronics, Vol.38, pp.1349-1352 (2002).
[42] M. Qiu and M. Swillo, “Contra-directional coupling between two-dimensional photonic crystal waveguides,” Photonic and Nanostructures – Fundamentals and Applications, Vol.1, pp.23-30 (2003).
[43] I. Park, H.-S. Lee, H.-J. Kim, K.-M. Moon, S.-G. Lee, B.-H. O, S.-G. Park and E.-H. Lee, “Photonic crystal power-splitter based on directional coupling,” Optics Express, Vol.12, pp.3599-3604 (2004).
[44] A. Martinez, F. Cuesta and J. Marti, “Ultrashort 2-D photonic crystal directional couplers,” IEEE Photonics Technology Letters, Vol.15, pp.694-696 (2003).
[45] J. Danglot, O. Vanbésien and D. Lippens, “A 4-port resonant switch patterned in a photonic crystal,” IEEE Microwave and Guide Wave Letters, Vol.9, pp.274-276 (1999).
[46] S. Noda, A. Chutinan and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature, Vol.407, pp.608-610 (2000).
[47] S. Y. Lin, E. Chow, S. G. Johnson and J. D. Joannopoulos, “Direct measurement of the quality factor in a two-dimensional photonic-crystal microcavity,” Optics Letters, Vol.26, pp.1903-1905 (2001).
[48] A. Sharkawy, S. Shi and D. W. Prather, “Multichannel wavelength division multiplexing with photonic crystal,” Applied Optics, Vol.40, pp.2247-2252 (2001).
[49] R. Costa, A. Melloni and M. Martinelli, “Bandpass resonant filters in photonic-crystal waveguides,” IEEE Photonic Technology Letters, Vol.15, pp.401-403 (2003).
[50] B.-K. Min, J.-E. Kim and H. Y. Park, “Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs,” Optics Communications, Vol.237, pp.56-63 (2004).
[51] G. P. Nordin, S. Kim, J. Cai and J. Jiang, “Hybrid integration of conventional waveguide and photonic crystal structures,” Optics Express, Vol.10, pp.1334-1341 (2002).
[52] J. Jiang, J. Cai, G. P. Nordin and L. Li, “Parallel microgenetic algorithm for photonic crystal and waveguide structures,” Optics Letters, Vol.28, pp.2381-2383 (2003).
[53] S. Kim, G. P. Bordin, J. Cai and J. Jiang, “Ultracompact high-efficiency polarizing beam splitter with a hybrid photonic crystal and conventional waveguide structure,” Optics Letters, Vol.28, pp.2384-2386 (2003).
[54] S. Kim, J. Cai, J. Jiang and G. P. Nordin, “New ring resonator configuration using hybrid photonic crystal and conventional waveguide structures,” Optics Express, Vol.12, pp.2356-2364 (2004).
[55] S. Kim, G. P. Nordin, J. Jiang and J. Cai, “Microgenetic algorithm design of hybrid conventional waveguide and photonic crystal structures,” Optical Engineering, Vol.43, pp.2143-2149 (2004).
[56] S. Kim and V. Gopalan, “Strain-tunable photonic band gap crystals,” Applied Physics Letters, Vol.78, pp.3015-3017 (2001).
[57] H. Hillmer, J. Daleiden, C. Prott, F. Römer, S. Irmer, V. Rangelov, A. Tarraf, S. Schüler and M. Strassner, “Potential for micromachined actuation of ultra-wide continuously tunable optoelectronic devices,” Applied Physics B, Vol.75, pp.3-13 (2002).
[58] H. Takeda and K. Yoshino, “Properties of two-dimensional photonic crystals in elastomers,” Physical Review B, Vol.66, pp.115207 (2002).
[59] W. Suh, M. F. Yanik, O. Solgaard and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Applied Physics Letters, Vol.82, pp.1999-2001 (2003).
[60] N. Malkova, S. Kim and V. Gopalan, “Strain tunable light transmission through a 90º bend waveguide in a two-dimensional photonic crystal,” Applied Physics Letters, Vol.83, pp.1509-1511 (2003).
[61] N. Malkova and V. Gopalan, “Strain-tunable optical valves at T-junction waveguides in photonic crystals,” Physical Review B, Vol.68, pp.245115 (2003).
[62] Z. Hou, F. Wu and Y. Liu, “Phonoic crystals containing piezoelectric material,” Solid State Communications, Vol.130, pp.745-749 (2004).
[63] A. D. Lustrac, F. Gadot, S. Cabaret, J.-M. Lourtioz, T. Brillat, A. Priou and E. Akmansoy, “Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths,” Applied Physics Letters, Vol.75, pp.1625-1627 (1999).
[64] J.-M. Lourtioz, A. D. Lustrac, F. Gadot, S. Rowson, A. Chelnokov, T. Brillat, A. Ammouche, J. Danglot, O. Vanbésien and D. Lippens, “Toward controllable pgotonic crystals for centimeter- and millimeter-wave devices,” Journal of Lightwave Technology, Vol.17, pp.2025-2031 (1999).
[65] P. Halevi and F. Ramos-Mendieta, “Tunable photonic crystals with semiconducting constituents,” Physical Review Letters, Vol.85, pp.1875-1878 (2000).
[66] C.-S. Kee and H. Lim, “Tunable complete photonic band gaps of two-dimensional photonic crystals with intrinsic semiconductor rods,” Physical Review B, Vol.64, pp.121103 (2001).
[67] Y.-K. Ha, J.-E. Kim, H. Y. Park, C.-S. Kee and H. Lim, “Tunable three-dimensional photonic crystals using semiconductors with varying free-carrier densities,” Physical Review B, Vol.66, pp.075109 (2002).
[68] M. S. Kushwaha and G. Martinez, “Magnetic-field-dependent band gaps in two-dimensional photonic crystals,” Physical Review B, Vol.65, pp.153202 (2002).
[69] A. Sharkawy, S. Shi and D. W. Prather, “Electro-optical switching using coupled photonic crystal waveguides,” Optics Express, Vol.10, pp.1048-1059 (2002).
[70] H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Optics Communications, Vol.219, pp.177-182 (2003).
[71] H. Takeda and K. Yoshino, “Tunable photonic band schemes in two-dimensional photonic crystals composed of copper oxide high-temperature superconductors,” Physical Review B, Vol.67, pp.245109 (2003).
[72] H. Takeda and K. Yoshino, “Properties of Abrikosov lattices as photonic crystals,” Physical Review B, Vol.70, pp.085109 (2004).
[73] M. Scalora, J. P. Dowling, C. M. Bowden and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap material,” Physical Review Letters, Vol.73, pp.1368-1371 (1994).
[74] P. Tran, “Optical switching with a nonlinear photonic crystal: a numerical study,” Optics Letters, Vol.21, pp.1138-1140 (1996).
[75] P. Tran, “All-optical switching with a nonlinear chiral photonic bandgap structure,” Journal of the Optical Society of America B, Vol.16, pp.70-73 (1999).
[76] H-B. Lin, R. J. Tonucci and A. J. Campillo, “Two-dimensional photonic bandgap optical limiter in the visible,” Optics Letters, Vol.23, pp.94-96 (1998).
[77] A. Haché and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Applied Physics Letters, Vol.77, pp.4089-4091 (2000).
[78] S. W. Leonard, H. M. V. Driel, J. Schilling and R. B. Wehrspohn, “Ultrafast band-edge tuning of a two-dimensional silicon photonic crystal via free-carrier injection,” Physical Review B, Vol.66, pp.161102 (2002).
[79] N. C. Panoiu, M. Bahl and R. M. Osgood, “All-optical tunability of a nonlinear photonic crystal channel drop filter,” Optics Express, Vol.12, pp.1605-1610 (2004).
[80] A. Figotin, Y. A. Godin and I. Vitebsky, “Two-dimensional tunable photonic crystals,”Physical Review B, Vol.57, pp.2841-2848 (1998).
[81] C.-S. Kee, J.-E. Kim and H. Y. Park, “Heliconic band structure of one-dimensional periodic metallic composites,” Physical Review E, Vol.57, pp.2327-2330 (1998).
[82] M. Golosovsky, Y. Saado and D. Davidov, “Self-assembly of floating magnetic into ordered structures: A promising route for the fabrication of tunable photonic band gap materials,” Applied Physics Letters, Vol.75, pp.4168-4170 (1999).
[83] Y. Saado, M. Golosovsky, D. Davidov and A. Frenkel, “Tunable photonic band gap in self-assembled clusters of floating magnetic particles,” Physical Review B, Vol.66, pp.195108 (2002).
[84] B. A. Grzybowski, H. A. Stone and G. M. Whitesides, “Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid-air interface,” Nature, Vol.405, pp.1033-1036 (2000).
[85] W. Wen, L. Zhang and P. Sheng, “Planar magnetic colloidal crystals,” Physical Review Letters, Vol.85, pp.5464-5467 (2000).
[86] B. Gates and Y. Xia, “Photonic crystals that can be addressed with external magnetic field,” Advanced Materials, Vol.13, pp.1605-1608 (2001).
[87] X. Xu, G. friedman, K. D. Humfeld, S. A. Majetich and S. A. Asher, “Superparamagnetic photonic crystal,” Advanced Materials, Vol.13, pp.1681-1684 (2001).
[88] E. L. Bizdoaca, M. Spasova, M. Farle, M. Hilgendorff and F. Caruso, “Magnetically directed self-assembly of submicron spheres with a Fe3O4 nanoparticle shell,” Journal of Magnetism and Magnetic Materials, Vol.240, pp.44-46 (2002).
[89] D. Lacoste, F. Donatini, S. Neveu, J. A. Serughetti and B. A. V. Tiggelen, “Photonic hall effect in ferrofluids: Theory and experiments,” Physical Review E, Vol.62, pp.3934-3943 (2000).
[90] J. Zhou, C. Q. Sun, K. Pita, Y. L. Lam, Y. Zhou, S. L. Ng, C. H. Kam, L. T. Li and Z. L. Gui, “Thermally tuning of the photonic band gap of SiO2 colloid-crystal infilled with ferroelectric BaTiO3,” Applied Physics Letters, Vol.78, pp.661-663 (2001).
[91] S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan and Y. H. Chao, “Control method for the tunable ordered structures in magnetic fluid microstrips,” Journal of Applied Physics, Vol.93, pp.3457-3460 (2003).
[92] K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: The tunable electromagnetic vacuum,” Physical Review Letters, Vol.83, pp.967-970 (1999).
[93] S. W. Leonard, J. P. Mondia, H. M. V. Driel, O. Toader, S. John, K. Busch, A. Birner and U. Gösele, “Tunable two-dimensional photonic crystals using liquid crystal infiltration,” Physical Review B, Vol.61, pp.R2389-R2391 (2000).
[94] N. Susa, “Transmittance for a two-dimensional photonic crystal structure consisting of cylinders and liquid crystal,” Japan Journal of Applied Physics, Vol.39, pp.3466-3467 (2000).
[95] D. Kang, J. E. Maclennan, N. A. Clark, A. A. Zakhidov and R. H. Baughman, “Electro-optic behavior of liquid-crystal-filled silica opal photonic crystals: Effect of liquid-crystal alignment,” Physical Review Letters, Vol.86, pp.4052-4055 (2001).
[96] Y.-K. Ha, Y.-C. Yang, J.-E. Kim, H. Y. Park, C.-S. Kee, H. Lim and J.-C. Lee, “Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band gap structure with liquid crystals,” Applied Physics Letters, Vol.79, pp.15-17 (2001).
[97] C.-S. Kee, H. Lim, Y.-K. Ha, J.-E. Kim and H. Y. Park, “Two-dimensional tunable metallic photonic crystals infiltrated with liquid crystals,” Physical Review B, Vol.64, pp.085114 (2001).
[98] C.-S. Kee, K. Kim and H. Lim, “Tuning of anisotropic optical properties of two-dimensional dielectric photonic crystals,” Physica B, Vol.338, pp.153-158 (2003).
[99] Y. Shimoda, M. Ozaki and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” Applied Physics Letters, Vol.79, pp.3627-3629 (2001).
[100] H. Takeda and K. Yoshino, “Tunable photonic band schemes of opals and inverse opals infiltrated with liquid crystals,” Journal of Applied Physics, Vol.92, pp.5658-5662 (2002).
[101] H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystal utilizing liquid crystals as linear defects,” Physical Review B, Vol.67, pp.073106 (2003).
[102] H. Takeda and K. Yoshino, “Tunable refraction effects in two-dimensional photonic crystals utilizing liquid crystals,” Physical Review E, Vol.67, pp.056607 (2003).
[103] H. Takeda and K. Yoshino, “Disappearances of uncoupled modes in two-dimensional photonic crystals due to anisotropies of liquid crystals,” Physical Review E, Vol.67, pp.056612 (2003).
[104] H. Takeda and K. Yoshino, “Coupling of the TE and TM modes of electromagnetic waves in two-dimensional photonic crystals with surface defects of liquid crystals,” Physical Review E, Vol.68, pp.046602 (2003).
[105] H. Takeda and K. Yoshino, “TE-TM mode coupling in two-dimensional photonic crystals composed of liquid crystal rods,” Physical Review E, Vol.70, pp.026601 (2004).
[106] D. M. Pustai, A. Sharkawy, S. Shi and D. W. Prather, “Tunable photonic crystal microcavities,” Applied Optics, Vol.41, pp.5574-5579 (2002).
[107] A. D’Orazio, M. D. Sario, V. Ingravallo, V. Petruzzelli and F. Prudenzano, “Infiltrated liquid crystal photonic bandgap devices for switching and tunable filtering,” Fiber and Integrated Optics, Vol.22, pp.161-172 (2003).
[108] H. Kitzerow, “Tunable photonic crystals,” Liquid crystals Today, Vol.11, pp.3-7 (2002).
[109] Ch. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp and A. Forchel, “Tunable photonic crystals fabricated in III-V semiconductor slab waveguides using infiltrated liquid crystals,” Applied Physics Letters, Vol.82, pp.2767-2769 (2003).
[110] T. T. Larsen, J. Broeng, D. S. Hermann and A. Bjarklev, “Thermo-optic switching in liquid crystal infiltrated photonic bandgap fibres,” Electronics Letters, Vol.39, pp.1719-1720 (2003).
[111] C. Y. Liu, and L. W. Chen, “Tunable photonic-crystal waveguide Mach-Zehnder interferometer achieved by nematic liquid-crystal phase modulation,” Optics Express, Vol. 12, No. 12, pp. 2616-2624 (2004).
[112] Y. Y. Wang and L. W. Chen, “Tunable negative refraction photonic crystals achieved by liquid crystals”, Optics Express, Vol. 14, No. 22, pp. 10580-10587 (2006).
[113] R. Kornbluh, R. Pelrine, Q. Pei, R. Heydt, S. Stanford, S. Oh, and J. Eckerle, “Electroelastomers: applications of dielectric elastomer transducers for actuation, generation and smart structures,” Proceedings of SPIE Vol. 4698 pp.254-270 (2002).
[114] R. E. Pelrine, R. D. Kornbluh and J. P. Joseph, “Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation,” Sensors and Actuators A, Vol.64, p.77 (1998).
[115] R. Pelrine, R. Kornbluh and G. Kofod, “High-strain actuator materials based on dielectric elastomers,” Advanced Materials, Vol.12, p.1223 (2000).
[116] R. Pelrine, R. Kornbluh, J. Joseph, R. Heydt, Q. Pei and S. Chiba, “High-field deformation of elastomeric dielectrics for actuators,” Materials Science and Engineering C, Vol.11, p.89 (2000).
[117] R. Pelrine, R. Kornbluh, Q. Pei and J. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science, Vol.287, p.836 (2000)
[118] Q. Pei, R. Pelrine, S. Stanford, R. Kornbluh and M. Rosenthal, “Electro-elastomer rolls and their application for biomimetic walking robots,” Synthetic Metals Vol.135-136, p.129 (2003).
[119] F. Carpi, P. Chiarelli, A. Mazzoldi and D. De Rossi, “Electromechanical character -risation of dielectric elastomer planar actuators: comparative evaluation of different electrode materials and different counterloads,” Sensors and Actuators A, Vol.107, p.85 (2003).
[120] F. Carpi and D. De Rossi, “Dielectric elastomer cylindrical actuators: electro -mechanical modeling and experimental evaluation,” Materials Science and Engineering C, Vol.24, p.555 (2004).
[121] F. Carpi and D. De Rossi, “Improvement of electromechanical actuating performances of a silicone dielectric elastomer by dispersion of titanium dioxide powder,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol.12, pp.835-843 (2005).
[122] G. Kofod, M. Paajanen and S. Bauer, “Self-organized minimum-energy structures for dielectric elastomer actuators,” Applied Physics A: Materials Science & Processing, Vol.85, pp.141-143 (2006).
[123] J. S. Plante and S. Dubowsky, “On the properties of dielectric elastomer actuators and their design implications,” Smart Materials and Structures, Vol.16, pp. S227-S236. (2007).
[124] M. Wissler, and E. Mazza, “Mechanical behavior of an acrylic elastomer used in dielectric elastomer actuators,” Sensors and Actuators A: Physical, Vol. 134, pp. 494-504 (2007).
[125] L. W. Liu, J. M. Fan, Z. Zhang, L. Shi, Y. J. Liu, and J. S. Leng, “Analysis of the novel strain responsive actuators of silicon dielectric elastomer,” Advanced Materials Research, Vol. 47-50, pp.298-301 (2008).
[126] Y. Liu, L. Liu, Z. Zhang, and J. Leng, “Dielectric elastomer film actuators: characterization, experiment and analysis,” Smart Materials and Structures, Vol.18, pp. 095024-095032. (2009).
[127] Y. Liu, L. Liu, Z. Zhang, Y. Jiao, S. Sun, and J. Leng, “Analysis and manufacture of an energy harvester based on a Mooney-Rivlin–type dielectric elastomer,” Europhysics Letters, Vol.90, pp. 36004-364009. (2010).
[128] S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw-Hill, New York (1986).
[129] R. Pelrine, P. Sommer-Larsen, R. Kornb1uh, R. Heydt, G. Kofod, Q. Pei and P. Gravesen, “Applications of dielectric elastomer actuators,” Proceedings of SPIE,Vol.4329, p.335 (2001).
[130] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Transactions on Antennas and Propagation, Vol.AP-14, pp.802-807 (1966).
[131] S. Guo, and S. Albin, “Simple plane wave implementation for photonic crystal calculation,” Opt. Express, Vol.11, pp.167-175 (2003).
[132] J. B. Berenger, “A perfectly matched layer for absorption of electromagnetic waves,” Journal of Computational Physics, Vol.114, pp.185-200 (1994).
[133] Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Transactions on Antennas and Propagation, Vol.43, pp.1460-1463 (1995).
[134] S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Transactions on Antennas and Propagation, Vol.44, pp.1630-1639 (1996).
[135] F. Xiang, H. Wang and X. Yao, “Dielectric properties of SrTiO3/POE flexible composites for microwave applications,” Journal of the European Ceramic Society, Vol.27, pp.3093-3097 (2007).
[136] A.Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, Oxford University Press, USA (2006).
[137] S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop tunneling through localized states,” Physical Review Letters, Vol.80, pp.960–963 (1998).
[138] S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature Vol.407, pp.608-610 (2000).
[139] H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Optics Express, Vol.14, pp.3491-3496 (2006).
[140] A. Gomyo, J. Ushida, and M. Shirane, “Highly drop-efficient channel-drop filters with Si-based photonic crystal slabs,” Thin Solid Films Vol.508, pp.422-425 (2006).
[141] H. Ren, W. Hu, Y. Jin, and C. Jiang,” Design of reconfigurable optical add/drop multiplexer based on two-dimensional photonic crystals,” Optical Engineering, Vol.47, pp.123001-123006 (2008).
[142] H. Habibiyan, H.Ghafoori-Fard and A. Rostami, “Tunable all-optical photonic crystal channel drop filter for DWDM systems,” Journal of Optics A: Pure and Applied Optics, Vol.11, pp.065102-065111 (2009).
[143] W. Zhang, J. Liu, and W. Zhao, “Design of a compact photonic-crystal-based polarization channel drop filter,” IEEE Photonics Technology Letters, Vol.21, pp.739-741 (2009).
[144] Y. Kanamori, K. Takahashi, and K. Hane, “An ultrasmall wavelength-selective channel drop switch using a nanomechnical photonic crystal nanocavity,” Applied Physics Letters, Vol.95, pp.171911-171913 (2009)
[145] J. J. V. Olmos, M. Tokushima, and K. Kitayama, “Photonci add-drop filter based on integrated photonic crystal structures,” IEEE Journal of Selected Topics in Quantum Electronics, Vol.16, pp.332-337 (2010).
[146] J. B. Bai, J. Q. Wang, X. Y. Chen, J. Z. Jiang, H. Li, Y. S. Qiu, and Z. X. Qiang, “Characteristics of 45o photonic crystal ring resonators based on square-lattice silicon rods,” Optoelectronics Letters, Vol.6, pp.203-206 (2010).
[147] T. T. Kim, S. G. Lee, S. H. Kim, J. E. Kim, H. Y. Park, and C. S. Kee, “Ring-type Fabry-Pérot filer based on the self-collimation effect in a 2D photonic crystal,” Optics Express, Vol.18, pp.17106-17113 (2010).
[148] S. Kim, I. Park, H. Lim, and C. S. Kee, “Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback,” Optics Express, Vol.12, pp.5518-5525 (2004).
[149] H. Ren, C. Jiang, W. Hu, M. Gao, and J. Wang, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Optics Express 14, 2446-2458 (2006).
[150] Z. Zhang, and M. Qiu, “Coupled mode analysis of in-plane channel drop filters with resonant mirros,” Photonics Nanostructures - Fundamentals and Applications, Vol.3, pp.84-89 (2005).
[151] C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE Journal of Quantum Electronics, Vol.35, pp.1322–1331 (1999).
[152] T. P. White, L. C. Botten, R. C. McPhedran and C. M. de Sterke, Optics Letters Vol.28 pp.2452-2454 (2003).