光子在其波長尺度下的週期排列晶體中，存在著光子晶體能隙，此種結構被稱之為光子晶體。由於光子晶體能隙俱有隔絕光波傳遞的效果，可以用來調變光波的傳播進而設計各式光學元件。本文提出並分析二維磁性光子晶體感測器，其結構是由空氣洞共振腔組成，在共振腔中填充俱有雙軸螺旋特性的磁性材料，並藉著外加磁場去作調變。分別將磁場施加於x方向及y方向討論其品質因子與靈敏度的變化。當外加磁場施於y方向時，發現會有退化模態分離的效果，因為電磁波入射此結構時，因左旋偏振波與右旋偏振波之速度不同的關係，造成折射率差異而分裂成兩個共振模態，比較一般光子晶體及外加磁場於x方向之光子晶體後，發現外加磁場於y方向時共振腔之品質因子較為理想。如果將其他空氣洞填充折射率不同的待測物作感測時，也可發現外加磁場施加於y方向時的靈敏度較高。此外，再進一步探討外加磁場強度的影響以及感測範圍的限制。經過設計後可以利用本文所提出之方法，使得感測器的品質因子、靈敏度與解析度比起文獻所提供之來的更好。最後以實際常見氣體來作感測，並凸顯其高解析度的特性。

Photonic crystals which possess the photonic bandgap due to their periodic structures have attracted intensive interests in science and technologies. Similar to electrons in solids, photons with some specific energy are forbidden within the photonic bandgap. In this study, we explore an ultrasensitive refractive index sensor using a magnetic photonic crystal (MPC) composed of a triangular lattice array of air holes with a Si background. Consider a microcavity created by altering the radius of an air hole in the middle of the photonic crystal. The defect filled with gyrotropic materials can serve as a refractive index sensor. By applying the external magnetic field in the y direction to the gyrotropic magnetic medium, we observe different refractive indices of the right-hand circular polarization mode and left-hand circular polarization mode. When the external magnetic field is applied in the y direction, the sensor has a better quality factor and the sensitivity. Furthermore we optimize the sensor by modulating the gyrotropic factor, which varies with the magnetic field applied in the y direction. Numerical results reveals that the proposed sensor has obtained the better quality factor, sensitivity and resolution of the sensor than preview ones. Finally, we show the characteristics of high resolution in the gyrotropic sensor by measuring the common gases.

[1] E. Yablonovitch “Inhibited spontaneous emission in solid-state physics and electronics,” Physical Review Letters, Vol.58, 2059-2062 (1987).
[2] S. John “Strong Localization of photons in certain disordered dielectric superlattices,” Physical Review Letters, Vol.58, 2486-2489 (1987).
[3] E. Yablonovitch and T. J. Gmitter “Photonic band structure: The face-centered-cubic case,” Physical Review Letters, Vol.63, 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, 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, 1476-1478 (1998).
[7] K. M. Ho, C. T. Chan and C. M. Soukoulis “Existence of a photonicgap in periodic dielectric structures,” Physical Review Letters Vol.65, 3152-3155 (1990).
[8] E. Yablonovitch, T. J. Gmitter and K. M. Leung “Photonic bandstructure: The face-centered-cubic case employing nonspherical atoms,” Physical Review Letters Vol.67, 2295-2298 (1991).
[9] M. Plihal, A. Shambrook, A. A. Maradudin and P. Sheng “Two-dimesional photonic band structures,” Optics Communications Vol.80, 199-204 (1991).
[10] M. Plihal and A. A. Maradudin “Photonic band structure of two-dimensional systems: The triangular lattice,” Physical Review B Vol.44, 8565–8571 (1991).
[11] 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,” Comput. Physical Communications Vol.85, 306-322 (1995).
[12] C. T. Chan, Q. L. Yu and K. M. Ho “Order-N spectral method for electromagnetic waves,” Physical Review B Vol.51, 16635–16642 (1995).
[13] X. Wang, X. G. Zhang, Q. Yu and B. N. Harmon “Multiple-scattering theory for electromagnetic waves,” Physical Review B Vol.47, 4161–4167 (1993).
[14] P. R . Villeneuve, S. Fan and J. D. Joannopoulos “Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency” Physical Review B Vol. 54, No. 11 7837-7842 (1996)
[15] M. Qiu ” Numerical method for computing defect modes in two dimensional photonic crystals with dielectric or metallic inclusions” Physical Review B Vol. 61, No. 19 (2000)
[16] J. Vučković, M. Lončar, H. Mabuchi and A. Scherer “Design of photonic crystal microcavities for cavity QED” Physical Review E, Vol.65,016608 (2001)
[17] H. G. Park J. K. Hwang, J. Huh, H. Y. Ryu and Y. H. Lee “Nondegenerate monopole-mode two-dimensional photonic band gap laser” Applied Physical Letters Vol. 79, No. 19, 3032-3034 (2001)
[18] T. Yoshie, J. Vučković, and A. Scherer “High quality two-dimensional photonic crystal slab cavities” Applied Physical Letters Vol. 79, No. 26, 4289-4291 (2001)
[19] Z. Zhang and M. Qiu “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs” Optics Express Vol. 12, No.17, 3988-3995 (2004)
[20] H. Altug and J. Vučković ”Photonic crystal nanocavity array laser” Optics Express Vol. 13, No. 22, 8819-8827 (2005)
[21] Z. Xu, L. Cao, C. Gu, Q. He, and G. Jin “Micro displacement sensor based on line-defect resonant cavity in photonic crystal” Optics Express Vol. 14, No. 1, 298-305 (2006)
[22] A. Sharkawy, S. Shi and D.W. Prather ”Electro-optical switching using coupled photonic crystal waveguides ” Optics Express Vol. 10, No.20 1048-1059 (2002)
[23] A. Shinya, S. Mitsugi, E. Kuramochi and M. Notomi ”Ultrasmall multi-channel resonant-tunneling filter using mode gap of width-tuned photonic crystal waveguide” Optics Express Vol. 13, No. 11 4202-4209 (2005)
[24] S. Fan, P. R. Villeneuve and J. D. Joannopoulos ”Channel Drop Tunneling through Localized States” Physical Review Letters 960-963 (1998)
[25] S. Fan, P. R. Villeneuve and J. D. Joannopoulos ”Channel drop filters in photonic crystals” Optics Express Vol. 3, No. 1 ,4-11 (1998)
[26] M. Qiu and B. Jaskorzynska “Design of a channel drop filter in a two-dimensional triangular photonic crystal” Applied Physical Letters Vol. 83, No. 6, 1074-1076(2003)
[27] Z. Zhang and M. Qiu ”Compact in-plane channel drop filter design using a single cavity with two degenerate modes in 2D photonic crystal slabs” Optics Express Vol. 13, No. 7, 2590-2604 (2005)
[28] A. Sharkawy, S.Shi, and D. W. Prather “Multichannel wavelength division multiplexing with photonic crystals” Applied Optics Vol. 40, No. 14 2247-2252 (2001)
[29] D. M. Pustai, A. Sharkawy, S. Shi, and D. W. Prather “Tunable photonic crystal microcavities” Applied Optics Vol. 41, No. 26 5574-5578(2002)
[30] 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, 1509-1511 (2003)
[31] N. Malkova and V. Gopalan, “Strain-tunable optical valves at T-junction waveguides in photonic crystals,” Physical Review B, Vol.68, 245115 (2003)
[32] Z. Hou, F. Wu and Y. Liu “Photonic crystals containing piezoelectric material,” Solid State Communications, Vol.130, 745-749 (2004)
[33] 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, 177-182 (2003)
[34] 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, 245109 (2003)
[35] H. Takeda and K. Yoshino, “Properties of Abrikosov lattices as photonic crystals,” Physical Review B, Vol.70, 085109 (2004)
[36] H-B. Lin, R. J. Tonucci and A. J. Campillo “Two-dimensional photonic bandgap optical limiter in the visible,” Optics Letters, Vol.23, 94-96 (1998)
[37] N. C. Panoiu, M. Bahl and R. M. Osgood “s,” Optics Express, Vol.12, 1605-1610 (2004)
[38] A. Figotin, Y. A. Godin and I. Vitebsky “Two-dimensional tunable photonic crystals,” Physical Review B, Vol.57, 2841-2848 (1998)
[39] 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, 661-663 (2001)
[40] 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, 073106 (2003)
[41] H. Takeda and K. Yoshino “Tunable refraction effects in two-dimensional photonic crystals utilizing liquid crystals,” Physical Review E, Vol.67, 056607 (2003)
[42] 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, 056612 (2003)
[43] 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, 046602 (2003)
[44] H. Takeda and K. Yoshino “TE-TM mode coupling in two-dimensional photonic crystals composed of liquid crystal rods,” Physical Review E, Vol.70, 026601 (2004)
[45] 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, 2616-2624 (2004)
[46] B. Liedberg, I. Lundstriim and E. Stenberg “Principles of biosensing with an extended coupling matrix and surface plasmon resonance,” Sensor. Actuator. B 11, 63–72 (1993)
[47] J. J. Saarinen, S. M. Weiss, P. M. Fauchet and J. E. Sipe “Optical sensor based on resonant porous silicon structures,” Opt Express. Vol.13, 3754–3764 (2005)
[48] Chung-Yen Chao, Wayne Fung and L. Jay Guo “Polymer Microring Resonators for Biochemical Sensing Applications,” IEEE J Sel Topics Quantum Electron. Vol.12, 134–142 (2006)
[49] K. D. Vos, I. Bartolozzi, E. Schacht, P. Bienstman and R. Baets “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt Express Vol.15, 7610-7615 (2007)
[50] A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan and K. J. Vahala “Label-Free, Single-Molecule Detection with Optical Microcavities,” Science. 317, 783–787 (2007)
[51] S. A. Taya and M. M. Shabat “Sensitivity enhancement in optical waveguide sensors using metamaterials,” Appl. Phys. A. Vol.103, 611–614 (2011)
[52] E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas and G. Girolami “Ultracompact biochemical sensor built with two-dimensional photonic crystal microcavity,” Opt. Lett. 29, 1093–1095 (2004)
[53] Chakravarty S, Topol’ancik J, Bhattacharya P, Kang Y “Ion detection with photonic crystal microcavities,” Opt Lett. 30, 2578-2580 (2005)
[54] M. R. Lee and P. M. Fauchet “Nanoscale microcavity sensor for single particle detection,” Opt. Lett. 32, 3284–3286 (2007)
[55] M. R. Lee and P. M. Fauchet “Two-dimensional silicon photonic crystal based biosensing platform for protein detection,” Opt. Lett. 15, 4530-4535 (2007)
[56] Junhua Li, Kan Qiang, Wang Chunxia, Su Baoqing, Xie Yiyang and Chen Hongda “Design of a photonic crystal microcavity for biosensing,” J. Semicond. Vol.32 (2011)
[57] J. Derbali, F. AbdelMalek, S. S. A. Obayya, H. Bouchriha and R. Letizia “Design of a compact photonic crystal sensor,” Opt Quant Electron. Vol. 42, 463-472 (2011)
[58] 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, 802-807 (1966).
[59] S. Guo and S. Albin “Simple plane wave implementation for photonic crystal calculation,” Opt. Express, Vol.11, 167-175 (2003)
[60] J. B. Berenger “A perfectly matched layer for absorption of electromagnetic waves,” Journal of Computational Physics, Vol.114, 185-200 (1994)
[61] 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, 1460-1463 (1995)
[62] S. D. Gedney “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Transactions on Antennas and Propagation, Vol.44, 1630-1639 (1996)
[63] A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method. ( Norwood, MA: Artech House, 1995)
[64] A.G.Gurevich and G.A. Melkov, Magnetization Oscillations and Waves, CRC Press, Boca Raton (1996)
[65] A.K.Zvezdin and V.A.Kotov, Modern MagnetoOptics and MagnetoOptical Materials, IOP,Bristol(1997)
[66] H. Kato, T. Matsushita, A. Takayama, and M. Egawa “Theoretical analysis of optical and magneto-optical properties of one-dimensional magnetophotonic crystals,” J. Appl. Phys. 93, 3906–3912 (2003)
[67] S. N. Kurilkina and M. V. Shuba “Propagation and transformation of the light waves in magnetoactive periodic structures,” Opt. Spectrosc. 93, 918–923 (2002)
[68] A. Figotin and I. Vitebskiy “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67, 165210 (2003)
[69] P. A. Belov, S. A. Tretyakov and A. J. Viitanen “Nonreciprocal microwave band-gap structures,” Phys. Rev. E 66, 016608 (2002)
[70] I. H. H. Zabel and D. Stroud “Photonic band structures of optically anisotropic periodic arrays,” Phys. Rev. B 48, 5004–5012 (1993)
[71] A. Soltani Vala, B. Rezaei and M. Kalafi “Tunable defect modes in 2D photonic crystals by means of external magnetic fields,” Physica B 405, 2996–2998 (2010).
[72] D. Jalas, A. Petrov, M. Krause, J. Hampe and M. Eich “Resonance splitting in gyrotropic ring resonators,” Opt. Lett. 35, 3438-3440 (2010)
[73] M. M. Sigalas, C. M. Soukoulis, R. Biswas and K. M. Ho “Effect of the magnetic permeability on photonic band gaps,” Phys. Rev. B, Vol. 56, 959-962 (1997)
[74] Smolenskii G A and Lemanov V V, Ferrites and their Technical Applications (Leningrad: Nauka)(1975)
[75] Hong Wanga, YSheng Luo, Yong-Tao Wang, Hong-Bing Zhang and Yun-Tuan Fang “Splitting of defect-mode in one-dimensional magnetic photonic crystal,” Physica B 406, 2977-2981 (2011)
[76] O. Painter, J. Vucˇkovic´, and A. Scherer“Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab”, J. Opt. Soc. Am. B, Vol. 16, 275 (1999)
[77] Xiaoling Wanga, Zhenfeng Xuc, Naiguang Lub, Jun Zhuc and Guofan Jinc “Ultracompact refractive index sensor based on microcavity in the sandwiched photonic crystal waveguide structure” Optics Communications. Vol.281, 1725-1731(2008)
[78] E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas and G. Girolami “Ultracompact biochemical sensor built with two-dimensional photonic crystal microcavity” Optics Letters, Vol.29, 1093-1095 (2004)