光子晶體(PCs)在過去十年的光電界及物理界中備受矚目。光子晶體的基本特徵是存在一些光子能隙(PBGs)，頻率介於其中的電磁波無法在光子晶體結構中傳播。近幾年為了開發有利用價值的設備而研究光子晶體能隙是引起大家興趣的技術。
在這篇論文中，我們的目標是設計一維光子晶體多通道濾波器。我們將使用所謂的單負材料(SNG)來設計多通道濾波器。在最初的設計，我們考慮含有負介電常數材料(ENG)的光子晶體異質結構。 第二個設計使用由負介電常數材料(ENG)和負導磁常數材料(MNG)所組成的雙週期結構光子晶體多通道濾波器。我們發現通道的數目和結構中堆疊的層數有密切的相關。我們也研究通道在TE和TM不同模態下改變入射角度的特性。
本篇論文第一章介紹光子晶體的基本性質。第二章詳細敘述本篇論文分析時所使用的轉移矩陣法。主要的議題分別在第三章和第四章。第五章作總結論。

[1] John, S., “Strong localization of photons in certain disordered lattices,” Phys. Rev. Lett., Vol. 58, 2486–2489, 1987.

[2] Yablonovitch, E., “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett., Vol. 58, 2059–2062, 1987.

[3] Bowden, C. M., J. P. Dowling, and H. O. Everitt, “Development and applications of materials exhibiting photonic band gaps: Introduction,” J. Opt. Soc. Am. B, Vol. 10, 280–413, 1993.

[4] Knight, J. C., J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science, Vol. 282, 1476–1478, 1998.

[5] Kuo, C.-W., S.-Y. Chen, Y.-D. Wu, and M.-H. Chen, “Analyzing the multilayer optical planar waveguides with double-negative metamaterial,” Progress In Electromagnetics Research, Vol. 110, 163–178, 2010.

[6] Sabah, C. and S. Uckun, “Multilayer system of Lorentz/drude type metamaterials with dielectric slabs and its application to electromagnetic filters,” Progress In Electromagnetics Research, Vol. 91, 349–364, 2009.

[7] Mirza, I. O., J. N. Sabas, S. Shi, and D. W. Prather, “Experimental demonstration of metamaterial based phase modulation,” Progress In Electromagnetics Research, Vol. 93, 1– 12, 2009.

[8] Lin, W.-H., C.-J. Wu, and S.-J. Chang, “Angular dependence of wave reflection in a lossy single-negative bilayer,” Progress In Electromagnetics Research, Vol. 107, 253–267, 2010.

[9] Rahimi, H., A. Namdar, S. R. Entezar, and H. Tajalli, “Photonic transmission spectra in one-dimensional Fibonacci multilayer structures containing single-negative metamaterials,” Progress In Electromagnetics Research, Vol. 102, 15–30, 2010.

[10] Yeh, D.-W. and C.-J. Wu, “Analysis of photonic band structure in a one-dimensional photonic crystal containing single-negative material,” Optics Express, Vol. 17, 16666–16680, 2009.

[11] Smolyakov, A. I., E. A. Fourkal, S. I. Krasheninnikov, and N. Sternberg, “Resonant modes and resonant transmission in multi-layer structures,” Progress In Electromagnetics Research, Vol. 107, 293–314, 2010.

[12] Bucinskas, J., L. Nickelson, and V. Shugurovas, “Microwave scattering and absorption by a multilayered lossy metamaterialglass cylinder,” Progress In Electromagnetics Research, Vol. 105, 103–118, 2010.

[13] Orfanidis, S. J., Electromagnetic Waves and Antennas, Ch. 7, Rutger University, 2008, www.ece.rutgers.edu/ orfanidi/ewa.

[14] Smith, D. R., R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, and P. M. Platzman, “Photonic band structure without and with defect in one-dimensional photonic crystal,” J. Opt. Soc. Am. B: Optical Physics, Vol. 10, 314–321, 1993.

[15] Wu, C.-J. and Z.-H. Wang, “Properties of defect modes in one-dimensional photonic crystals,” Progress In Electromagnetics Research, Vol. 103, 169–184, 2010.

[16] Qiao, F., C. Zhang, and J. Wan, “Photonic quantum-well structure: Multiple channeled filtering phenomena,” Appl. Phys. Lett., Vol. 77, 3698–3700, 2000.

[17] Jiang, H.-T., H. Chen, N.-H. Liu, and S.-Y. Zhu, “Engineering photonic crystal impurity bands for multiple channeled optical switches,” Chin. Phys. Lett., Vol. 21, 101–103, 2004.

[18] Zhang, Y. and B.-Y. Gu, “Aperiodic photonic quantum-well structures for multichanneled filtering at arbitrary preassigned frequencies,” Optics Express, Vol. 12, 5910–5915, 2004.

[19] Liu, J., J. Sun, C. Huang, W. Hu, and M. Chen, “Improvement of spectral efficiency based on spectral splitting in photonic quantum-well structures,” IET Optoelectron., Vol. 2, 122–127, 2008.

[20] Liu, J., J. Sun, C. Huang, W. Hu, and D. Huang, “Optimizing the spectral efficiency of photonic quantum well structures,” Optik, Vol. 120, 35–39, 2009.

[21] Caloz, C, and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, John Wiley & Sons, NJ, 2006.

[22] Rotman, W, “Plasma simulation by artificial dielectric and parallel-plate media,” IEEE Trans. Antenna Propag., Vol. 10, 82– 95, 1962.

[23] Pendry, J. B., J. A. Holden, J. D. Robbins, and J. W. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condensed Matter, Vol. 10, 4785–4809, 1998.

[24] Tretyakov, S., Analytical Modeling in Applied Electromagnetics, Artech House, Norwood, MA, 2003.

[25] Pendry, J. B., J. A. Holden, J. D. Robbins, and J. W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech., Vol. 47, 2075–2084, 1999.

[26] Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “A composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett., Vol. 84, 4184– 4187, 2000.

[27] Shelby, R. A., D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett., Vol. 78, 489–491, 2001.

[28] Yeh, P., Optical Waves in Layered Media, John Wiley & Sons, Singapore, 1991.

[29] Hu, X., Z. Liu, and Q. Gong, “A multichannel filter in a photonic crystal heterostructure containing single-negative materials,” J. Optics A, Vol. 9, 877–883, 2007.

[30] Sukhoivanov, I. A. and I. V. Guryev, Photonic Crystals, Springer- Verlag, Berlin, Heidelberg, 2009.

[31] N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575, 1998.

[32] Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,”Science 282, 1679–1682, 1998.

[33] N. Krumbholz, K. Gerlach, F. Rutz, M. Koch, R. Piesiewicz, T. Kürner, and D. Mittleman, “Omnidirectional terahertz mirrors: A key element for future terahertz communication systems,”Appl. Phys. Lett. 88, 202905, 2006.

[34] V. Kochergin, Omnidirectional Optical Filters (Kluwer, 2003).

[35] Y. H. Lu, M. D. Huang, S. Y. Park, P. J. Kim, T. U. Nahm, Y. P. Lee, and J. Y. Rhee, “Controllable switching behavior of defect modes in one-dimensional heterostructure photonic crystals,” J. Appl. Phys. 101, 036110, 2007.

[36] H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111, 2005.

[37] N. E. J. Hunt, E. F. Schubert, and G. J. Zydzik, “Resonant-cavity p-i-n photodetector utilizing an electron-beam evaporated Si-SiO2 microcavity,” Appl. Phys. Lett. 63, 391–393, 1993.

[38] Y. Chen, “Tunable omnidirectional multichannel filters based on dual-defective photonic crystals containing negative-index materials,” J. Phys. D 42, 075106, 2009.

[39] X. H. Deng, L. G. Fang, J. T. Liu, L. E. Zou, and N. H. Liu, “Multichannel filtering properties of photonic crystals containing single-negative materials,” Appl. Phys. B 99, 507–511, 2010.

[40] A. Mishra, S. K. Awasthi, S. K. Srivastava, U. Malaviya, and S. P. Ojha, “Tunable and omnidirectional filters based on one-dimensional photonic crystals composed of single-negative materials,” J. Opt. Soc. Am. B 28, 1416-1422, 2011.

[41] X. H. Deng, L. G. Fang, J. T. Liu, L. E. Zou, and N. H. Liu, “Multichannel filtering properties of photonic crystals containing single-negative materials,” Appl. Phys. B 99, 507–511, 2010.

[42] Y. Xiang, X. Dai, S. Wen, Z. Tang, and D. Fan, “Zero-effective-phase bandgaps in photonic multilayers: analytic expressions for band-edge frequencies and broadband omnidirectional reflection,” J. Opt. Soc. Am. B 28, 1187-1193, 2011.

[43] P. Li, and Y. Liu, “Multichannel filtering properties of photonic crystals consisting of single-negative materials,” Physics Letters A 373, 1870–1873, 2009.

[44] V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514, 1968.

[45] V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48, 2007.

[46] J. S. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901, 2003.

[47] H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388, 2003.

[48] Y. J. Xiang, X. Y. Dai, S. C. Wen, and D. Y. Fan, “Enlargement of zero averaged refractive index gaps in the photonic heterostructures containing negative-index materials,” Phys. Rev. E 76, 056604, 2007.

[49] Y. J. Xiang, X. Y. Dai, S. C. Wen, and D. Y. Fan, “Independently tunable omnidirectional multichannel filters based on the fractal multilayers containing negative-index materials,” Opt. Lett. 33, 1255–1257, 2008.

[50] H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607, 2004.

[51] L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102, 2004.