吾人提出兩種不同型式的光子晶體多通道波長分波多工器，第一種為結合二維三角晶格和正方晶格光子晶體的波長分波多工器，第二種為僅使用二維正方晶格的波長分波多工器。這兩種多工器在結構上主要是藉由五個不同晶格常數的光子晶體單元彼此相互接合而成。兩多工器均在背景環境為空氣的狀態下，由材質為矽、半徑為120nm的介電圓柱所構成。利用平面波展開法和時域有限差分法針對兩多工器進行數值模擬後，我們發現在所有介電圓柱半徑均維持不變的情況下，當兩多工器之光子晶體單元的晶格常數以4nm的固定間隔遞增時，則從輸出端波導所得到的輸出電磁波波長會以平均約8nm的固定間隔遞增。第一種多工器具有高解析度的特性，第二種多工器則具有各輸出電磁波的傳遞效率相當一致的特性。

Characteristics of two different multichannel wavelength division multiplexing (WDM) systems composed of two-dimensional (2D) hetero photonic crystals (HPCs) are introduced. One utilizes five photonic crystal (PC) units, each fabricated with triangular and rectangular lattice. The other consists of five PC units in rectangular lattice. Both systems have a lattice constant difference of 4 nm between adjacent PC units, and both systems apply silicon rods with a radius of 120 nm. Finite-difference time-domain (FDTD) method and plan wave expansion (PWE) method reveal the ability of wavelength spacing ~8 nm with high quality factor (Q) in a system based on triangular and rectangular lattice; and ~8 nm with almost constant transmission efficiency based on rectangular lattice.

1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
3. R. H. Lipson and C Lu, “Photonic crystals: a unique partnership between light and matter,” Eur. J. Phys. 30, S33-S48 (2009).
4. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
5. E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67. 2295-2298 (1991).
6. M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199-204 (1991).
7. M. Plihal, and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B 44, 8565-8571 (1991).
8. 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,” Phys. Rev. Lett. 77, 3787-3790 (1996).
9. 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 282, 274-276 (1998).
10. J. Yonekura, M. Ikeda, and T. Baba, “Analysis of finite 2-D photonic crystals and lightwave devices using the scattering matrix method,” J. Lightwave Technol. 17, 1500-1508 (1999).
11. M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952 (2000).
12. A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at ,” Appl. Phys. Lett. 80, 547 (2002).
13. A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phy. Rev. B 62, 4488-4492 (2000).
14. A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80, 1698 (2002).
15. T. Søndergaard and K. H. Dridi, “Energy flow in photonic crystal waveguides, “ Phys. Rev. B 61, 15688-15696 (2000).
16. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus “Channel drop filters in photonic crystals,” Opt. Express 3, 4-11 (1998).
17. H. Ren, C. Jiang, W. Hu, M. Gao, and J. Wang, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Opt. Express 14, 2446-2458 (2006).
18. Z. Qiang, W. Zhou, and R. A. Soref, “Optical add-drop filters based on photonic crystal ring resonators,” Opt. Express 15, 1823-1831 (2007).
19. W. Y. Chiu, T. W. Huang, Y. H. Wu, Y. J. Chan, C. H. Hou, H. T. Chien, and C. C. Chen, “A photonic crystal ring resonator formed by SOI nano-rods,” Opt. Express 15, 15500-15506 (2007).
20. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608-610 (2000).
21. M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and Tomoko Tanaka, “Channel drop filter using a single defect in a 2-D photonic crystal slab waveguide,” IEEE J. Lightwave Technol. 20, 873-878 (2002).
22. Y. Akahane, T. Asano, B. S. Song, and Susumu Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944-947 (2003).
23. H. Ren, C. Jiang, W. Hu, M. Gao, Y. Qu, and F. Wang, “Channel drop filter in two-dimensional triangular lattice photonic crystals,” J. Opt. Soc. Am. A 24, 7-11 (2007).
24. P. T. Lee, T. W. Lu, C. M. Yu, and C. C. Tseng, “Photonic crystal circular-shaped microcavity and its uniform cavity-waveguide coupling property due to presence of whispering gallery mode,” Opt. Express 15, 9450-9457 (2007).
25. A. Rostami, A. Haddadpour, F. Nazari, and H. Alipour, “Proposal for an ultracompact tunable wavelength-division-multiplexing optical filter based on quasi-2D photonic crystals,” J. Opt. 12, 015405 (2010).
26. C. Dragone, “Efficient star couplers using Fourier optics,” J. Lightwave Technol. 7, 479-489 (1989).
27. H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on arrayed-waveguide grating,” J. Lightwave Technol. 12, 989-995 (1994).
28. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263-1276 (1997).
29. A. Sharkawy, S. Shi, and D. W. Prather, “Multichannel wavelength division multiplexing with photonic crystals,” Appl. Opt. 40, 2247-2252 (2001).
30. 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,” Opt. Express 12, 5518-5525 (2004).
31. C. W. Kuo, C. F. Chang, M. H. Chen, Shih. Y. Chen, and Y. D. Wu, “A new approach of planar multi-channel wavelength division multiplexing system using asymmetric super-cell photonic crystal structures,” Opt. Express 15, 198-205 (2007).
32. Y. D. Wu, K. W. Hsu, T. T. Shih, and J. J. Lee, “New design of four-channel add-drop filters based on double-resonant cavity photonic crystals,” J. Opt. Soc. Am. B 26, 640-644 (2009).
33. Y. D. Wu, T. T. Shih, and J. J. Lee, “High-quality-factor filter based on a photonic crystal ring resonator for wavelength division multiplexing applications,” Appl. Opt. 48, F24-F30 (2009).
34. B. S. Song, T. Asano, Y. Akahane, Y. Tanaka, and S. Noda, “Multichannel add/drop filter based on in-plane hetero photonic crystals,” IEEE J. Lightwave Technol. 23, 1449-1455 (2005).
35. S. Guo, and S. Albin, “Simple plane wave implementation for photonic crystal calculation,” Opt. Express 11, 167-175 (2003).
36. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s Equations in isotropic media,” IEEE Trans. Antennas Propagat. AP-14, 802-807 (1966).
37. J. B. Berenger, “A perfectly matched layer for absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
38. 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 Trans. Antennas Propagat. 43, 1460-1463 (1995).
39. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propagat. 44, 1630-1639 (1996).