波導光柵在特定條件下，會產生波導模態共振，這種現象造成繞射效率會急遽的變化。利用這種特性可以設計出許多光學元件，諸如偏振器、濾波器等。傳統的方法是利用對稱型波導光柵及薄層的多層相互堆疊，達到單層對稱結構無法做到的共振效應。本論文提出新的設計結構─單層多折射率非對稱型波導光柵，這種結構是在一個周期中，置入超過兩種折射率且填充因子也跟著變化，利用這種結構，可以設計出達到多層波導光柵同樣的效應，且能大幅減低堆疊的層數，提供更簡便的設計和製程方法。

Guided-mode resonance (GMR) effect occurring in waveguide grating causes the dramatic change of diffraction efficiency under particular conditions. It finds applications to the optical devices, such as filters and polarizers. Typically, GMR phenomenon cannot be realized by using single-layer grating, but can be realized in the structure consisting of a symmetrical waveguide gratings and thin-film layers. In this paper, we design a new type of optical filters. The structure uses only single asymmetric waveguide grating, without thin-film layers. The asymmetric waveguide is formed by periodically arranging more than two kinds of dielectric materials. This new type of filters can achieve the same effects as in the traditionally designed multilayer structures. In addition, they have the advantages of more compact sizes and are easier to be fabricated.

[1] A. Hessel and A.A. Oliner, “Anew theory of Wood’s anomalies on optical gratings,” AQppl. Opt., vol. 10, pp.1275-1297, October 1965.
[2] R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396 (1902).
[3] S.S. Wang, R. Magnusson, J.S. Bagby, and M.G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” J. Opt. Soc. Am. A, vol. 8, pp. 1470-1475, August 1990.
[4] Z.S. Liu, S. Tibuleac, D. Shin, P.P. Young, and R. Magnusson, “High-efficiency guided-mode resonance laser mirror,” Proceeding of the Topical Meeting on Diffractive Optics and Micro-Optics, Kailua-Kona, Hawaii, June, 1998 and Optics & Photonics News, vol. 9, p.40, October 1998.
[5] A. Sharon, D. Eosenblatt, A.A. Friesem, H.G. Weber, H. Engel, and R. Steingrueber, “Light modulation with resonant grating-waveguide structures,” Opt. Lett., vol. 21, pp.1564-1566, October 1996.
[6] D.L. Brundrett, E.N. Glytsis, and T.K. Gaylord, “Normal-incidence guided-mode resonant grating filters: design and experimental demonstration,” Opt. Lett., vol. 23, pp.700-702, May1998.
[7] R. Magnusson, D. Shin, and Z.S. Liu, ”Guided-mode resonance Brewster filter,” Opt. Lett., vol. 23, pp.612-614, April 1998.
[8] R. Magnusson and S.S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Opt., vol. 34, pp.8106-8109, December 1995.
[9] S. Tibuleac and R. Magnusson, “Diffractive narrow-band transmission filters based on guided-mode resonance effect in thin-film multilayers,” IEEE Photon. Tech. Lett., vol. 9, pp.464-467, April 1997.
[10] S. Peng and G. M. Morris, “Experimental demonstration of resonant anomalies in diffraction from two-dimensional gratings,” Opt. Lett. 21, 549-551 (1996).
[11] D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structure,” IEEE J. Quant. Electronics 33, 2038-2059 (1997).
[12] Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, "High-efficiency guided-mode resonance filter," Opt. Lett. 23, 1556-1558 (1998).
[13] P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83, 3248-3250, 20 October 2003.
[14] M. T. Gale, K. Knop, and R. H. Morf, "Zero-order diffractive microstructures for security applications," Proc. SPIE on Optical Security and Anticounterfeiting Systems 1210, 83-89 (1990).
[15] D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Normal-incidence guided-mode resonant grating filters : design and experimental demonstration,” Opt. Lett. 23, 700-702 (1998).
[16] C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photonics Tech. Lett. 16, 518-520 (2004).
[17] C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 m) using a subwavelength grating,” IEEE Photonics Tech. Lett. 16, 1676-1678 (2004).
[18] W. Suh and S. Fan, "All-pass transmission or flattop reflection filters using a single photonic crystal slab," Appl. Phys. Lett. 84, 4905-4907 (2004).
[19] Z. S. Liu and R. Magnusson, “Concept of multiorder multimode resonant optical filters,” IEEE Photonics Tech. Lett. 14, 1091-1093 (2002).
[20] Y. Ding and R. Magnusson, “Doubly-resonant single-layer bandpass optical filters,” Opt. Lett. 29, 1135-1137 (2004).
[21] M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
[22] M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar grating diffraction—E-mode polarization and losses,” J. Opt. Soc. Am. 73, 451–455 (1983).
[23] M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
[24] M. G. Moharam, “Coupled-wave analysis of two-dimensional gratings,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 883, 8–11 (1988).
[25] E. N. Glytsis and T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. A. 4, 2061–2080 (1987).
[26] M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupledwave analysis for surface-relief dielectric gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A
12, 1077–1086 (1995).
[27] T. K. Gaylord and M. G. Moharam , “Analysis and Applications of Optical
Diffraction by Gratings,” PROCEEDINGS OF THE IEEE, VOL. n, NO. 5, MAY 1985.
[28] S. Tibuleac, Characteristics of reflection and transmission waveguide-grating filters, MS Theses, The University of Texas at Arlington, August 1996.
[29] S.S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt., vol. 32, pp.2606-2613, May 1993.
[30] S.S. Wang and R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett., vol. 19, pp. 919-921, June 1994
[31]. S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26, 584-586 (2001).
[32]. Y. Ding and R. Magnusson, “Use of nondegenerate resonant leaky modes to fashion diverse optical spectra,” Opt. Express. 12, 1885-1891 (2004).
[33] D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, and J. M. Bendickson, “Effects of modulation strength in guided-mode resonant subwavelength gratings at normal incidence,” J. Opt. Soc. Am. A. 17, 1221-1230 (2000).
[34] Y. Ding and R. Magnusson, ” Resonant leaky-mode spectral-band engineering
and device applications,” OPTICS EXPRESS Vol. 12, No 23, pp.5661-5674, 15 November 2004
[35] M. G. Moharam, Eric B. Grann, and Drew A. Pommet, ”Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A/Vol. 12, No. 5/May 1995 pp.1068-1076
[36] S. Tibuleac, Characteristics of reflection and transmission waveguide-grating filters, MS Thesis, The University of Texas at Arlington, August 1996
[37] S. Tibuleac, S.S. Wang. R. Magnusson, T.A. Maldonado, and A. Oberhofer, “Linewidth broadening mechanisms of waveguide-grating filters,” Optical Society of America Annual Meeting, Portland, Oregon, September 10-15,1995.
[38]R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation loss,” IEEE J. Quantum Electron QE-21, 144-150 (1985).