負折射在最近是相當熱門的一個學術研究方向，其起源是來至於擁有類似負的介電係數和負的導磁係數之左手材料。而在最近這幾年，光子晶體結構因為在其傳導區擁有獨特的色散特性，因此也會發生類似左手性材料的特殊波傳性質，此種新概念不久後就在學術界引起極大的興趣和研究。在左手性材料中，最為人熟知的一項應用為完美透鏡，此種新型透鏡可以克服傳統透鏡的繞射極限問題，最後將光束聚焦於一點。
固態浸沒透鏡於二十世紀末應用於光學顯微鏡和光儲存系統。由於能夠有效縮小成像端聚焦點的大小，因此不僅在光儲存設計中可看見其身影，也被廣泛地應用於超解析度之光學顯微鏡和高敏感度之光譜儀。
在此篇文章裡，我們將固態浸沒透鏡加入光子晶體負折射成像系統中，並且分析透鏡之折射率和幾何參數對於整體解析度之影響。其中所採用的數值方法有平面波展開法，時域有限差分法和有限元素法。相較於單一片之光子晶體薄板，加入固態浸沒透鏡後其解析度最多可提高25%。此種由光子晶體和固態浸沒透鏡組合之光學元件，可以應用於光微影製程技術。

Negative refraction has attracted a lot of attentions recently. Negative refraction studies originated from left-hand materials (LHM), which are materials with simultaneously negative dielectric permittivity and negative magnetic permeability. In recent years, it has been proved that the diffraction effects of photonic crystals (PCs) can account for the effective negative refraction. One of the most fascinating applications of LHM is the so-called perfect lens capable of overcoming the diffraction limit imposed by the wave nature of light on the smallest spot to which light can be focused.
Solid immersion lens (SIL) was introduced in 1990 for optical microscopic and applied in 1994 for optical recording. The reduction in focused spotsize makes SIL techniques potentially very attractive not only for data storage device but also in the area of high light throughput super-resolution optical microscopy and spectroscopy with high sensitivity. In this thesis, we consider the SIL technology in imaging system and analyze the influence of SIL refractive index and geometric parameters on imaging resolution by using the plane wave expansion method, the finite-difference time-domain method, and the finite element method. The resolution of our optical system has been improved 25 %. The optical component, combine PCs with SIL, provides novel application in the optical lithography.

[1] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Physical Review Letters, Vol.58, No.20, pp.2058-2062 (1987)
[2] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Physical Review Letters, Vol.58, No.23, pp.2486-2489 (1987)
[3] J. D. Jannopolous, R. D. Meade and J. N. Winn, “Photonic Crystal,” (Princeton U. Press, Princeton, N.J., 1995)
[4] V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,”Sov. Phys. Usp, Vol.10, No.4, pp.509-514 (1968)
[5] R. A. Shelby, D. R .Smith and S. Schultz, “Experimental verification of a negative index of refraction,” Science, Vol.292, pp.77-79 (2001)
[6] K. H. Ho, C. T. Chan and C. M. Soukoulis, “Existence of photonic gap in periodic dielectrics structures,”Physical Review Letters, Vol.65, No.25, pp.3152-3155 (1990)
[7] 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, No.17, pp.2295-2298 (1991)
[8] M. Phihal, A. Shambrook, A. A. Maradudin and P. Sheng, “Two-dimensional photonic band structures,” Optics Communications, Vol.80 , pp.199-204 (1991)
[9] M. Phihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Physical Review B, Vol.44, No.16, pp.8565-8571 (1987)
[10] T. Hass, A. Hesse and T. Doll, “Omnidirectional two-dimensional photonic crystal band gap structures,” Physical Review B, Vol.73,No.4, pp.045130 (2006)
[11] 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)
[12] C. Y. Liu and L. W. Chen, “Tunable band gap in a photonic crystal modulated by a nematic liquid crystal,” Physical Review B, Vol.72, pp.045133 (2005)
[13] W. Park and J. B. Lee, “Mechanically tunable photonic crystal structure,” Applied Physics Letters, Vol.85, No.21, pp4845-4847 (2004)
[14] D. Scymgeour, N. Malkova, S. Kim and V. Gopalan,“Electro-optic control of the superprism effect in photonic crystal,” Applied Physics Letters, Vol.82, No.19, pp3176-3178 (2003)
[15] S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou and H. A. Haus, “Waveguide branches in photonic crystal,” Journal of the Optical Society of America B, Vol.18, No.2, pp.162-165 (2001)
[16] S. Boscolo, M. Midrio and T. F. Krauss, “Y junctions in photonic crystal channel waveguides: High tramission and impedance matching,” Optics Letters, Vol.27, No.12, pp.1001-1003 (2002)
[17] J. Broeng, D. Mogilevstev, S. E. Barkou and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Optical Fiber Technology, Vol.5, pp.305-330 (1999)
[18] P. Russell, “Photonic crystal fibers,” Science, Vol.299, pp.358-362 (2003)
[19] M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Physical Review B, Vol.62, No.16, pp.10696-10705 (2000)
[20] B. Gralak, S. Enoch and G. Taybe, “Anomalous refractive properties of photonic crystals,” Journal of the Optical Society of America A, Vol.17, No.6, pp.1012-1020 (2000)
[21] R.Gajić, R.Meisels, F.Kuchar and K.Hingerl, “Refraction and rightness in photonic crystals,” Optics Express, Vol.13, No.21, pp. 8596-8605 (2005)
[22] 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)
[23] X. Ao and S. He, “Polarization beam splitters based on a two-dimensional photonic crystal of negative refraction,” Optics Letters, Vol.30, No.16, pp.2152-2154 (2005)
[24] E. Centeno and D. Cassagne, “Graded photonic crystals,” Optics Letters, Vol.30, No.17, pp.2278-2280 (2005)
[25] J. B. Pendry, “Negative refraction makes a perfect lens,” Physical Review Letters, Vol.85, No.18, pp.3966-3969 (2000)
[26] P. V. Parimi, W. T. Lu, P. Vodo and S. Sridhar, “Imaging by flat lens using negative refraction,”Nature, Vol.426, pp.404 (2003)
[27] Z. Lu, S. Shi, C. A. Schuetz and D. W. Prather, “Experimental demonstration of negative refraction imaging in both amplitude and phase,” Optics Express, Vol.13, No.3, pp.2007-2012 (2005)
[28] A. Berrier, M. Mulot, M. Swillo, M. Qu, L.Thylén, A. Talneau and S. Anand, “Negative refraction at infrared wavelength in a two-dimensional photonic crystal,”Physical Review Letters, Vol.93, No.7, pp.073902 (2004)
[29] R. Moussa, S. Foteinopoulu, L. Zhang, G. Tuttle, K. Guven, E. Ozbay and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Physical Review B, Vol.71, No.8, pp.085106 (2005)
[30] P. Vodo, P.V. Parimi, W. T. Lu and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Applied Physics Letters, Vol.86, No.20, pp.201108 (2005)
[31] P. Vodo, W. T. Lu, Y. Huang and S. Sridhar, “Negative refraction and plano-concave lens focusing in one-dimensional photonic crystal” Applied Physics Letters, Vol.89, No.8, pp.084104 (2006)
[32] C. Hafner, C. Xudong and R. Vahldieck, “Resolution of negative-index slabs,” Journal of the Optical Society of America A, Vol.23, No.7, pp.1768-1778 (2006)
[33] G. Sun, A. S. Jugessur and A. G. Kirk, “Imaging properties of dielectric photonic crystal slabs for large object distances,” Optics Express, Vol.14, No.15, pp.6755-6765 (2006)
[34] H. Zhang, L. Shen, L. Ran and Y.Yuan, “Layered superlensing in two-dimensional photonic crystals,” Optics Express, Vol.14, No.23, pp.11178-11183 (2006)
[35] L. Novothy and B. Hecht,“PRINCIPLES OF NANO-OPTICS”Cambridge University Press, New York, pp.144-147 (2006)
[36] K. S. Yee, ”Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Transactions on Antennas and Propagation, Vol.14, pp.302-307 (1996)
[37] A. Taflove and S. S. Hagness, Computational electrodynamics: The finite-difference time-domain method, Artech House, Boston (2000)
[38] J. P.Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” Journal of Computational Physics, Vol.114, pp.185-200 (1994)
[39] 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)
[40] S. D. Gedney, “A anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Transactions on Antennas and Propagation, Vol.44, pp.1630-1639 (1996)
[41] X. Zhang, “Effect of interface and disorder on the far-field image in a two-dimensional photonic-crystal-based flat lens,” Physical Review B, Vol.71, No.16, pp.165116 (2005)
[42] K. Ren, S. Feng, Z. F. Feng, Y. Sheng, Z.Y. Li, B. Y. Cheng and D. Z. Zhang, “ Imaging properties of triangular lattice photonic crystal at the lowest band,” PHYSICS LETTERS A, Vol.348, pp.405-409 (2006)
[43] L. Liu and S. He, “Near-field optical storage system using a solid immersion lens with a left-handed material slab,” Optics Express, Vol.12, No.20, pp.4835-4840 (2004)