本論文應用平行化的三維有限時域差分法(FDTD)去模擬電磁波之增強穿透效應行為於一具有次波長狹縫之無窮大完美導體(PEC)平面。對於一個遠小於波長之狹縫，高解析度成為模擬的需求，因此計算量很可觀。
為了達到降低計算資源的需求，我們應用光學轉換這項技術。我們設計了一個物理系統使狹縫附近區域具有需要之高解析度，而在其餘區域給予較低解析度來進行模擬，因此可大量減少整體計算資源的需求。透過轉換光學，我們將物理系統之不均勻格點轉換成數值模擬系統之均勻格點，而同時材料特性卻從均勻轉換成不均勻。
首先，我們推導維持數值穩定性的Courant condition。此數值模擬系統乃透過有限時域差分法(FDTD)的軟體(MEEP)來進行模擬。我們得到的數值模擬結果，轉換為物理系統後，發現與需要大量計算資源之均勻格點物理系統的結果與分析結果都相符。

We employ the parallel 3D finite-difference time domain (FDTD) method to simulate the enhanced transmission of electromagnetic wave through a rectangle subwavelength slit in an infinite film of perfect electric conductor (PEC). Since the slit is much smaller than the wavelength, high resolution is required for the simulation so that the computation can be extremely large.
To reduce the computation requirement, we applies the technique of transformation optics. We design a physical system that has a higher resolution around the slit area as required while the resolution is lower at other areas so that the overall cell numbers are greatly reduced. With transformation optics, the non-uniform physical cell system is transformed into a uniform numerical cell system while the uniform material properties become non-uniform.
The Courant condition for numerical stability is derived. This numerical cell system is then simulated by a FDTD code, MEEP. The numerical result yielded is then transformed back to physical system and is found to be consistent with a large computation with uniform physical cells and with the analytical result.

[1] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat ., vol. AP-14, pp. 302-307( 1966).
[2] 葛德彪, 闫玉波, 电磁波时域有限差分方法(第二版)，西安电
子科技大学出版社2005。
[3] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House (2005).
[4] H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163-182 (1944).
[5] T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “ Extraordinary optical transmission through sub-wavelength hole arrays,” Nature, 391, 667 (1998).
[6] A.Degiron, H. J. Lezec,N. Yamamoto,and T. W.Ebbesen, Opt. Commun. 239, 61 (2004).
[7] F. J. Garc ́ıa-Vidal , “Transmission of Light through a Single Rectangular Hole,” Phys. Rev. 95, 103901 (2005).
[8] A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Modern Optics, vol. 43, no. 4, pp. 773–793 (1996).
[9] J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science, vol. 312, pp. 1780–1782 (2006).
[10] F. L. Teixeira and W. C. Chew, “Gen- eral closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave and Guided Wave Lett., vol. 8, no. 6, pp. 223–225 (1998).
[11] S. G. Johnson, M. Ibanescu, M. Skorobo- gatiy, O. Weisberg, T. D. Engeness, M. Sol- jacić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single- mode propagation in large-core OmniGu- ide fibers,” Optics Express, vol. 9, no. 13, pp. 748–779 (2001).
[12] C. Kottke, A. Farjadpour, and S. G. Johnson, “Perturbation theory for anisotropic dielec- tric interfaces, and application to sub-pixel smoothing of discretized numerical meth- ods,” Phys. Rev. E, vol. 77, p. 036611 (2008).
[13] Berenger, J. P., “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computational physics 114, 185-200 (1994).