本篇論文提出一個準確且簡便的方法使用BeamProp模擬梯形脊狀光波導，我們成功使用舒瓦茲-克里斯多福轉換(Schwarz-Christoffel Transformation)將梯形波導結構等效成一般矩形截面脊狀光波導，並且將等效之場形轉回梯形坐標系。由此可見，不論截面形狀如何，我們都可利用Schwarz-Christoffel Transformation來做BeamProp模擬，故未來在研究乾蝕刻之側壁光學損耗上，亦可應用此方法模擬。

[1]Richard A. Soref, Joacim Schmidtchen, and Klaus Petermann, " Large single-mode rib waveguides in GeSi-Si and Si-on-SO2,” IEEE Journal of Quantum Electronics, Vol. 27, p. 1971, 1911
[2]Olly Powell, ”Single-mode condition for silicon rib waveguides”, Journal of Lightwave Technology, Vol. 20, p. 1851, 2002
[3]Souren P. Pogossian, Lili Vescan, and Adrian Vonsovici, ”The single-mode condition for semiconductor rib waveguides with large cross section”, Journal of Lightwave Technology, Vol. 16, p. 1851, 1998
[4]K. D. Been, “Anisotropic etching of silicon, ”IEEE Trans. Electron Devices, Vol.ED-25, p. 1185, 1978
[5]Hong Xiao, Introduction to Semiconductor Manufacturing Technology, upper Saddle River, New jersey, the pearson prentice Hall, pp. 250-251, 2001
[6]Wikipedia , “http://en.wikipedia.org/wiki/Etching_(microfabrication)”
[7]Kittel Charles, Introduction to Solid State Physics, 1st ed. 1953 - 8th ed., 2005
[8]Henghua Deng, Member, David O. Yevick, Chris Brooks, and Paul E. Jessop, “Design rules for slanted-angle polarization rotators”, Journal of Lightwave Technology, Vol. 23 , 2005
[9]Dr. Stephen Greedy, Advances in the Spectral Index Method for Optoelectronic design”, 2002(Ph.D. dissertation).
[10] M. Aoki, M. Komori, T. Tsuchiya, H. Sato, K. Nakahara, and K. Uomi, “InPbased
reversed-mesa ridge-waveguide structure for high-performance long wavelength laser diodes”, IEEE Journal of Selected Topics in Quantum Electronics, Vol. 3(2), pp. 672-683, 1997
[11]P. M. Pelosi, P. Vandenbulcke, C. D. W. Wilkinson, and R. M. De La Rue,
“Propagation characteristics of trapezoidal cross-section ridge optical
waveguides: an experimental and theoretical investigation”, Applied Optics,
Vol. 17, pp. 1187-1193, 1978.
[12]J. G. Gallagher, “Mode dispersion of trapezoidal cross-section rib
waveguides by the effective-index method”, Electronics Letters, Vol. 15(23),
pp. 734-736, 1979.
[13]T.M. Benson et al, “New results for rib waveguide propagation constants”, IEE Proceedings, Vol. 136, Pt. J , No. 2, p. 97, 1989
[14]黃維傳, 在矽基板上使用金氧半導體電光效應之環形共振腔特性模擬與分析, 清華大學, 碩士論文(2006)
[15]Clifford R. Pollock, Michal. Lipson, Integrated Photonics, Springer, 2003
[16]Okamoto K., Fundamentals of Optical Waveguides, San Diego, CA: Academic, 2000
[17]Devang Parekh, BPM course slides, University of Berkeley, CA, “http://www-inst.eecs.berkeley.edu/~ee290f/sp04/”
[18]Chun-Te Wu, Yi-Hsin Pang, and Ruey-Beei Wu, “An improved formalism for FDTD analysis of thin-slot problems by conformal mapping technique, “IEEE Transactions and Antennas and Propagation, Vol. 51, p.2530, 2003
[19]Driscoll, Tobin A.; Trefethen, Lloyd N., Schwarz-Christoffel mapping, Cambridge Monographs on Applied and Computational Mathematics 8, Cambridge University Press, 2002
[20]Linlong Tang et al, “General conformal transformation method based on Schwarz-Christoffel approach”, Optics Express, Vol. 19, p. 15119, 2011
[21]Wolfram Mathword, “http://mathworld.wolfram.com/ConformalMapping.html”
[22]Matlab, “http://www.mathworks.com/products/demos/image/conformal_mapping/tform4.html”
[23] Wolfram Blog, ” http://blog.wolfram.com/2009/04/24/droste-effect-with-mathematica/”
[24]Hong Zhao, Yue-e Li, Guan-mao Zhang, “On the characteristics of commonly nonideal rectangular ridge dielectric-loaded surface plasmon polariton waveguides in practical fabrication processing”, Optics Communications, Vol. 285, pp. 1091-1096, 2012