eyliu's Blog

A few days ago I stumbled upon a recent PhD thesis (N. P. van der Aa, “Sensitivity analysis for grating reconstruction,” Ph.D. dissertation, Technische Universiteit Eindhoven, November 2007. [Online]. Available: http://alexandria.tue.nl/extra2/200711746.pdf ) which then led to a recent journal paper (N. P. van der Aa and R. M. M. Mattheij, “Computing shape parameter sensitivity of the field of one-dimensional surface-relief gratings by using an analytical approach based on RCWA,” J. Opt. Soc. Am. A, vol. 24, no. 9, pp. 2692–2700, 2007. [Online]. Available: http://www.opticsinfobase.org/abstract.cfm?id=140162 ) which shows promise to be the self-contained exposition of rigorous coupled-wave analysis (RCWA) of diffraction gratings. Before discovering this paper, the most recent and complete presentation I was aware of were the two papers by Moharam, Gaylord, and co-workers (M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A, vol. 12, no. 5, pp. 1068–1076, 1995. [Online]. Available: http://www.opticsinfobase.org/abstract.cfm?URI=JOSAA-12-5-1068 ; M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A, vol. 12, no. 5, pp. 1077–1086, 1995. [Online]. Available: http://www.opticsinfobase.org/abstract.cfm?URI=JOSAA-12-5-1077 ), but those papers are riddled with typographical errors, and they have a serious flaw in their formulation of RCWA for TM polarization in planar diffraction and for conical diffraction. This formulation was corrected independently by Lalanne and Morris (P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A, vol. 13, no. 4, pp. 779–784, 1996. [Online]. Available: http://www.opticsinfobase.org/abstract.cfm?URI=JOSAA-13-4-779 ) and Granet and Guizal (G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A, vol. 13, no. 5, pp. 1019–1023, 1996. [Online]. Available: http://www.opticsinfobase.org/abstract.cfm?URI=JOSAA-13-5-1019 ), and the corrections explained mathematically by Li (L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A, vol. 13, no. 9, pp. 1870–1876, September 1996. [Online]. Available: http://www.opticsinfobase.org/abstract.cfm?URI=JOSAA-13-9-1870 ), but until I stumbled upon this paper by van der Aa and Mattheij, I had not found a complete presentation of the corrected formulation of RCWA that was to my liking.