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Journal of Lightwave Technology

Journal of Lightwave Technology


  • Vol. 30, Iss. 10 — May. 15, 2012
  • pp: 1393–1398

Higher-Order Finite-Difference Modal Method With Interface Conditions for the Electromagnetic Analysis of Gratings

Yih-Peng Chiou and Chi-Kai Shen

Journal of Lightwave Technology, Vol. 30, Issue 10, pp. 1393-1398 (2012)

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We present a finite-difference modal method (FDMM) combined with higher-order interface conditions to analyze the diffraction of grating structures. The generalized Douglas (GD) scheme is also adopted to further enhance the convergence. Numerical results show the FDMM generally results in faster convergence than the commonly used coupled-wave analysis (RCWA) as higher-order formulation, such as the GD with five points, is adopted in both TE and TM polarizations. The FDMM is also relatively stable in a highly conductive lossless rectangular grating, while the RCWA suffers instabilities in such a frequently studied structure.

© 2012 IEEE

Yih-Peng Chiou and Chi-Kai Shen, "Higher-Order Finite-Difference Modal Method With Interface Conditions for the Electromagnetic Analysis of Gratings," J. Lightwave Technol. 30, 1393-1398 (2012)

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  1. Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
  2. A. Wirgin, "A new theoretical approach to scattering from a periodic interface," Opt. Commun. 27, 189-194 (1978).
  3. D. Maystre, "A new general integral theory for dielectric coated gratings," J. Opt. Soc. Am. 68, 490-495 (1978).
  4. D. E. Tremain, K. K. Mei, "Application of the unimoment method to scattering from periodic dielectric structures," J. Opt. Soc. Am. 68, 775-783 (1978).
  5. K. C. Chang, V. Shah, T. Tamir, "Scattering and guiding of waves by dielectric gratings with arbitrary profiles," J. Opt. Soc. Am. 77, 1385-1392 (1980).
  6. M. G. Moharam, T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 71, 811-818 (1981).
  7. M. G. Moharam, D. A. Pommet, E. B. Grann, T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: Enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995).
  8. F. Montiel, M. Nevière, "Differential theory of gratings: Extension to deep gratings of arbitrary profile and permittivity through the R-matrix propagation algorithm," J. Opt. Soc. Am. A 11, 3241-3250 (1994).
  9. P. Lalanne, G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. A 13, 779-784 (1996).
  10. G. Granet, B. Guizal, "Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996).
  11. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
  12. E. Popov, B. Chernov, M. Nevière, N. Bonod, "Differential theory: Application to highly conducting gratings," J. Opt. Soc. Am. A 21, 199-206 (2004).
  13. K. Watanabe, "Study of the differential theory of lamellar gratings made of highly conducting materials," J. Opt. Soc. Am. A 23, 69-72 (2006).
  14. N. M. Lyndin, O. Parriaux, A. V. Tishchenko, "Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings," J. Opt. Soc. Am. A 24, 3781-3788 (2007).
  15. B. Guizal, H. Yala, D. Felbacq, "Reformulation of the eigenvalue problem in the Fourier modal method with spatial adaptive resolution," Opt. Lett. 34, 2790-2792 (2009).
  16. Y.-P. Chiou, W.-L. Yeh, N.-Y. Shih, "Analysis of highly conducting lamellar gratings with multidomain pseudospectral method," IEEE/OSA J. Lightw. Technol. 27, 5151-5159 (2009).
  17. P. Lalanne, J.-P. Hugonin, "Numerical performance of finite-difference modal methods for the electromagnetic analysis of one-dimensional lamellar gratings," J. Opt. Soc. Am. A 17, 1033-1042 (2000).
  18. Y.-P. Chiou, Y.-C. Chiang, H. C. Chang, "Improved three-point formulae considering the interface conditions in the finite-difference analysis of step-index optical devices," IEEE/OSA J. Lightwave Technol. 18, 243-251 (2000).
  19. Y.-P. Chiou, C.-H. Du, "Arbitrary-order interface conditions for slab structures and their applications in waveguide analysis," Opt. Express 18, 4088-4102 (2010).
  20. Y.-P. Chiou, C.-H. Du, "Arbitrary-order full-vectorial interface conditions and higher-order finite-difference analysis of optical waveguides," IEEE/OSA J. Lightw/ Technol. 29, 3445-3452 (2011).

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