volume | PIER Journals

Abstract

The differential method for arbitrary profiled onedimensional gratings made of anisotropic media is reformulated by taking into account Li's Fourier factorization rules [10] though the present formulation uses the intuitive Laurent rule only. The study concerns arbitrary profiled gratings with both types of electric and magnetic anisotropy, and includes the case of lossy materials. Diffraction efficiencies computed by the present formulation are compared with previous ones, and numerical results show that convergence of the present formulation is superior to the conventional one and comparable convergence with the previous works based on Li's rules.

1. Petit, R., "Diffraction d'une onde plane par un reseau metallique," Rev. Opt., Vol. 45, 353-370, 1966.

2. Vincent, P., "Differential methods," Electromagnetic Theory of Gratings, Vol. 22 of Topic in Current Physics, 101-121, 1980.

3. Peng, S. T., T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech., Vol. 23, No. 1123-133, 1123-133, 1975.

4. Moharam, M. G. and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am., Vol. 71, No. 7, 811-818, 1981.

5. Moharam, M. G. and T. K. Gaylord, "Rigorous coupled-wave analysis of dielectric surface-relief gratings," J. Opt. Soc. Am., Vol. 72, No. 10, 1385-1392, 1982.

6. Li, L., "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A, Vol. 13, No. 5, 1024-1035, 1996.

7. Montiel, F., M. Neviere, and P. Peyrot, "Waveguide confinement of Cerenkov second-harmonic generation through a graded-index grating coupler: Electromagnetic optimization," J. Mod. Opt., Vol. 45, No. 10, 2169-2186, 1998.
doi:10.1080/095003498150646

8. Watanabe, K., "Numerical integration schemes used on the differential theory for anisotropic gratings," J. Opt. Soc. Am. A, Vol. 19, No. 11, 2245-2252, 2002.

9. Neviere, M., P. Vincent, and R. Petit, "Sur la theorie du reseau conducteur et ses applications `a l'optique," Nouv. Rev. Opt., Vol. 5, No. 2, 65-77, 1974.
doi:10.1088/0335-7368/5/2/301

10. Li, L., "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A, Vol. 13, No. 9, 1870-1876, 1996.

11. Li, L., "Reformulation of the Fourier modal method for surfacerelief grating made with anisotropic materials," J. Mod. Opt., Vol. 45, No. 71313-1334, 71313-1334, 1998.

12. Popov, E., M. Neviere, B. Gralak, and G. Tayeb, "Staircase approximation validity for arbitrary shaped gratings," J. Opt. Soc. Am. A, Vol. 19, No. 1, 33-42, 2002.

13. Popov, E. and M. Neviere, "Grating theory: New equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A, Vol. 17, No. 10, 1773-1784, 2000.

14. Watanabe, K., R. Petit, and M. Neviere, "Differential theory of gratings made of anisotropic materials," J. Opt. Soc. Am. A, Vol. 19, No. 2, 325-334, 2002.

15. Watanabe, K. and K. Yasumoto, "Reformulation of differential method for anisotropic gratings in conical mounting," Proc. 8th Int. Symp. Microwave and Opt. Technol., No. 6, 443-446, 2001.

16. Popov, E. and M. Neviere, "Maxwell equations in Fourier space: Fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media," J. Opt. Soc. Am. A, Vol. 18, No. 11, 2886-2894, 2001.

17. Watanabe, K., "Fast converging formulation of the differential theory for cylindrical rod gratings made of anisotropic materials," Turkish J. Telecommunications.

18. Watanabe, K., "Fast converging formulation of differential theory for non-smooth gratings made of anisotropic materials," Radio Sci., Vol. 38, No. 2, 2003.
doi:10.1029/2001RS002562

19. Li, L., "Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited," J. Opt. Soc. Am. A, Vol. 11, No. 11, 2816-2828, 1994.

20. Tayeb, G., "Contribution a l'etude de la diffraction des ondes electromagnetiques par des reseaux. Reflexions sur les methodes existantes et sur leur extension aux milieux anisotropes," Ph.D. dissertation, No. 90/Aix 3/0065, 1990.

Prof. Koki Watanabe