Scattering characteristics of periodic dielectric gratings can be accurately and efficiently computed via a spectral volume integral equation combined with normal-vector fields defined on the grating geometry. We study the impact of the geometrical discretization on the convergence rate of the scattering characteristics for two-dimensional gratings in both TE and TM polarization and compare these with an independent semi-analytical reference for circular cylinders. We demonstrate that geometrically conforming normal vector fields lead to substantially faster convergence and shorter computation times, as opposed to the commonly applied staircasing or slicing.
1. Neviere, M., and Type: journal book conference other, "About the theory of optical grating coupler-waveguide systems," Optics Communications, Vol. 8, No. 2, 113-117, 1973. doi:10.1016/0030-4018(73)90150-8
2. Moharam, , M. G. and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," Journal of the Optical Society of America, Vol. 71, No. 7, 811-818, 1981. doi:10.1364/JOSA.71.000811
3. Botten, L. C., , M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta, , Vol. 28, 413-428, 1981. doi:10.1080/713820571
4. Chandezon, , J., G. Raoult, and D. Maystre, "A new theoretical method for diffraction gratings and its numerical application," J. of Optics, Vol. 11, No. 4, 235-240, 1980. doi:10.1088/0150-536X/11/4/005
5. Li, , L., , "Use of Fourier series in the analysis of discontinuous periodic structures," Journal of the Optical Society of America A , Vol. 13, No. 9, 1870-1876, 1996. doi:10.1364/JOSAA.13.001870
6. Popov, , E., M. Neviµere, B. Gralak, and G. Tayeb, "Staircase approximation validity for arbitrary-shaped gratings," Journal of the Optical Society of America A, Vol. 19, No. 1, 33-42, 2002. doi:10.1364/JOSAA.19.000033
7. Schuster, , T., , J. Ruoff, N. Kerwien, S. Rafler, and W. Osten, "Normal vector method for convergence improvement using the RCWA for crossed gratings ," Journal of the Optical Society of America A, Vol. 24, No. 9, 2880-2890, 2007. doi:10.1364/JOSAA.24.002880
8. Rafler, , S., , P. Gotz, M. Petschow, T. Schuster, K. Frenner, and W. Osten, "Investigation of methods to set up the normal vector field for the differential method," Proc. SPIEz, Vol. 6995, 9, 2008 .
9. Magath, T. and A. Serebryannikov, "Fast iterative, coupled integral-equation technique for inhomogeneous profiled and periodic slabs," Journal of the Optical Society of America A , Vol. 22, No. 11, 2405-2418, 2005. doi:10.1364/JOSAA.22.002405
10. Magath, T., "Coupled integral equations for diffraction by pro¯led, anisotropic, periodic structures," IEEE Transactions on Antennas and Propagation, Vol. 54, 681-686, 2006. doi:10.1109/TAP.2005.861527
11. van Beurden, , M. C., "Fast convergence with spectral volume integral equation for crossed block-shaped gratings with improved material interface conditions," Journal of the Optical Society of America A, Vol. 28, No. 11, 2269-2278, 2011. doi:10.1364/JOSAA.28.002269
12. Shcherbakov, A. A. and A. V. Tishchenko, "New fast and memory-sparing method for rigorous electromagnetic analysis of 2D periodic dielectric structures," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 113, 158-171, 2012. doi:10.1016/j.jqsrt.2011.09.019
13. van Beurden, M. C., "A spectral volume integral equation method for arbitrary bi-periodic gratings with explicit Fourier factorization," Progress In Electromagnetics Research B, Vol. 36, 133-149, 2012. doi:10.2528/PIERB11100307
14. Popov, , E. and M. Neviere, "Grating theory: New equations Grating theory: New equations in Fourier space leading to fast converging results for TM polarization," Journal of the Optical Society of America A, Vol. 17, No. 10, 1773-1784, 2000. doi:10.1364/JOSAA.17.001773
15. Sturmberg, , B. C. P., K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, C. M. de Sterke, and R. C. McPhedran, "Modal analysis of enhanced absorption in silicon nanowire arrays," Optics Express, Vol. 19, No. S5, A1067-A1081, 2011. doi:10.1364/OE.19.0A1067
16. Popov, , E. , M. Neviµere, and , "Maxwell equations in Fourier space: Fast-converging formulation for dIffraction by arbitrary shaped, periodic, anisotropic media," Journal of the Optical Society of America A, Vol. 18, No. 11, 2886-2894, 2001. doi:10.1364/JOSAA.18.002886
17. Elsherbeni, , A. Z. and A. A. Kishk, "Modeling of cylindrical objects by circular dielectric and conducting cylinders," IEEE Transactions on Antennas and Propagation, Vol. 40, No. 1, 96-99, 1992. doi:10.1109/8.123363
18. Abramowitz, , M. and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publishing, New York, 1972.