A vectorial modal analysis of two-dimensional (2-D) dielectric grating is presented. The transmission and reflection from the 2-D dielectric-grating slab are computed by combining the generalized scattering matrix and the modal analysis. New insights on the boundary conditions between two grating structures are presented to be suitable for two-dimensional gratings. The results obtained using the present analysis are verified with published experimental and numerical results for both one- and two-dimensional dielectric-grating slabs. The present approach provides fast convergence and provides good agreement with other numerical techniques. This technique is used to study the effects of different parameters for designing a wide band FSS composed of multilayered 2-D grating slabs.
2. Coves, A., B. Gimeno, A. A. San Blas, A. Vidal, V. E. Boria, and M. V. Andres, "Three-dimensional scattering of dielectric gratings under plane-wave excitation," IEEE Antennas and Wireless Propagation Letters, Vol. 2, 215-218, 2003.
3. Peng, S. T., T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Techniques, Vol. 23, 123-133, 1975.
4. Peng, S. T., "Rigorous formulation of scattering and guidance by dielectric grating waveguides: General case of oblique incidence," J. Opt. Soc. Amer. A., Vol. 6, No. 12, 1869-1883, 1989.
5. Bertoni, H. L., L. H. S. Cheo, and T. Tamir, "Frequency-selective reflection and transmission by a periodic dielectric layer," IEEE Trans. Antennas Propagat., Vol. 37, 78-83, 1989.
6. Pai, D. M. and K. A. Awada, "Analysis of dielectric gratings of arbitrary profiles and thicknesses," J. Opt. Soc. Amer. A., Vol. 8, No. 5, 755-762, 1991.
7. Yang, H. Y. D., R. Diaz, and N. G. Alexopoulos, "Reflection and transmission of waves from multilayer structures with planar- implanted periodic material blocks," J. Opt. Soc. Amer. B., Vol. 14, 2513-2521, 1997.
8. Tibuleac, S., R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, "Dielectric frequency-selective structures incorporating waveguide gratings," IEEE Trans. Microwave Theory Tech., Vol. 48, 553-561, 2000.
9. Mosallaei, H. and Y. Rahmat-Samii, "Periodic bandgap and effective dielectric materials in electromagnetics: characterization and applications in nanocavities and waveguides," IEEE Trans. Antennas Propagat., Vol. 60, 549-563, 2003.
10. Costa, J. C. W. A. and A. J. Giarola, "Electromagnetic wave propagation in multilayer dielectric periodic structures," IEEE Trans. Antennas Propagat., Vol. 41, 1432-1438, 1993.
11. Jarem, J. M. and P. P. Banerjee, Computational Methods for Electromagnetic and Optical Systems, Marcel Dekker, Inc., 2000.
12. Moharam, M. G., E. B. Grann, D. A. Pommet, and T. K. Gaylord, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary grating," J. Opt. Soc. Am. A., Vol. 12, 1068-1076, 1995.
13. Silvestre, E., M. A. Abian, B. Gimeno, A. Ferrando, M. V. Andres, and V. E. Boria, "Analysis of inhomogeneously filled waveguides using a bi-orthonormal-basis method," IEEE Trans. Microwave Theory Tech., Vol. 48, 589-596, 2000.
14. Mittra, R., C. H. Chan, and T. Cwik, "Techniques for analyzing frequency selective surfacesa review," Proc. IEEE, Vol. 76, 1593-1615, 1988.