volume | PIER Journals

Abstract

A hybrid approach to find the optical response of periodic photonic structures to incident light is presented. The approach is based on a scattering matrix combination of the Finite Element Method (FEM) and the Fourier Modal Method (FMM). Optical response calculations include: scattering in both reflection and transmission directions, absorption and electric and magnetic field distributions inside the structure. The approach is tested on a structure --- composed of dielectric and metallic materials --- that is periodic in one direction. An analysis of the calculation accuracy shows that the approach depends on the subdivision into FEM and FMM domains and that the optimal subdivision depends on the calculations frequency range as well as on the structure geometry. For testing, we use the commercial FEM solver contained in CST Microwave Studio and a based on C/C++ Fourier Modal Method implementation.

1. Hiptmair, R., "Finite elements in computational electromagnetism," Acta Numerica, 237-339, 2002.

2. Li, L. F., "New formulation of the fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A, Vol. 14, 2758-2767, 1997.
doi:10.1364/JOSAA.14.002758

3. Tikhodeev, S. G., A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B, Vol. 66, No. 4, 045102, 2002.
doi:10.1103/PhysRevB.66.045102

4. Christ, A., T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, "Optical properties of planar metallic photonic crystal structures: Experiment and theory," Phys. Rev. B, Vol. 70, No. 3, 125113, Sep. 2004.
doi:10.1103/PhysRevB.70.125113

5. Hafner, Ch. and R. Ballisti, "The multiple multipole method (MMP)," Compel --- The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 2, No. 1, 1-7, 1983.
doi:10.1108/eb051970

6. Talebi, N., M. Shahabadi, and Ch. Hafner, "Analysis of a lossy microring using the generalized multipole technique," Progress In Electromagnetics Research, Vol. 66, 287-299, 2006.
doi:10.2528/PIER06112801

7. Sannomiya, T. and Ch. Hafner, "Multiple multipole program modelling for nano plasmonic sensors," Journal of Computational and Theoretical Nanoscience, Vol. 7, 1587-1595, 2010.
doi:10.1166/jctn.2010.1523

8. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Transactions on Antennas and Propagation, Vol. 14, 302-307, 1966.

9. Shlager, K. L. and J. B. Schneider, "A selective survey of the finite-difference time-domain literature," IEEE Antennas and Propagation Magazine, Vol. 37, No. 4, 39-57, 1995.
doi:10.1109/74.414731

10. Kagami, S. and I. Fukai, "Application of boundary-element method to electromagnetic field problems," IEEE Transactions on Microwave Theory and Techniques, Vol. 32, No. 4, 455-461, 1984.
doi:10.1109/TMTT.1984.1132702

11. Buffa, A., M. Costabel, and C. Schwab, "Boundary element methods for Maxwells equations on non-smooth domains," Numer. Math., Vol. 92, 679-710, 2002.
doi:10.1007/s002110100372

12. Komarevskiy, N., V. Shklover, L. Braginsky, and C. Hafner, "Ultrasensitive switching between resonant reflection and absorption in periodic gratings," Progress In Electromagnetics Research, Vol. 139, 799-819, 2013.

13. Deceglie, M. G., V. E. Ferry, A. Paul Alivisatos, and H. A. Atwater, "Design of nanostructured solar cells using coupled optical and electrical modeling," Nano Lett., Vol. 12, 2894-2900, 2012.
doi:10.1021/nl300483y

14. Wilson, E. L. and R. E. Nickell, "Application of the finite element method to heat conduction analysis," Nuclear Engineering and Design, Vol. 4, 276-286, 1966.
doi:10.1016/0029-5493(66)90051-3

15. Petyt, M., J. Lea, and G. H. Koopmann, "A finite element method for determining the acoustic modes of irregular shaped cavities," Journal of Sound and Vibration, Vol. 45, 495-502, 1976.
doi:10.1016/0022-460X(76)90730-6

16. Ko, D. Y. K. and J. C. Inkson, "Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems," Phys. Rev. B, Vol. 38, No. 14, 9945-9951, 1988.
doi:10.1103/PhysRevB.38.9945

Mr. Alexander Dorodnyy

Dr. Valery Shklover

Dr. Christian Hafner