volume | PIER Journals

Abstract

Numerical solution is presented for light scattering from two kinds of free-standing periodic arrays, that is, disks made of noble-metal and circular apertures perforated in a thin noble-metal sheet. The shapes of them are complementary to each other, and the circular areas are allocated along two orthogonal coordinates with the same periodicity. Using the generalized boundary conditions of the surface impedance type, we formulate the boundary value problem into a set of integral equations for unknown electric and magnetic current densities defined over the circular area. Employment of the method of moments allows us to solve the integral equations and give the expansion coefficients of the current densities, from which we can find reflected, transmitted, and absorbed powers. Dependence of the powers on the array parameters and wavelength is discussed in detail from the viewpoint of grating resonance. Special attention is paid to the extraordinary transmission which occurs in the arrays of apertures of sub-wavelength size by analytical derivation of the quasi-static solutions.

1. Maier, S. A., Plasmonics: Fundamentals and Applications, Springer, 2007.

2. Kim, K. Y., Plasmonics: Principles and Applications, InTech, 2012.
doi:10.5772/2633

3. Natarov, D. M., V. O. Byelobrov, R. Sauleau, T. M. Benson, and A. I. Nosich, "Periodicity-induced effects in the scattering and absorption of light by infinite and finite gratings of circular silver nanowires," Optics Express, Vol. 19, No. 22, 22176-22190, 2011.
doi:10.1364/OE.19.022176 Google Scholar

4. Shapoval, O. V., R. Sauleau, and A. I. Nosich, "Modeling of plasmon resonances of multiple flat noble-metal nanostrips with a median-line integral equation technique," IEEE Trans. Nanotechnology, Vol. 12, No. 3, 442-449, 2013.
doi:10.1109/TNANO.2013.2256365 Google Scholar

5. Shapoval, O. V., A. I. Nosich, and J. Ctyroky, "Resonance effects in the optical antennas shaped as finite comb-like gratings of noble-metal nanostrips," SPIE Proc. 8781 (Integrated Optics: Physics and Simulations), No. 87810U, 1-8, 2013. Google Scholar

6. Ebbesen, T. W., H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature, Vol. 391, 667-669, 1998.
doi:10.1038/35570 Google Scholar

7. Glushko, O., R. Brunner, R. Meisels, S. Kalchmair, and G. Strasser, "Extraordinary transmission in metal hole array-photonic crystal hybrid structures," Optics Express, Vol. 20, No. 15, 17174-17182, 2012.
doi:10.1364/OE.20.017174 Google Scholar

8. Bleszynski, E., M. Bleszynski, and T. Jaroszewicz, "Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets," IEEE Antennas Propag. Mag., Vol. 35, No. 6, 14-25, 1993.
doi:10.1109/74.248480 Google Scholar

9. Senior, T. B. A. and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics, IEE, 1995.
doi:10.1049/PBEW041E

10. Shapoval, O. V., R. Sauleau, and A. I. Nosich, "Scattering and absorption of waves by flat material strips analyzed using generalized boundary conditions and Nystrom-type algorithm," IEEE Trans. Antennas Propagat., Vol. 59, No. 9, 3339-3346, 2011.
doi:10.1109/TAP.2011.2161547 Google Scholar

11. Munk, B. A., Frequency Selective Surfaces: Theory and Design, John Wiley & Sons, 2000.
doi:10.1002/0471723770

12. Amitay, N. and V. Galindo, "The analysis of circular waveguide phased arrays," Bell Syst. Tech. J., Vol. 47, No. 9, 1903-1932, 1968.
doi:10.1002/j.1538-7305.1968.tb01096.x Google Scholar

13. Chen, C. C., "Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes," IEEE Trans. Microwave Theory Tech., Vol. 19, No. 5, 475-481, 1971.
doi:10.1109/TMTT.1971.1127548 Google Scholar

14. Chen, C. C., "Transmission of microwave through perforated flat plates of finite thickness," IEEE Trans. Microwave Theory Tech., Vol. 21, No. 1, 1-6, 1973.
doi:10.1109/TMTT.1973.1127906 Google Scholar

15. Koledintseva, M. Y., J. Huang, J. L. Drewniak, R. E. DuBroff, and B. Archambeault, "Modeling of metasheets embedded in dielectric layers," Progress In Electromagnetics Research B, Vol. 44, 89-116, 2012.
doi:10.2528/PIERB12070910 Google Scholar

16. Hamdi, B., T. Aguili, and H. Baudrand, "Floquet modal analysis to modelize and study 2-D planar almost periodic structures in finite and infinite extent with coupled motifs," Progress In Electromagnetics Research B, Vol. 62, 63-86, 2015.
doi:10.2528/PIERB14111602 Google Scholar

17. Matsushima, A., T. L. Zinenko, H. Nishimori, and Y. Okuno, "Plane wave scattering from perpendicularly crossed multilayered strip gratings," Progress In Electromagnetics Research, Vol. 28, 185-203, 2000.
doi:10.2528/PIER99102801 Google Scholar

18. Matsushima, A., Y. Momoka, M. Ohtsu, and Y. Okuno, "Efficient numerical approach to electromagnetic scattering from three-dimensional periodic array of dielectric spheres using sequential accumulation," Progress In Electromagnetics Research, Vol. 69, 305-322, 2007.
doi:10.2528/PIER06123002 Google Scholar

19. Harrington, R. F., Field Computation by Moment Methods, Macmillan, 1968.

20. Braver, I. M., P. Sh. Fridberg, K. L. Garb, and I. M. Yakover, "The behavior of the electromagnetic field near the edge of a resistive half-plane," IEEE Trans. Antennas Propagat., Vol. 36, No. 12, 1760-1768, 1988.
doi:10.1109/8.14398 Google Scholar

21. Mittra, R., T. Itoh, and T. S. Li, "Analytical and numerical studies of the relative convergence phenomenon arising in the solution of an integral equation by the moment method," IEEE Trans. Microwave Theory Tech., Vol. 20, No. 2, 96-104, 1972.
doi:10.1109/TMTT.1972.1127691 Google Scholar

22. Johnson, P. B. and R. W. Christy, "Optical constants of the noble metals," Phys. Rev., Vol. 6, 4370-4379, 1972.
doi:10.1103/PhysRevB.6.4370 Google Scholar

23. Amitay, N. and V. Galindo, "On energy conservation and the method of moments in scattering problems," IEEE Trans. Antennas Propagat., Vol. 17, No. 7, 747-751, 1969.
doi:10.1109/TAP.1969.1139549 Google Scholar

24. Lee, S. W., G. Zarrillo, and C. L. Law, "Simple formulas for transmission through periodic metal grids or plates," IEEE Trans. Antennas Propagat., Vol. 30, No. 5, 904-909, 1982.
doi:10.1109/TAP.1982.1142923 Google Scholar

25. Widenberg, B., S. Poulsen, and A. Karlsson, "Scattering from thick frequency selective screens," Journal of Electromagnetic Waves and Applications, Vol. 14, No. 9, 1303-1328, 2000.
doi:10.1163/156939300X01265 Google Scholar

Dr. Xiaowei Ji

Dr. Daiki Sakomura

Prof. Akira Matsushima

Dr. Taikei Suyama