Investigation of an effective medium theory for metallic periodic structures: A fitting-based approach

While the effective medium theory (EMT) has been useful to explain optical characteristics of a dielectric periodic structure analytically, it has failed to describe metallic structures correctly. In this paper, a fitting-based approach is introduced to applying an effective medium theory to structures that include metallic material. The effective indices of a metallic medium were first obtained by numerically fitting to reflectance characteristics calculated with rigorous coupled wave analysis (RCWA). Searching for an effective medium has been performed through binary searches rather than a time-consuming simulated-annealing algorithm. The calculated effective medium showed results that are in good agreement with RCWA. The deviation was minimal in the long-wavelength limit when angles of incidence, grating depths, or refractive indices of a superstrate are varied. In particular, TE polarization showed more robust features against the variations while TM polarization was more sensitive to the modeling parameters. In terms of the standard deviation, the calculated effective medium was the least affected by the change of grating depths. The applicability of the fitting-based approach was investigated by applying it to a three-dimensional metallic photonic crystal. Simulation results based on the fitting-based EMT perfectly reproduced broad photonic bandgap as observed in published experimental data. Also, the fitting-based approach provided valid results in the wider wavelength range than a traditional EMT.