Effective permittivities of a metallic periodic structure for which the second-order effective-medium theory does not yield correct results were obtained by numerically fitting to rigorous-coupled-wave analysis (RCWA). The calculated effective medium showed good agreement with RCWA and minimal deviation in the long-wavelength limit with variation in angle of incidence, grating depth, superstrate, and fill factor. In terms of the standard deviation, the effective medium was least affected by the change in grating depths. The calculated effective permittivities were applied to a three-dimensional metallic photonic-crystal structure and produced a photonic bandgap that is consistent with published experimental data.
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