Using of Transmission Matrixes and Pseudospectral Method in Time Domain to Investigate Light Diffraction on Planar Periodic Structures

Abstract

A new mathematical model is proposed for computational investigation of diffraction of electromagnetic waves of optical and infrared bands on a planar periodic structure of resonance metal elements of complex shape located on a dielectric substrate of thickness much exceeding the wavelength. The model employs the pseudo-spectral time domain method in combination with the transmission matrices method in frequency domain. The mathematical model built accounts for dispersion of metal and dielectric permittivities of a periodic structure and a substrate, respectively. For the infrared band, the reflection coefficient calculated for the grating of aluminum C-shaped resonant elements is shown vs. wavelength. The grating has a square periodic cell with the size of 500 nm, the substrate being a 0.5 mm thick layer of quartz glass.