Transmission of polarized light in LHM and RHM materials with periodic refractive index

Purpose: The paper presents the implementation of the Transfer Matrix Method algorithm using Mathematica and the impact of the structure discretization steps number on the filters transmission. Tested materials were made with periodically varying refractive index. Design/methodology/approach: The properties of the filter transmission made of a materials having a periodically varying refractive index were analyzed. The study used a Transfer Matrix Method algorithm. The materials have a thickness of one micrometer. The refractive index of the analyzed material changed sinusoidally with a wavelength of 500nm. Sinusoid quantizing was performed each for 8, 16, 32, 50 and 60 layers. Findings: Maps show the nature of the transmission bands. Band structure of RHM materials (positive refractive index) is similar to the structure of the filter constructed of LHM material, characterized by a negative refractive index. Transmission band in a left-handed material has less width at half maximum. Thirty two layers discretization stabilizes the simulations of the tested materials filtration properties. Research limitations/implications: The paper had not been analyzed for materials with extinction coefficient different from zero. It would be worthwhile to conduct research for materials with variable refractive index of a different nature, for example a triangular or saw tooth shape. Practical implications: Analysis of the filter materials for a variety of photonic structures allows the prediction and design of materials with specified properties. These tests allow to design filters and mirrors for with very good applications parameters. Originality/value: The influence of the discretization level of continuous medium with periodically changing material properties on the transmission map stability was analyzed.