Modeling of Photon Crystals of Microwave Range Using Interference Matrixes

Abstract

The ability to control the properties of photonic crystals by changing the parameters of the layers allows to create unique optoelectronic devices. Properties of such environments are due to the formation of permitted and forbidden areas for electromagnetic radiation. The behavior of forbidden and permitted zones (high reflection and high-transmission areas) is well described by the theory of multilayer coatings. Photonic crystals may be considered using multilayer interference structures. Interference systems consisting of alternating films of the required optical thickness with high and low refractive indexes allow reducing the reflection of light in a narrow or wide spectral region, to increase reflection of incident light at different sections of spectral width, to separate narrow spectral region of monochromatic light. Theoretical studies can be carried out using both matrix methods and analytical formulas developed for multilayer. The simulation of a heterogeneous layer is carried out by replacing the smooth distribution of the refractive index with a stepped profile. Each layer is described using matrices of interference. The developed calculation programs using the matrix method make it possible to obtain the given optical characteristics (reflection, transmission, etc.) for any multilayer coatings. We simulated an interference mirror with quarterwave optical thicknesses of alternating layers and normal incidence of light. The graphs presented show a remarkable coincidence of the results of optical characteristics of multilayer coatings obtained using the matrix method with experimental and numerical FDTD (Finite-Difference Time-Domain) method. A multilayer system with a defective layer has a bandwidth in the band gap; it is a conventional interference filter. Thus, this confirms that photonic crystals can be modeled using multilayer interference structures and calculations using matrix methods.