Analysis of layering dielectrics on effective permittivity using wave matrices

New materials are being developed which are composite mixtures of different dielectrics and sometimes magnetic materials. The paper focuses on the composition of layered dielectrics. More specifically, the layering of two materials with different permittivities is investigated. Increasing the number of layers while keeping the total volume of the composition constant is shown to achieve different effective permittivities. This analysis is done using the method of wave matrices to determine the S-parameters. The calculation of permittivity is then done by creating theoretical values for those S-parameters in terms of the dielectric constants, which are solved for simultaneously in conjunction with the wave matrix S-parameters using a 2 dimensional Newton´s root searching algorithm (Hansen, G.W. et al., 1993). The wave matrix method provides a simple, yet useful, tool in the analysis of layered dielectric materials. Upon analysis of the graphs presented, one should be able to design a composite layered material such that the effective permittivity can be adjusted based on the contrast ratio of the dielectrics and the number of layers within the material.