Study on the variation in dielectric properties of heterogeneous substrates composed of nanomaterials

An analytical study of heterogeneous substrates created by including small particles arranged in a cubic lattice within a host medium is presented in this paper. Rapid advances in nanomaterial fabrication techniques will allow in the near future, heterogeneous samples to be created with nano or micro-sized inclusions, and this paper investigates the electromagnetic (EM) properties of these structures. Analytical equations by various authors for the effective permittivity and permeability of such artificial materials have been analysed and compared over microwave frequencies. The particle size, spacing and frequency were examined individually to understand their role in determining the effective EM parameters of the heterogeneous mixture. Furthermore, results from FDTD simulations with micro-sized cuboids were processed using an inverse scattering algorithm to obtain the effective permittivity and permeability of these heterogenous structures using a complimentary technique. The canonical formulations showed reasonable agreement with the EM simulations and the two methods can be used to design novel dielectric substrates.