Perturbation of multilayered structures of positive and negative index materials

Abstract

In this work, we illustrate a framework that can model propagation through a dispersive, homogeneous periodic/quasiperiodic/ randomly perturbed, layer lengths in a multilayered structure of positive and negative index materials. We achieve this by using a transfer matrix-based multilayered approach. In the quasi-periodic case the layers lengths vary according to a predetermined function like a sinusoidal function for example. In the random case we use zero mean random variables as the perturbation around a nominal layer length of positive and negative index materials. We also use the trace of the transfer matrix to determine the limiting case of the transmittance when the number of periods become infinitely large, and determine the locations of the bandgaps in the multi-layered structure. This helps in reducing the calculations since only one unit cell is needed. Plane wave propagation is investigated, and aggregated transmittivity is calculated in the different cases. Finally we study wave localization in the randomly perturbed structure and compare it with the periodic case.