Photonic band gap consequences in one-dimensional exponential graded index photonic crystals

Abstract

We have investigated the photonic bandgap characteristics in one-dimensional (1-D) exponential graded photonic crystals (GPCs) in the microwave region. Proposed 1-D GPC structures are the stacked of the exponential graded index layers. In an exponential graded index layer, the refractive index between the boundaries of the layer modulates in an exponential fashion in terms of the layer's depth. We observe that the number of photonic bands increases with an increase in the graded layer's thicknesses. When the graded layer's thicknesses are proportional to one-quarter of the optical wavelength relative to the mean refractive index, observed photonic bands increase with an integral multiple of λ0/4 (λ0 represents the optical wavelength of the selected frequency). The bandwidth of photonic band gaps can be tuned with the modulations of the initial and final refractive index of the graded layer. Therefore, the desirable photonic bands can be controlled and achieved in a selected frequency range by choosing the GPC structure's convenient parameters. This work will facilitate the design of filters and multi-channel filters and provide more design freedom for other photonic devices. This work may also provide the basis for understanding the effect of exponentially graded material on photonic band gap characteristics in 1-D GPCs.