Multi-channel photonic bandgap consequences in one-dimensional linear, exponential, and hyperbolic graded-index photonic crystals

Abstract

We present the structuring of different graded-index materials in the form of one-dimensional (1D) photonic crystals (PCs) for highly efficient light trapping and controlling photonic devices in terms of tuned and controlled photonic bandgap (PBG) performance. We consider hyperbolic, exponential, and linear refractive index variation in the graded-index layer. We systematically study the influence of structural and grading parameters on the bandgap performance for two different graded photonic crystal (GPC) structures formed by stacking different graded-index layers. Compared with conventional PCs, the GPC bandgaps can be changed and tuned by the refractive index profile of the graded-index layer. We show that the number of bandgaps increases with the graded-index layer thickness and the bandgap frequencies can be tuned by the grading profiles. We observe the sequential increment in bandwidth for the complete PBGs in the GPC structures with linear, exponential, and hyperbolic graded-index materials. We also study the influence of the stacking pattern and grading profiles on the bandgap, phase shift, group velocity, delay time, and field distribution. The proposed GPC configurations facilitate the design of reflectors, multi-channel filters, detectors, and other photonic devices. The study may also provide the basis of understanding of the influence of graded-index materials on the PBG characteristics in the GPCs.