Investigation and Comparison of Light Propagation in Two Graded Photonic Crystal Structures

In this paper, we study two different Graded Index (GRIN) photonic crystal (PC) structures which are named as structure type I and type II. The PC structures are made of the square rod in an air background. To design a GRIN PC structure the lattice constant has been altered in the direction transverse to propagation. We investigated focusing effect and waveguiding behavior of electromagnetic waves propagating throughout the GRIN structures. Wide incident beam with a Gaussian profile is illuminated to the both GRIN structures. In the case of structure type I, the incident wave bend toward the central part of the structure and after getting out of it focuses on the narrow area. The designed structure shows the strong focusing effect and increase normalized intensity and decreases the width of the outgoing wave. In the case of structure type II, the incoming beam after traveling short distance becomes distracted to the central part and remains confine in the middle of the structure. The exiting wave can be coupled to a photonic crystal waveguide. Plane wave expansion method has been used for analyzing dispersion relation. Propagation of electromagnetic wave within the graded structure has been simulated using finite-difference time-domain method.