Mach-Zehnder interferometer based on self-collimation phenomenon in two-dimensional photonic crystals

Abstract

In this study, we suggest a waveguideless MZI structure based on the self-collimation phenomenon in two-dimensional photonic crystal (PhC). The PhC structure considered is a square array of circular silicon rods of dielectric constant 12 and the radius 0.35\\textit{a}. The equi-frequency contours for the $\\Gamma$M direction are drawn and the self-collimation frequency for our structure is found to be 0.194(c/\\textit{a}). The continuous Gaussian beam of this frequency with the beam width of 7\\textit{a} is launched into this structure. When the light beam reaches two line defects, which is created by removing 30 rods per each line along the $\\Gamma$X direction, almost all the incident light is reflected and there occurs a $\\lambda$/2 phase change after reflection. Instead of removing the rods, when the radius of one line of 30 rods along the $\\Gamma$X direction is varied, this line defect splits the incoming light into two light beams with some phase shifts. When the defect radius $r_d$ is 0.268\\textit{a}, the incident beam is divided into the reflected beam and the transmitted beam like a 50:50 beam splitter. With the $r_d$ fixed at 0.268\\textit{a} as the refractive index of the defect line is varied, the incident beam splits into two beams and they experience different phase shifts at the line defect. \\\\From these results, we present a MZI based on the self-collimation phenomenon in the PhC. Without any path difference between the path 1 and the path 2, the power of the incident beam is detected only at one detector. Varying the radius of the defect rods or the refractive index of the line defect of the second beam splitter, we get the power distributions at each detector. Analysis of this proposed MZI sructure is performed by the finite-difference time-domain method at the self-collimation frequency of the PhC.