Effect of random structural variations on the optical properties of honeycomb photonic crystals

Periodic dielectric structures called photonic crystals are being used in various sensors and devices. Since photonic crystals are designed to operate within certain frequency ranges, accuracy in structure becomes important. In this work, we investigate the effects of two types of randomness, surface roughness and positional randomness, on the optical properties of the honeycomb photonic crystal. We employed the plane wave expansion method to investigate the effects of random perturbations of the shape and the position of the structure on the density of states. We also employ the finite-difference time-domain method to calculate the transmission spectrum as a consistency check. We find that both surface roughness and positional imperfections cause significant changes in the DOS. As the degree of randomness is increased, transverse electric and transverse magnetic gaps are narrowed and complete gaps totally disappear at $ 45\% $ 45% of surface roughness.