Theoretical Investigation on Photonic Bandgap Tailoring in One-Dimensional Photonic Crystal Using Different Numerical Methods

Abstract

An comparative study is performed for calculating the bandgap of one-dimensional photonic crystal structure using two widely used numerical methods, namely Transfer Matrix Method (TMM) and Plane Wave Expansion method (PWM). Numerical computation is carried out under different structural conditions and different operating wavelength spectrum for analysis purpose. Result reveals that TMM is specifically advantageous to some extent in the case of one dimensional photonic crystal, but we will see that it fails miserably in case of two and three dimensional structures which are characterized by complicated boundary conditions at their interfaces. Even for the one-dimensional case, with the increase in the number of periodic layers, the TMM method fails to approximate the band structure. The PWM method on the other hand is a relatively slow in terms of computation time but fairly accurate method for band structure calculation. Result provides fundamental insights in understanding the differences between the methods of calculation and the corresponding modifications in the photonic bandgaps found in the band structure. Knowledge of such analysis helps to effectively tailor the bandgap structure in photonic crystals.