Stochastic analysis for one dimensional photonic crystals

Abstract

Tolerance variations of the design parameters of the photonic crystals due to fabrication processes have a strong effect on the performance of the photonic crystals and their operating wavelengths. In this work, the uncertainties of the design parameters of one-dimensional photonic crystals (1D-PCs) and their impacts on the PCs optical properties and the operating performance are investigated. The effects of these uncertainties for different tolerances are studied for both defect-free PCs and PCs with a defect air layer. The probability distribution function and the standard deviations of the photonic gap bandwidth, the defect mode wavelength and the trust gap width are studied. These stochastic analyses and modeling are based on the transfer matrix and Monte Carlo simulations.