Modeling the impact of manufacturing imperfections on photonic crystal device performance: design of perturbation-tolerant PBG components

Abstract

Standard perturbation theory (PT) and coupled mode theory (CMT) formulations fail or exhibit very slow convergence when applied to the analysis of geometrical variations in high index-contrast optical components such as Bragg fibers and photonic crystals waveguides. By formulating Maxwell's equations in perturbation matched curvilinear coordinates, we have derived several rigorous PT and CMT expansions that are applicable in the case of generic non-uniform dielectric profile perturbations in high index-contrast waveguides. In strong fiber tapers and fiber Bragg gratings we demonstrate that our formulation is accurate and rapidly converges to an exact result when used in a CMT framework even in the high index-contrast regime. We then apply our method to investigate the impact of hollow Bragg fiber ellipticity on its Polarization Mode Dispersion (PMD) characteristics for telecom applications. Correct PT expansions allowed us to design an efficient optimization code which we successfully applied to the design of dispersion compensating hollow Bragg fiber with optimized low PMD and very large dispersion parameter. We have also successfully extended this methodology to treat radiation scattering due to common geometric variations in generic photonic crystals. As an example, scattering analysis in strong 2D photonic crystal tapers is demonstrated.