Investigation of wave propagation characteristics in photonic crystal micro-structure containing circular shape with varied nonlinearity

Abstract

We begin by deriving the nonlinear Schrödinger equation (NLSE) in the presence of nonlinear microstructures, where the refractive index undergoes periodic modulation in the transverse direction for photonic crystal containing circular shape. Our investigation delves deeply into the intricate mechanisms behind transverse and longitudinal modulation of the refractive indexes, which aligns with the design of numerous manufactured slab microstructure waveguides. Theory of solitary waves in nonlinear microstructure, here unconventional fiber has been studied and examined in detail. In this work, composite methods leading both transverse and longitudinal modulation of refractive indexes have been presented in detail. The work also presents the diverse characteristics of this NLSE for both homogeneous and nonhomogeneous medium, encompassing various orders of nonlinearity specific to the nonlinear microstructure under consideration. Additionally, we analyze the wave propagation profiles for wide signals, which are wider than the periodicity of micro-structured photonic crystal. We also conduct a perturbation analysis for narrow signals that are even narrower than the periodicity of photonic crystal in transverse direction.