Original Solution of Coupled Nonlinear Schrödinger Equations for Simulation of Ultrashort Optical Pulse Propagation in a Birefringent Fiber

Abstract

This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system, different from the generally accepted approach based on the method of splitting according to physical processes. A combined explicit/implicit finite-difference integration scheme based on the implicit Crank–Nicolson finite-difference scheme is proposed and substantiated. It allows the integration of a nonlinear system of equations with a choice of nonlinear terms from the previous integration step. The main advantages of the proposed method are: its absolute stability through the use of an implicit finite-difference integration scheme and an integrated mechanism for refining the numerical solution at each step; integration with automatic step selection; performance gains (or resolutions) up to three or more orders of magnitude due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step, as is required in the method of splitting according to physical processes. An additional advantage of the proposed method is the ability to calculate the interaction with an arbitrary number of propagation modes in the fiber.

Qualitative analysis and new soliton solutions for the coupled nonlinear Schrödinger type equations

“…The authors in [25], have investigated CNLSEs for the fiber couplers with cross-phase modulation and asymmetric self-phase modulation. In [26], a numerical integration method has been proposed for solving the CNLSEs system. The existence of purely vector semiclassical solutions has been proved for critical coupled Schrödinger system [27].…”

Solitary waves described by a high‐order system in optical fiber Bragg gratings with arbitrary refractive index

“…The type of optical fiber is also taken into account in the construction of mathematical models. Birefringent fiber 22–26 and Bragg gratings optical fiber 27–32 are studied most of the time. A fiber Bragg grating is a periodic perturbation of the refractive index along the fiber length 33 …”