Numerical Method for Coupled Nonlinear Schrödinger Equations in Few-Mode Fiber

This paper discusses novel approaches to the numerical integration of the coupled nonlinear Schr&ouml
dinger equations system for few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schr&ouml
dinger equation system, where propagation of each mode is described by own Schr&ouml
dinger equation with other modes&rsquo
interactions. In this case, the coupled nonlinear Schr&ouml
dinger equation system (CNSES) solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails due to the non-stability of the computing scheme. Owing to this, here we use the combined explicit/implicit finite-difference integration scheme, which is based on the implicit Crank&ndash
Nicolson finite-difference scheme. It ensures the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has a higher performance (resolution)&mdash
up to three times or more in comparison with the split-step Fourier method&mdash
since there is no need to produce direct and inverse Fourier transforms at each integration step. The key advantage of the developed approach is the calculation of any number of modes propagated in the fiber.