Algorithm for Solving a System of Coupled Nonlinear Schrödinger Equations by the Split-Step Method to Describe the Evolution of a High-Power Femtosecond Optical Pulse in an Optical Polarization Maintaining Fiber
Anton V. Bourdine,
Vladimir A. Burdin,
Oleg G. Morozov
Affiliations
Anton V. Bourdine
Department of Communication Lines, Povozhskiy State University of Telecommunications and Informatics, 23 Lev Tolstoy Street, 443010 Samara, Russia
Vladimir A. Burdin
Department of Communication Lines, Povozhskiy State University of Telecommunications and Informatics, 23 Lev Tolstoy Street, 443010 Samara, Russia
Oleg G. Morozov
Department of Radiophotonics and Microwave Technologies, Kazan National Research State University Named after A.N. Tupolev-KAI, 10 Karl Marx Street, 420111 Kazan, Russia
This article proposes an advanced algorithm for the numerical solution of a coupled nonlinear Schrödinger equations system describing the evolution of a high-power femtosecond optical pulse in a single-mode polarization-maintaining optical fiber. We use the algorithm based on a variant of the split-step method with the Madelung transform to calculate the complex amplitude when executing a nonlinear operator. In contrast to the known solution, the proposed algorithm eliminates the need to numerically solve differential equations directly, concerning the phase of complex amplitude when executing the nonlinear operator. This made it possible, other things being equal, to reduce the computation time by more than four times.
