On the efficiency of different numerical methods for the calculation of intrapulse Raman scattering of optical solitons

• Published in: Optical and quantum electronics Vol. 51; no. 8; pp. 1 - 16
• Main Authors: Uzunov, Ivan M., Arabadzhiev, Todor N.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2019; Springer Nature B.V
• Subjects: ASYMMETRY; Asymptotic methods; Asymptotic properties; ASYMPTOTIC SOLUTIONS; BOUND STATE; Characterization and Evaluation of Materials; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computer Communication Networks; EFFICIENCY; Electrical Engineering; Evolution; FIBER OPTICS; FORECASTING; Frequency shift; Lasers; Methods; NONLINEAR PROBLEMS; Numerical analysis; Numerical methods; NUMERICAL SOLUTION; Optical Devices; OPTICAL FIBERS; Optics; PERTURBATION THEORY; Photonics; Physics; Physics and Astronomy; Propagation; RAMAN EFFECT; Raman spectra; RESOLUTION; Runge-Kutta method; Schrodinger equation; Solitary waves; SOLITONS; Methods for the numerical solution of the nonlinear Schrödinger equation (NLSE) and a perturbed NLSE; Intrapulse Raman scattering; Nonlinear fiber optics; Optical solitons
• ISSN: 0306-8919; 1572-817X
• DOI: 10.1007/s11082-019-1999-1

In this paper we compare the performance of different numerical methods for the calculation of the asymptotic evolution of soliton self-frequency shift in the presence of intrapulse Raman scattering (IRS) in optical fibers. First we have calculated the order of global accuracy for the fundamental soliton and the second-order bound state of the unperturbed nonlinear Schrödinger equation for the following numerical methods: the simple split step (SS) method, the full SS method, the reduced SS method, the reduced SS method with fourth order Runge–Kutta (RK4), the Blow–Wood method, the fourth order Runge–Kutta in the interaction picture (RK4IP) method and the Agrawal SS method with one and two iterations. We have shown that the asymptotic evolution of soliton self-frequency shift in the presence of IRS in optical fiber can be best described by the Agrawal SS method (compared to the Blow–Wood method and the RK4IP method). The obtained numerical results for the soliton position and frequency are in agreement with the predictions for these parameters according to the perturbation theory. We have shown that in the presence of IRS the fundamental soliton quickly develops an oscillating tail on its left. The generated tail hardly influences the soliton propagation at large distances. At large distances the form of the soliton gradually becomes asymmetric. The increase of the frequency resolution leads to a notable increase of the maximum propagation distance of the numerical soliton under the influence of IRS.