TY - JOUR

T1 - Numerical Splitting Schemes for Solving the Ginzburg–Landau Equation with Saturated Gain and Cubic Mode Locked

AU - Medvedev, S. B.

AU - Shtyrina, O. V.

AU - Vaseva, I. A.

AU - Paasonen, V. I.

AU - Fedoruk, M. P.

N1 - The work of S.B. Medvedev, O.V. Shtyrina (the development of the algorithm with moments), and I.A. Vaseva (numerical studies) was supported by the Russian Science Foundation (project no. 22-11-00287), and the work of the V.I. Paasonen (the development of the modified algorithm) and of M.P. Fedoruk (problem formulation) was supported by the Russian Science Foundation (project no. 20-11-20040). Публикация для корректировки.

PY - 2023/12

Y1 - 2023/12

N2 - The general characteristics of an optical signal as a result of generation in a resonator can be described using a dynamic model based on the complex cubic Ginzburg–Landau equation, which takes into account the saturated gain and dissipative terms responsible for the distributed action of various intracavity devices. The paper proposes two new effective modifications of the split-step Fourier method for a numerical solution to equations of this type. The first algorithm is based on the application of a new way of separating physical processes affecting the optical signal during propagation in a fiber, which made it possible to express the action of both nonlinear and dispersive spatial steps by explicit analytical expressions. The second proposed method enabled significant improvement in the accuracy of calculations due to including energy evolution in the coefficients of the equation. Numerical experiments have shown that the new schemes can produce the second order of approximation with respect to the evolutionary variable in contrast to the classical scheme that provides only the first order of approximation.

AB - The general characteristics of an optical signal as a result of generation in a resonator can be described using a dynamic model based on the complex cubic Ginzburg–Landau equation, which takes into account the saturated gain and dissipative terms responsible for the distributed action of various intracavity devices. The paper proposes two new effective modifications of the split-step Fourier method for a numerical solution to equations of this type. The first algorithm is based on the application of a new way of separating physical processes affecting the optical signal during propagation in a fiber, which made it possible to express the action of both nonlinear and dispersive spatial steps by explicit analytical expressions. The second proposed method enabled significant improvement in the accuracy of calculations due to including energy evolution in the coefficients of the equation. Numerical experiments have shown that the new schemes can produce the second order of approximation with respect to the evolutionary variable in contrast to the classical scheme that provides only the first order of approximation.

KW - Ginzburg–Landau equation

KW - mathematical modeling of pulse generation

KW - split-step Fourier method

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85187906943&origin=inward&txGid=3ae5ecfdd05c1aea40a96b7e15faab88

UR - https://www.mendeley.com/catalogue/bbc35a6e-5ae2-3c67-a392-5060ba936c80/

U2 - 10.3103/S1068335623602443

DO - 10.3103/S1068335623602443

M3 - Article

VL - 50

SP - S1484-S1491

JO - Bulletin of the Lebedev Physics Institute

JF - Bulletin of the Lebedev Physics Institute

SN - 1068-3356

IS - Suppl 13

ER -