Numerical methods for accurate description of ultrashort pulses in optical fibers
| Autor: | Shalva Amiranashvili, Raimondas Čiegis, Uwe Bandelow, Mindaugas Radziunas |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
02.60.Jh
Splitting algorithm 02.70.Hm 42.81.Dp 65M06 02.70.Bf symbols.namesake Nonlinear medium Forward Maxwell Equation Nonlinear Schrödinger Equation Nonlinear Schrödinger equation 65M70 Numerical experiments Envelope (waves) Physics Numerical Analysis Slowly varying envelope approximation Applied Mathematics 65M12 Mathematical analysis Lax Wendroff method Wave equation Pulse (physics) 35Q55 Nonlinear system Modeling and Simulation symbols Spectral method |
| Zdroj: | Communications in Nonlinear Science and Numerical Simulation. 67:391-402 |
| ISSN: | 1007-5704 |
| DOI: | 10.1016/j.cnsns.2018.07.031 |
| Popis: | We consider a one-dimensional first-order nonlinear wave equation, the so-called forward Maxwell equation (FME), which applies to a few-cycle optical pulse propagating along a preferred direction in a nonlinear medium, e.g., ultrashort pulses in nonlinear fibers. The model is a good approximation to the standard second-order wave equation under assumption of weak nonlinearity and spatial homogeneity in the propagation direction. We compare FME to the commonly accepted generalized nonlinear Schrodinger equation, which quantifies the envelope of a quickly oscillating wave field based on the slowly varying envelope approximation. In our numerical example, we demonstrate that FME, in contrast to the envelope model, reveals new spectral lines when applied to few-cycle pulses. We analyze and compare pseudo-spectral numerical schemes employing symmetric splitting for both models. Finally, we adopt these schemes to a parallel computation and discuss scalability of the parallelization. |
| Databáze: | OpenAIRE |
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