Numerical methods for accurate description of ultrashort pulses in optical fibers
- Amiranashvili, Shalva
- Radziunas, Mindaugas
- Bandelow, Uwe
- Čiegis, Raimondas
2010 Mathematics Subject Classification
- 35Q55 65M70 65M06 65M12
2008 Physics and Astronomy Classification Scheme
- 02.70.Hm 02.70.Bf 02.60.Jh 42.81.Dp
- Forward Maxwell Equation, Nonlinear Schrödinger Equation, Splitting algorithm, Lax Wendroff method, Numerical experiments
We consider a one-dimensional first-order nonlinear wave equation (the so-called forward Maxwell equation, FME) that 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. We compare FME to the commonly accepted generalized nonlinear Schrödinger 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.
- Commun. Nonlinear Sci. Numer. Simul., (2018), published online on 23.07.2018, DOI 10.1016/j.cnsns.2018.07.031 .