Practitioner's guide to laser pulse propagation models and simulation

The purpose of this article is to provide practical introduction into numerical modeling of ultrashort optical pulses in extreme nonlinear regimes. The theoretic background section covers derivation of modern pulse propagation models starting from Maxwell's equations, and includes both envelope-based models and carrier-resolving propagation equations. We then continue with a detailed description of implementation in software of Nonlinear Envelope Equations as an example of a mixed approach which combines finite-difference and spectral techniques. Fully spectral numerical solution methods for the Unidirectional Pulse Propagation Equation are discussed next. The modeling part of this guide concludes with a brief introduction into efficient implementations of nonlinear medium responses. Finally, we include several worked-out simulation examples. These are mini-projects designed to highlight numerical and modeling issues, and to teach numerical-experiment practices. They are also meant to illustrate, first and foremost for a non-specialist, how tools discussed in this guide can be applied in practical numerical modeling.