A bidirectional pulse propagation model for extreme nonlinear optics: derivation and implementation.

Abstract

With growing capabilities of high-intensity laser beams to generate ultra-short pulses of light, the simulation of pulse propagation in nonlinear media is expected to catch up with the front-line experimental setups. Among the challenges of nonlinear material response modeling is the ability to capture the back-scatter effect - a phenomenon inherently elusive for the well-established methods of unidirectional type. In this paper we consider a bidirectional shooting method proposed by P. Jakobsen in "Bidirectional pulse propagation equation for extreme nonlinear optics.", Physica Scripta, 89:095502, 2014. We derive the method for a Transverse Magnetic (TM) field, propagating in a material slab with a Kerr-type nonlinear polarization response, and delimited by two material interfaces. By performing a proof-of-concept implementation of the method, we demonstrate that it is indeed capable of reconstructing the expected quantitative and qualitative properties of the modeled physical system, including reflection from interfaces and third harmonic generation. Nevertheless, we find that both the accuracy of the solution, as well as the convergence of the iterative process, are negatively impacted by an increase in the relative scale of the nonlinearity coefficient. That points to the limitations of the underlying implementation and, potentially, the BPPE method itself. In that context we conclude with a brief discussion of the interdependence between the BPPE method and its numerical incarnations.