Semiclassical numerical modeling of gain materials with a high order Discontinuous Galerkin time-domain solver

Description

This paper is concerned with numerical modeling of the interaction between an electromagnetic field and a gain medium in the context of laser physics, with the goal of simulating the gain process that results in an increase in optical power. This phenomenon can be modelled by a four-level atomic differential system that couples Maxwell's equations with a set of non-linear Ordinary Differential Equations (ODEs) to describe the electronic density evolution for each energy level. Most of the existing works dealing with this model consider the Finite Difference Time-Domain method (FDTD) as seen in [1]. In this article, we will present a novel numerical modeling leveraging a Discontinuous Galerkin Time-Domain method (DGTD) in 3D that we have formulate to solve this model and will propose an estimation for the continuous energy associated to the system. Based on the work done in [5], we used a second order LeapFrog temporal scheme and made approximation for the nonlinear terms present in the ODEs. An energy estimate, for both continuous problem and the discrete scheme, inspired by the work done in [3] allows us to prove stability of the scheme. The method is validated in a 3D framework using a model problem with manufactured solution.

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