Effective Numerical Integration of Traveling Wave Model for Edge‐emitting Broad‐area Semiconductor Lasers and Amplifiers

Abstract

Abstract. We consider a system of 1 + 2 dimensional partial differential equations which describes dynamics of edge-emitting broad area semiconductor lasers and amplifiers. The given problem is defined on the unbounded domain. After truncating this domain and defining an auxiliary 1 + 1 dimensional linear Schrödinger problem supplemented with different artificial boundary conditions, we propose an effective strategy allowing to get a solution of the full problem with a satisfactory precision in a reasonable time. For further speed up of the numerical integration, we develop a parallel version of the algorithm.

Effective Numerical Algorithm for Simulations of Beam Stabilization in Broad Area Semiconductor Lasers and Amplifiers

“…(n: background refraction index, k 0 = 2π λ0 : central wavenumber, λ 0 : central wavelength, c 0 : speed of light in vacuum, n g : group velocity index) and a suitable normalization of parameters and dynamical variables, the TW model can be written as follows [5]:…”

“…In our previous paper [5] we have investigated the performance of the standard Crank-Nicolson scheme supplemented with different BCs, including the exact discrete transparent boundary conditions (DTBCs) [8], and the approximate DTBCs suggested by Szeftel [26]. High order numerical approximations of BCs on nonuniform space grids are considered in [7,21].…”

“…Normalization of the equations and typical values of the normalized parameters were given in [5]. It is noteworthy, that typical values of γ ≈ 10 2 ÷ 10 3 and µ ≈ 10 −3 represent the fast relaxation of the polarization functions P ± and the slow dynamics of the carrier density N , respectively.…”

“…This model is based on the TW equations for counter-propagating and laterally diffracted slowly varying optical fields which are coupled to the ODE for induced polarizations and diffusive rate equation for carrier densities [3,25]. The well-posedness of this model was studied in [14], while different algorithms used for the numerical integration of the model were investigated in [5,6,13]. A possibility to formulate various boundary conditions and compact numerical approximations of these conditions are considered in [21].…”

“…The approximation of all equations is done on the same space grid, while a staggered grid was used in our previous papers [5,6]. A parallel version of this finite difference scheme is developed.…”