Simulation of amplified spontaneous emission in high gain KrF laser amplifiers

Abstract

High gain KrF amplifier simulations require a realistic model of amplified spontaneous emission (ASE). We have recently developed an accurate three-dimensional time-dependent code to model ASE and parasitic oscillations in the Nike and Electra amplifiers. It currently includes arbitrary specular reflections at all of the walls and can be easily extended to nonspecular reflections. It can also simulate the ASE that would be seen by another amplifier stage or a camera located outside the amplifier module. The code approximates the ASE light by a discrete set of ordinates or quasi-plane waves whose propagation vectors represent all directions, but cluster preferentially around the amplifier axis, where the gain is highest. At each grid point, it updates the directed intensity by adding an analytic solution of the radiation transport equation within time increment Δt to the earlier intensity at a “local look-back” (LLB) point; this point is located a distance cΔt back along the ordinate’s characteristic direction. Because the LLB does not generally lie at a grid point, interpolation is required to calculate the earlier flux. Trilinear interpolation is simple and computationally fast, but it can introduce numerical spatial diffusion in the specific intensity. This diffusion is usually tolerable, but it can be a significant limitation if one attempts to treat a problem where the operating conditions or ASE viewing position favor a narrow range of directions that are not parallel to one of the Cartesian axes. For those conditions, we use an alternative interpolation scheme based on the flux-corrected transport algorithm, which previously has been used only to treat shock wave propagation in fluids. This article describes the code in detail, then shows ASE simulations illustrating the code’s capabilities and the effects of transient excitation, diffusion, and gain narrowing.