A new method for computing eigenmodes of a laser resonator by the use of finite element analysis is presented. For this purpose, the scalar wave equation (delta + k2)E(x, y, z) = 0 is transformed into a solvable three-dimensional eigenvalue problem by the separation of the propagation factor exp(-ikz) from the phasor amplitude E(x, y, z) of the time-harmonic electrical field. For standing wave resonators, the beam inside the cavity is represented by a two-wave ansatz. For cavities with parabolic optical elements, the new approach has successfully been verified by the use of the Gaussian mode algorithm. For a diode-pumped solid-state laser with a thermally lensing crystal inside the cavity, the expected deviation between Gaussian approximation and numerical solution could be demonstrated clearly.
a LASCAD is a protected trademark of LAS-CAD GmbH Numerical Simulation of Diode Pumped Solid State Lasers (DPSSL) .In DPSSL the beam of a laser diode is used to pump a laser crystal (see [2]). After entrance into the crystal the pump beam is absorbed by the lasing atoms. The absorbed photons raise the atoms into a higher energy level. The population inversion generated in this way is used to amplify the laser beam by stimulated emission. However, only a fraction of the absorbed power is converted into laser light, dependent on the quantum efficiency of the laser up to about 30% can be converted into heat. The heat distribution remaining in the crystal constitutes an important technical problem for the design of solid state lasers. There is not only the necessity to remove the heat through heat sinks, but due to the temperature dependence of the refractive index of the crystal a 3D refractive index distribution is generated that modifies the optical properties of the laser resonator built around the crystal. Together with the thermal deformation of the surfaces of the crystal this can seriously effect beam quality and efficiency of the laser. Also there is the risk that high stress levels destroy the crystal. Therefore, it is important to support design of DPSSL by numerical simulation. The latter can be carried through in four steps:1. Calculation of the heat source in the resonator by the use of analytical approximations or by ray-tracing.2. Calculation of the temperature in the resonator by a FE-approximation.3. Calculation of the deformation and stresses of the laser crystal by a FE-approximation.4. Calculation of the mode structure of the laser beam by a Gaussian-mode analysis in combination with parabolic fits of FE-results or by a wave optics code solving Maxwell equations.These methods analyze the laser beam on a structured grid. Therefore, the temperature and deformation of the crystal are needed on a structured grid.For the calculation of the temperature T and the deformation u, one has to solve a non-linear heat equationand a linear elasticity equation:where C is a suitable 6 × 6 matrix (see [1]). To solve these differential equations, we applied a finite element discretization on semi-unstructured grids (see [4]) that have several properties which are very useful in the application of laser simulation:
Abstract. Semi-unstructured grids consist of a large structured grid in the interior of the domain and a small unstructured grid near the boundary. It is explained how to implement differential operators and multigrid operators in an efficient way on such grids. Numerical results for solving linear elasticity by finite elements are presented for grids with more than 10 8 grid points.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.