A Beam Propagation Method for Distorted Gaussian Beams. Issue 1 (18th November 2019) - Pflaum, Christoph
Abstract: Distorted Gaussian beams arise in several applications in optics. One of them is a laser amplifier. In a laser amplifier a Gaussian beam is distorted by thermal lensing effects, polarization effects and gain guiding. This leads to a decrease of the beam quality at the output of a laser amplifier. An important question is how to calculate this decrease of the beam quality and how to compute the amplified beam. There exist several difficulties of existing simulation techniques for the computation of optical beams. These are the high computational amount in order to resolve the phase of the beam and modelling non‐absorbing boundary conditions. We present a new beam propagation method, which circumvents these difficulties. The idea is to decompose the beam as a product of a Gaussian Beam TEM00 and an unknown distortion function Ξ. This leads to an interesting partial differential equation for Ξ, which contains a beam spreading convection term. This PDE is solved numerically by finite elements and a Crank‐Nicolson space stepping discretization. The resulting linear equation system is solved by GMRES. The q‐parameter of the Gaussian beam is calculated in advance by an ABCD matrix method. This leads to a highly efficient simulation technique. It can be applied to simulate the amplification of Gaussian beams in laser amplifiers.