Analysis of birefringence effects in laser crystals by full vectorial beam propagation method

Abstract

Modern laser technology demands powerful numerical tools to predict the efficiency of laser configurations. Birefringence has a strong influence on the beam quality and output power of a laser amplifier. We developed a complex physical model for simulating laser amplifiers and analyzing the birefringence effects. This model includes pump configuration, thermal lensing effects, birefringence, and beam propagation in the laser amplifier. The pump configuration is simulated using a complete three-dimensional ray tracing or by an approximation based on super-Gaussian functions. For an accurate modeling of the thermal lensing effect, the deformation of the end faces and the polarization dependent index of refraction was taken into account. Temperature, deformation and stress inside the laser crystal were calculated by a three-dimensional finite element analysis (FEA). In particular, the refractive index was accurately calculated by considering its temperature dependency and the photo elastic effect. This refractive index was used in the simulation of laser beam propagation through an amplifier. These simulations were performed by a complete three-dimensional vectorial beam propagation method (VBPM). The advantage of VBPM is that it can be applied to a polarization dependent index of refraction. This is important when taking into account the birefringence obtained by the photo elastic effect inside the laser crystal. The beam propagation method is based on finite elements on block structured grids as well as a Crank-Nicolson approximation in the propagation direction (FE-BPM). Reflecting boundaries were eliminated by introducing a perfect matching layer (PML). Simulation results show that a complete three-dimensional simulation model was useful in analyzing and optimizing high power laser amplifiers. The value of our model lies in the fact that it can take into account the crystal cut direction. Based on this the birefringence for simulating the laser beam quality and output power can be calculated.