Numerical Tool for Calculating Birefringence in Mirror-Substrates for Gravitational-Wave Detectors

Abstract

The influence of birefringence on rays entering and exiting a non-isotropic medium is a complex process that depends on its dielectric tensor, the orientation and geometry of the medium, the surrounding material, and the inclination of the incident ray. Thus, when aiming for a calculation of the effects, many parameters need to be taken into account while simplifications are generally not applicable. Moreover, the complexity of the general issue makes it almost impossible to find an analytical solution for backward calculations of stress-birefringence from polarization measurements. In this paper, a report is given on the formulation of a birefringence ray-tracing program in Python for the convenient evaluation of optical effects inside uniaxial crystals under stress. The aim thereby is to have an easily applicable tool that can be used in interferometer commissioning for current and future gravitational-wave detectors. Results from test simulations using realistic parameters for a sapphire mirror as used in the gravitational-wave detector KAGRA are implemented and show the capabilities of this tool.