Mathematical modelling of a crystal spatial light mixer

Abstract

We establish a mathematical model of a crystal spatial light mixer based on the principle of crystal birefringence and splitting. The spatial light mixer consists of two crystals, three quarter-wave plates, four half-wave plates, two planar mirrors and two polarization beam splitting prisms (PBS). After the signal light and the local oscillator light pass through the spatial optical mixer, four channels of coherent light with 90° relative phase differences are output. According to the established mathematical model of spatial optical mixers, the fabrication error of components, the monochromaticity of the light source, the angle between the PBS and the light beam are simulated and analyzed. Error simulation results show that the phase noise is 4.14° when the crystal processing error is 10 nm and the refractive index error is 0.172 when the angle between the beam and the PBS is 0.0183°. The maximum phase noise that can be generated is 2.278°. The phase error of a new spatial optical mixer evolved from the mathematical model satisfies the allowable range of the Costas phase-locked loop error. It can be used in a space coherent laser communication system to improve its detection sensitivity.