Polarization control of an x-ray free electron laser oscillator

High-intensity, fully coherent x-ray pulse with a tunable polarization over a wide spectral range is of great importance to many experiments. In this paper, we propose a tapered crossed-polarized undulator configuration for an x-ray free electron laser oscillator (XFELO) to produce arbitrarily polarized x-ray pulses in the hard x-ray region. A numerical example utilizing the parameters of the Shanghai High-Repetition-Rate XFEL and Extreme Light Facility (SHINE) is presented to demonstrate the generation of polarization controllable, fully coherent hard x-ray pulses with 99.9% polarization degree and 20 kHz polarization switching rate. The analysis presents that this scheme holds the possibility to be used in an energy tunable XFELO built from multiple Bragg mirrors.