  High-intensity, fully coherent X-ray radiation 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 X-ray
free electron laser oscillator (XFELO) to produce arbitrarily polarized X-ray
pulses in 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. This scheme also holds the possibility to be used
in cavity tunable XFELO.
