Statistical analysis of crossed undulator for polarization control in a self-amplified spontaneous emission free electron laser

There is a growing interest in producing intense, coherent x-ray radiation with an adjustable and arbitrary polarization state. In this paper, we study the crossed-undulator scheme [K.-J. Kim, Nucl. Instrum. Methods Phys. Res., Sect. A 445, 329 (2000)] for rapid polarization control in a self-amplified spontaneous emission (SASE) free electron laser (FEL). Because a SASE source is a temporally chaotic light, we perform a statistical analysis on the state of polarization using FEL theory and simulations. We show that, by adding a small phase shifter and a short (about 1.3 times the FEL power gain length), 90 degrees rotated planar undulator after the main SASE planar undulator, one can obtain circularly polarized light with over 80% polarization-near the FEL saturation.