Polarization Analysis of Nonlinear Harmonic Radiation in a Crossed-Planar Undulator

There is growing interest in producing intense, coherent x-ray radiation with an adjustable and arbitrary polarization state. The crossed-planar undulator, which was first proposed by Kim, could achieve rapid polarization control in synchrotron radiation sources and free electron lasers (FELs) through the manipulation of a phase shifter. Recently, a statistical analysis shows that a polarization degree of over 80% is obtainable for a Self-Amplified Spontaneous Emission (SASE) FEL near saturation. In such a scheme, nonlinear harmonic radiation is also generated in each undulator and the polarization of the radiation is controllable in the same manner. In this paper, we study the degree of polarization achievable at the third harmonic in a crossed-planar undulator. We also propose a method for generating second harmonic radiation with arbitrary polarization.