Design of broad angular phase retarders for the complete polarization analysis of extreme ultraviolet radiation

A method of designing broad angular phase retarders in the extreme ultraviolet (EUV) region is presented. The design is based on a standard Levenberg-Marquardt algorithm combined with a common merit function. Using this method, a series of broad angular EUV phase retarders were designed using aperiodic Mo/Si multilayers. At photon energy of 90 eV, broad angular phase retarders with 30°, 60°, and 90° phase retardations have been realized in the angular range of 39°-51°. By analyzing and comparing the performances of the designed broad angular phase retarders, we found that the Mo/Si multilayer with more layers could obtain higher phase retardation in broader angular range when used to design the broad angular phase retarder. Broad angular phase retarders possess lower sensitivity toward changing incident angle compared with the traditional phase retarders designed with transmission periodic multilayers, and can be used for the polarization control of broad angular EUV sources.