The quarter wave plate applied to the extreme ultraviolet (EUV) region can realize the conversion of linear polarization and circular polarization EUV light source, so it has a wide range of applications such as magnetic microscopy techniques based on circularly polarized light. In this paper, a lineally chirped Mo/Si multilayer mirror is used to design a EUV quarter-wave plate. With the increasing thickness variation value of linearly chirped multilayer, the reflective phase delay between s- and p-polarized light increases at first and then realizes its maximum value. In this case, a quarter wave plate that can realize 90° phase delay can be designed by optimizing the structure parameters of a linearly chirped multilayer mirror. A linearly chirped Mo/Si multilayer which contains 13 pairs of bilayers with 14.7 nm central thickness and 1.94 nm thickness variation can achieve a reflective phase retardation of 89.95° at 90 eV under 30° grazing incidence. At the same time, the reflectivity of s- and p-polarized light are 47.65% and 10.09% respectively. The development of an EUV quarter wave plate based on a linearly chirped multilayer mirror could promote the research on the production and application of circularly polarized EUV light sources.
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