Design of efficient broadband extreme ultraviolet multilayer mirrors using a two-parametric merit function

Broadband reflection is a basic need in extreme ultraviolet (EUV) optics, especially for the control of a broadband source such as attosecond pulse. In this paper, we propose a design method of broadband EUV multilayer mirrors based on genetic algorithm with a two-parametric merit function. Compared with a traditional merit function, which generally employs the root-mean-square deviation of the calculated reflectivity from the target reflectivity, the proposed two-parametric merit function consisting of mean value and mean square deviation of the reflectivity can realize higher mean value and lower mean square deviation of reflectivity in the desired band, without setting the target reflectivity in advance. Using this two-parametric merit function, a broadband EUV mirror with 20.35% mean value and 0.5% mean square deviation of reflectivity is realized in the wavelength range from 60 eV to 80 eV by optimizing an aperiodic Mo/Si multilayer. In addition, the broadband EUV mirrors for different bands are designed, and their performances of broadband reflection are analyzed and compared. Our research provides a way of designing an efficient broadband multilayer with absorbing materials, and could improve the study on the control of broadband EUV sources.