Validity range of the improved Rayleigh-Sommerfeld method in analyzing metallic cylindrical focusing micromirrors

Through changing various parameters, the validity range of the improved Rayleigh-Sommerfeld method (IRSM) in analyzing metallic cylindrical focusing micromirrors (MCFMs) is studied in detail. Focal properties of the MCFMs including the focal spot size, diffraction efficiency, and real focal position are calculated by the IRSM. Rigorous performance results by the boundary element method are also presented as an accurate reference. Numerical results reveal that the IRSM performs well for cylindrically continuous micromirrors even when the f-number decreases to f/0.25. In addition, it is found that for continuous micromirrors the IRSM validity range is insensitive to the incident wavelength and the material refractive indices. However, for continuously diffractive or multilevel diffractive micromirrors, the IRSM is no longer valid when the f-number is less than f/1.0.