Applicability of improved Rayleigh-Sommerfeld method 1 in analyzing the focusing characteristics of cylindrical microlenses

The applicability of an improved Rayleigh-Sommerfeld method 1 (IRSM1) is investigated by analyzing the focal characteristics of various cylindrical microlenses in both cases of the TE and TM polarizations. The IRSM1 and original Rayleigh-Sommerfeld method 1 (ORSM1) are compared with rigorous boundary element method (BEM) by calculating the average square-root deviation (ASRD) of the intensity distribution on the focal plane for the continuously refractive microlens and diffractive microlenses with continuously varying or 8-level quantized profiles. The results indicate that the applicability of the IRSM1 has limitation in some parametric ranges, for instance, the number of sampling points, f-number, relatively refractive index, and wavelength of the incident light are restricted to some appropriate values.