Based on the previous Letter [Opt. Lett.29, 2345 (2004) ], we significantly extend the applications of the improved first Rayleigh–Sommerfeld method (IRSM1) to analyze the focusing performance of cylindrical microlenses for different types of profile (continuous or stepwise), different f-numbers (from f∕1.5 to f∕0.75), and different polarizations (the TE or TM). A number of performance measures of the cylindrical microlenses, such as the focal spot size, the diffraction efficiency, the real focal position, and the normalized sidelobe power, are studied in detail. We compare numerical results obtained by the IRSM1, by the original first Rayleigh–Sommerfeld method (ORSM1), and by the rigorous boundary element method (BEM). For continuously refractive lenses, the results calculated by the IRSM1 are quite close to those obtained by the BEM; in contrast, the results calculated by the ORSM1 significantly deviate from those obtained from the rigorous BEM. For multilevel diffractive lenses, the IRSM1 also provides much more accurate results than the ORSM1. In addition, compared with the BEM, a notable advantage of the IRSM1 is much lower computer memory and time consumption in computations.
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