Asymptotic methods for evaluation of diffractive lenses

We employ asymptotic methods to speed up the computation of fields in the f ocal region of diffractive lenses (DLs). Each DL is treated locally as a li near grating with slowly varying period and groove orientation. Rigorous el ectromagnetic diffraction theory is employed locally to obtain the field ju st behind the DL. The field in the focal region is then obtained by use of Rayleigh-Sommerfeld's first diffraction formula, and accurate asymptotic te chniques are employed for efficient evaluation of diffraction patterns. The asymptotic techniques provide a significant reduction in the computing tim e at negligible loss of accuracy. Thus, to an accuracy of better than 1% th ey are two orders of magnitude faster than numerical evaluations of the dif fraction integrals.