Analysis and synthesis of 2-D diffractive lens using the local linear grating model and the coupled-wave theory

Abstract

Large numerical aperture diffractive lenses have many applications for imaging and beam coupling. Since the minimum Fresnel zone width of a diffractive lens is approximately proportional to F-number: rM - rM-1 = 2λF/#, the grating period in the region close to the lens edge is comparable with the wavelength λ, for a fast lens. The diffraction of such surface relief wavelength-scale structures should be solved with rigorous electromagnetic theory. Most methods with the resonance domain diffraction theory for analysis and synthesis of diffractive optics elements are for 1-D and 2-D separable gratings, 1-D cylindrical lens and 2-D lens arrays1. Those elements are treated with the 1-D grating model. However, rigorous analysis of a single 2-D radially symmetrical diffractive lens needs solutions of the 3-D Maxwell The numerical solutions with the finite-element methods2 are usually computational expansive.