Rigorous analysis and design of diffractive cylindrical lenses with high numerical and large geometrical apertures

Abstract

A concept is presented for the analysis of diffractive cylindrical lenses with apertures larger than 100 wavelengths which are denoted as large geometrical apertures throughout this paper. The transmitted field of a cylindrical lens is calculated by the use of rigorous electromagnetic diffraction theory. Large geometrical apertures are subdivided into smaller overlapping areas that are treated in sequence. The wave propagation from the lens plane to the focal plane is calculated with the spectrum of plane waves. A design concept is presented which ensures that the performance of diffractive cylindrical lenses with high numerical apertures (NA≥0.3) is almost independent of the polarization of the illuminating light. The design concept is based on the local grating model in combination with the phase detour principle. As an example we design and analyze a F/0.5 cylindrical lens (NA=0.71) with a geometrical aperture of 600 wavelengths.