Axial focusing characteristics of diffractive micro-lenses based on a rigorous electromagnetic theory

In order to determine the assembling error at the receiving plane and to obtain the maximum energy efficiency, it is necessary to study the axial focusing characteristics of diffractive micro-lenses such as the focal depth and the focal shift. When the diffractive optical elements' features are of the order of or smaller than the wavelength of the incident illumination, their electromagnetic characteristics must be considered. By using a two-dimensional finite-difference time-domain (FDTD) method, we present a rigorous electromagnetic analysis of diffractive micro-lenses that are finite in extent, in the case of a normally incident light wave. Compared with the scalar theory, the axial intensity distributions of diffractive micro-lenses are analysed rigorously, for different incidence polarizations (TE polarization and TM polarization), different profile structures (continuous profile, 16-level profile, 8-level profile, and 2-level profile) and different f-numbers of lenses. The numerical results show that the focal shifts calculated by the electromagnetic theory are larger than those made by the scalar theory, and the focal depths calculated by these two methods are basically consistent. The focal depth and the focal shift will increase when the f-number increases, for both the rigorous electromagnetic theory and the scalar theory.