Hybrid scalar-vector method for the analysis of electrically large finite aperiodic diffractive optical elements

In this paper we present a hybrid diffraction model that uses a scaler-based approximation over those regions of the boundary that satisfy the scalar criteria and a vector-based solution over those that do not. In analyzing diffractive optical elements (DOEs) it is necessary to use a vector-based model when the feature sizes within the DOE profile approach the scale of the illumination wavelength. However, in many instances only certain regions of a profile contain such small scale features. In these cases it is inefficient, to perform a vector-based analysis over the entire profile. Therefore, we have developed a method that allows for the concatenation of scalar- and vector-based solutions. This is achieved by simply assigning the surface held values according to the scaler approximation over those regions of the profile that satisfy the scalar criteria, and using the the finite-difference time-domain method (FDTD) to determine the surface fields over those regions that contain small scale features. In combination these methods create a surface profile that can be propagated to any plane, or region, of interest. In the course of our paper we will discuss the formulations of scalar diffraction theory and the FDTD, in addition to the method for propagating the concatenated boundary fields.