Combined scalar-vector method for the analysis of diffractive optical elements

Abstract

We present a hybrid diffraction model for the efficient analysis of diffractive optical elements. This model uses a scalar-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 becomes necessary to use a vectorbased model as 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 field values according to the scalar approximation over those regions of the profile that satisfy the scalar criteria, and using the the finite-difference time-domain (FDTD) method 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 this paper we discuss the formulations of scalar diffraction theory, the FDTD method, and the method for propagating the concatenated boundary fields.