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

We present a hybrid diffraction model for the efficient analysis of diffrac tive optical elements. This model uses a scalar-based approximation over th ose regions of the boundary that satisfy the scalar criteria and a vector-b ased solution over those that do not. In analyzing diffractive optical elem ents (DOEs) it becomes necessary to use a vector-based model as the feature sizes within the DOE profile approach the scare of the illumination wavele ngth. However, in many instances only certain regions of a profile contain such small-scale features, in these cases it is inefficient to perform a ve ctor-based analysis over the entire profits. Therefore, we have developed a method that allows for the concatenation of scalar- and vector-based solut ions. This is achieved by simply assigning the surface field values accordi ng to the scalar approximation over those regions of the profile that satis fy the scalar criteria, and using the the finite-difference time-domain (FD TD) 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, th e FDTD method, and the method far propagating the concatenated boundary fie lds. (C) 2000 Society of Photo-Optical Instrumentation Engineers. [S0091-32 86(00)01707-4].