Generalized Curvilinear Diffraction Gratings: II. Generalized ray equations and caustics

Abstract

This paper is the second in a series [1] of papers on the diffraction and imaging properties of generalized curvilinear diffraction gratings. In this article, a set of generalized ray equations is derived and applied to the calculation of the caustic properties of generalized gratings. No restriction is placed on the form of the ruling pattern or on the shape of the grating surface. For generalized uncrossed and off-axis plane gratings, the ruling pattern may be regarded as a contour map of some abstract surface. In this case, it is shown that the far-field caustic properties of the grating are determined by the regions of vanishing gaussian curvature on the abstract surface. As an application of the theory, a new method for laser material processing is discussed.