Wave-optical structure design with the local plane-interface approximation

Abstract

The design of an optical element profile with specified transmission function for a given incident wave is of fundamental concern in optical design. A well-known example is the design of an aspherical surface in order to realize a spherical phase-only transmission. Various wave-optical system design methods lead to transmission functions as a first step. Then, often the thin-element approximation is applied in a second step to obtain an element structure with the desired transmission. However, if the refraction at the optical interface cannot be neglected, the thin-element approximation is not valid. In this case, a higher version of the local plane-interface approximation can be used for the element structure design. An algorithm for this model is introduced and its characteristics are discussed for the example of a non-paraxial Gaussian-to-tophat beam shaping element

Parabasal thin-element approximation approach for the analysis of microstructured interfaces and freeform surfaces

“…Then field properties, e.g., field value, polarization state, and so on are traced along the ray within one tube. The interaction between a ray and the related local tangential plane is assumed to be that between a plane wave and a plane interface [8]. In GeOp, four physical effects are discussed: (1) the optical path length (OPL); (2) the absorption factor α n along the optical path in the media; (3) the boundary effect operator β n ; and (4) the intensity law of geometrical optics, α GeOp n , which is related to the section of the tube [7].…”

Step-discontinuity approach for non-paraxial diffractive optics

“…This provides further support to our expectation that the primary reason for the early failure of the thin-element approximation in the non-paraxial domain is boundary diffraction at the abrupt transitions in the profile. The results of the perturbation approach could probably be improved further by involving considerations such as those presented in [8] where refraction at the analogue boundary is considered locally. However, such considerations are beyond the scope of this paper.…”