Physical-optics propagation through curved surfaces

Curved surfaces are the basic elements of various optical components and systems such as microscopy systems, diffractive optical elements, freeform components, microlens arrays, etc. In order to model the propagation through curved surfaces fully vectorially and fast, the local plane interface approximation (LPIA) [Appl. Opt.39, 3304 (2000)APOPAI0003-693510.1364/AO.39.003304] is often used. However, the evaluation of the validity and accuracy of this method has, to our knowledge, not yet been fully addressed in the literature. In this work, we compare the field on the curved surface obtained by LPIA with that obtained with the finite element method. We find it is highly accurate even when the size of the curved surface is on the scale of micrometers. We further evaluate the limitation of LPIA in the cases of multi-reflection/transmission and internal resonance.