Exact vectorial model for nonparaxial focusing by arbitrary axisymmetric surfaces

Abstract

We present a new approach, based on Richards-Wolf formalism, to rigorously model nonparaxial focusing of radially and azimuthally polarized electromagnetic beams by axisymmetric systems without a single-point focus. Our approach is based on a combined method that uses ray tracing and diffraction integrals. Our method is validated by comparing known results obtained with a parabolic mirror. Our integral representation of the focused beams, compliant with diffraction theory, is thoroughly discussed and solved for various conics that, so far, have not been treated analytically. The extension of the method to other polarization states is straightforward.

General diffraction integral for converging freeform vectorial fields

“…We observe that equation (6) guarantees that k â are always orthogonal despite the possible values of θ(x, y). This aspect is crucial and usually ignored by other diffraction integrals [18,19,[33][34][35][36]. The method presented here differs from the paradigm presented in [18,35,36].…”