Analytical inversion of the focusing of high-numerical-aperture aplanatic systems.

We propose a method for an analytical inversion of the electric and magnetic fields at the focus of a high-NA aplanatic system to obtain incident light beam distribution. Our approach is based on an inverse Fourier transform of the Richards-Wolf formalism for targeted longitudinal fields along the radial or axial directions at the non-paraxial focus. Analytical solutions are discussed for both axial and radial focal fields for a radially polarized incident light beam, and a criterion is defined to access a physically valid solution. We also validate the method according to results found in the literature. Finally, we show how the method can be generalized to other incident field distributions.

Exact vectorial model for nonparaxial focusing by arbitrary axisymmetric surfaces.

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.