Solving the inverse problem of high numerical aperture focusing using vector Slepian harmonics and vector Slepian multipole fields

TL;DR

This paper introduces a novel method employing vector Slepian harmonics and multipole fields to solve the inverse problem of high numerical aperture focusing, enabling the design of specific focal field distributions.

Contribution

It presents a general technique for inverse high-NA focusing using vector Slepian functions, with numerical optimization to construct input fields for desired focal patterns.

Findings

Successfully approximates target focal fields

Demonstrates method with three literature examples

Provides a systematic approach for inverse focusing

Abstract

A technique using vector Slepian harmonics and multipole fields is presented for a general treatment of the inverse problem of high numerical aperture focusing. A prescribed intensity distribution or electric field distribution in the focal volume is approximated using numerical optimization and the corresponding illuminating field at the entrance pupil is constructed. Three examples from the recent literature have been chosen to illustrate the method.