Focused Fields of given Power with Maximum Electric Field Components

TL;DR

This paper derives formulas for optimizing the electric field components at the focus of a diffraction-limited lens, enabling maximum specific field components with given input power, and details the optimal pupil distributions for such fields.

Contribution

It provides closed-form solutions for the optimal pupil fields that maximize specific electric field components at the focus, advancing focused field design techniques.

Findings

Closed formulas for maximum electric field components at focus.

Optimal pupil field distributions for maximum longitudinal or transverse fields.

Comparison of maximum transverse field with linearly polarized plane wave.

Abstract

Closed formulas are derived for the field in the focal region of a diffraction limited lens, such that the electric field component in a given direction at the focal point is larger than that of all other focused fields with the same power in the entrance pupil of the lens. Furthermore, closed formulas are derived for the corresponding optimum field distribution in the lens pupil. Focused fields with maximum longitudinal or maximum transverse are considered in detail. The latter field is similar, but not identical, to the focused linearly polarized plane wave.