On Maximum Focused Electric Energy in Bounded Regions

TL;DR

This paper introduces a method to determine the maximum electric energy in various bounded regions using eigenfield analysis, applicable to different geometries, and demonstrates how to realize these fields through optical focusing.

Contribution

It presents a novel eigenvalue-based approach to optimize electric energy in bounded regions for optical fields, excluding evanescent waves, with practical focusing strategies.

Findings

Eigenfield solutions correspond to maximum energy configurations.

Method applies to diverse geometries including points, curves, surfaces, and volumes.

Numerical simulations validate the approach for a circular disc region.

Abstract

A general method is presented for determining the maximum electric energy in a bounded region of optical fields with given time-averaged flux of electromagnetic energy. Time-harmonic fields are considered whose plane wave expansion consists of propagating plane waves only, i.e., evanescent waves are excluded. The bounded region can be quite general: it can consist of finitely many points, or be a curve, a curved surface or a bounded volume. The optimum optical field is eigenfield corresponding to the maximum eigenvalue of a compact linear integral operator which depends on the bounded region. It is explained how these optimum fields can be realized by focusing appropriate pupil fields. The special case that the region is a circular disc perpendicular to the direction of optical axis is investigated by numerical simulations.