Sum rules for energy deposition eigenchannels in scattering systems

TL;DR

This paper derives universal sum rules and constraints for energy deposition eigenchannels in various scattering systems, applicable across different geometries, dimensions, and wave types, enhancing understanding of wave energy delivery.

Contribution

It introduces general sum rules for eigenvalues and eigenchannels in scattering systems of arbitrary geometry and wave type, expanding theoretical understanding.

Findings

Derived sum rules for eigenvalues in scattering systems.

Established constraints on eigenchannel intensity distributions.

Applicable to electromagnetic, acoustic, and matter waves.

Abstract

In a random-scattering system, the deposition matrix maps the incident wavefront to the internal field distribution across a target volume. The corresponding eigenchannels have been used to enhance the wave energy delivered to the target. Here we find the sum rules for the eigenvalues and eigenchannels of the deposition matrix in any system geometry: including two and three-dimensional scattering systems, as well as narrow waveguides and wide slabs. We derive a number of constraints on the eigenchannel intensity distributions inside the system as well as the corresponding eigenvalues. Our results are general and applicable to random systems of arbitrary scattering strength as well as different types of waves including electromagnetic waves, acoustic waves, and matter waves.