Joint control of coherent transmission, reflection, and absorption

TL;DR

This paper develops a theoretical framework for simultaneously controlling transmission, reflection, and absorption of waves in linear systems, revealing mathematical structures and non-commutative effects, and providing an algorithm for arbitrary response targeting.

Contribution

It introduces a novel theory based on the numerical range for joint wave control, including non-abelian effects and an algorithm for achieving desired responses.

Findings

Numerical range governs achievable wave responses.

Non-abelian effects arise from non-commutativity of matrices.

An algorithm for arbitrary response control is provided.

Abstract

Controlling multiple wave properties simultaneously poses a key challenge in coherent control of wave transport. We present a theory for joint coherent control of transmission, reflection, and absorption in linear systems. We prove that the numerical range provides the mathematical structure governing achievable responses, and reveal non-abelian effects due to non-commutativity between transmission, reflection, and absorption matrices. We provide an algorithm to achieve arbitrary target responses. Our results establish a theoretical foundation for joint coherent control of waves.