Scattering concentration bounds: Brightness theorems for waves

TL;DR

This paper extends the brightness theorem from ray optics to general wave scattering, deriving bounds on power concentration and introducing a wave étendue concept applicable to complex, nonreciprocal systems.

Contribution

It generalizes the brightness theorem to wave systems, introduces a wave étendue measure based on the density matrix rank, and demonstrates design near theoretical limits in nanophotonics.

Findings

Derived power-concentration bounds for arbitrary coherence systems.

Introduced wave étendue as a measure of incoherence among scattering channels.

Designed metasurfaces operating near the theoretical power concentration limits.

Abstract

The brightness theorem---brightness is nonincreasing in passive systems---is a foundational conservation law, with applications ranging from photovoltaics to displays, yet it is restricted to the field of ray optics. For general linear wave scattering, we show that power per scattering channel generalizes brightness, and we derive power-concentration bounds for systems of arbitrary coherence. The bounds motivate a concept of "wave \'{e}tendue" as a measure of incoherence among the scattering-channel amplitudes, and which is given by the rank of an appropriate density matrix. The bounds apply to nonreciprocal systems that are of increasing interest, and we demonstrate their applicability to maximal control in nanophotonics, for metasurfaces and waveguide junctions. Through inverse design, we discover metasurface elements operating near the theoretical limits.