Optical theorem and generalized energy conservation for scattering of time-modulated waves

TL;DR

This paper develops a generalized energy conservation law and optical theorem for time-modulated wave scattering, enabling power-based imaging without phase information, even in systems with gain or loss.

Contribution

It introduces a new energy conservation relation and optical theorem for time-modulated waves, expanding understanding beyond conventional energy conservation.

Findings

Derived a generalized energy conservation relation for time-modulated wave scattering.

Formulated an optical theorem applicable to systems with energy gain, loss, or conservation.

Proposed a phase-independent method for image reconstruction based on power measurements.

Abstract

We introduce and study a generalized energy conservation relation for scattering of time-modulated waves, where conventional energy conservation does not hold. Based on this relation, we derive an optical theorem and compute the active power describing the power input or output due to scattering. Notably, the same system may be subject to energy gain, energy loss, or energy conservation depending on the frequency harmonics present in the wave field. Moreover, we show how the optical theorem derived herein may be used for image reconstruction based on measurements of the power. In particular, such measurements do not require information about the phase of the scattered field.