Unitary control of partially coherent waves. I. Absorption

The coherent control of wave absorption has important applications in areas such as energy harvesting, imaging, and sensing. However, most practical scenarios involve the absorption of partially coherent rather than fully coherent waves. Here we present a systematic theory of unitary control over the absorption of partially coherent waves by linear systems. Given an absorbing system and incident partially coherent wave, we provide analytical expressions for the range of attainable absorptivity under arbitrary unitary transformations of the incident field. We also present an explicit algorithm to construct the unitary control scheme that achieves any desired absorptivity within that attainable range. As applications of our theory, we derive the conditions required for achieving two phenomena---partially coherent perfect absorption and partially coherent zero absorption. Furthermore, we prove a theorem relating the coherence properties of the incident field, as quantified by majorization, to the resulting absorption intervals. Our results provide both fundamental insights and practical prescriptions for exploiting unitary control to shape the absorption of partially coherent waves. The theory applies across the electromagnetic spectrum as well as to other classical wave systems such as acoustic waves.