Unitary control of partially coherent waves. II. Transmission or reflection

TL;DR

This paper develops a comprehensive theory for the unitary control of partially coherent wave transmission and reflection, enabling precise manipulation of these properties in practical wave systems like electromagnetic and acoustic waves.

Contribution

It introduces analytical expressions and algorithms for controlling partially coherent wave transmission and reflection, including conditions for perfect and zero transmission or reflection.

Findings

Derived attainable transmittance and reflectance ranges under unitary transformations.

Established conditions for partially coherent perfect transmission and reflection.

Proved symmetry constraints imposed by reciprocity on wave control.

Abstract

Coherent control of wave transmission and reflection is crucial for applications in communication, imaging, and sensing. However, many practical scenarios involve partially coherent waves rather than fully coherent ones. We present a systematic theory for the unitary control of partially coherent wave transmission and reflection. For a linear time-invariant system with an incident partially coherent wave, we derive analytical expressions for the range of attainable total transmittance and reflectance under arbitrary unitary transformations. We also introduce an explicit algorithm to construct a unitary control scheme that achieves any desired transmission or reflection within the attainable range. As applications of our theory, we establish conditions for four novel phenomena: partially coherent perfect transmission, partially coherent perfect reflection, partially coherent zero transmission, and partially coherent zero reflection. We also prove a theorem that relates the degree of coherence of the incident field, quantified by the majorization order, to the resulting transmission and reflection intervals. Furthermore, we demonstrate that reciprocity (or energy conservation) imposes direct symmetry constraints on bilateral transmission (or transmission and reflection) of partially coherent waves under unitary control. Our results provide fundamental insights and practical guidelines for using unitary control to manipulate the transmission and reflection of partially coherent waves. This theory applies to various wave systems, including electromagnetic and acoustic waves.