Unitary control of multiport wave transmission

Controlling wave transmission is crucial for various applications. In this work, we apply the concept of unitary control to manipulate multiport wave transmission. Unitary control aims to control the behaviors of a set of orthogonal waves simultaneously. The approach fully harnesses the capability of wavefront shaping techniques, with promising applications in communication, imaging, and photonic integrated circuits. Here we present a detailed theory of unitary control of wave transmission, focusing on two key characteristics: total (power) transmittance and direct (field) transmission. The total transmittance for an input port represents the fraction of total transmitted power with respect to the input power for wave incident from an input port. The direct transmission for an input port denotes the complex transmission amplitude from that input port to its corresponding output port. We address two main questions: (i) the achievable total transmittance and direct transmission for each port, and (ii) the configuration of unitary control to attain desired transmission values for each port. Our theory illustrates that unitary control enables uniform total transmittance and direct transmission across any medium. Furthermore, we show that reciprocity and energy conservation enforce direct symmetry constraints on wave transmission in both forward and backward directions under unitary control.