Reciprocity-induced symmetry in the round-trip transmission through complex systems

TL;DR

This paper investigates the reciprocal symmetry in wave transmission through complex media using transmission matrices, revealing fundamental limitations and implications for optical imaging and wave control.

Contribution

It experimentally verifies the transpose symmetry of forward and round-trip transmission matrices in a multimode fiber, highlighting the impact of loss and system limitations.

Findings

Confirmed transpose symmetry between forward and round-trip TMs

Loss and power conservation affect wave focusing and control

Round-trip TM measurements do not directly calibrate forward transmission

Abstract

Reciprocity is a fundamental principle of wave physics and directly relates to the symmetry in the transmission through a system when interchanging the input and output. The coherent transmission matrix (TM) is a convenient method to characterize wave transmission through general media. Here we demonstrate the optical reciprocal nature of complex media by exploring their TM properties. We measured phase-corrected TMs of forward and round-trip propagation through a looped 1m-long step-index optical multimode fiber (MMF) to experimentally verify a transpose relationship between forward and backward transmission. This symmetry impedes straightforward MMF calibration from proximal measurements of the round-trip TM. Furthermore, we show how focusing through the MMF with digital optical phase conjugation is compromised by system loss, since time reversibility relies on power conservation. These insights may inform development of new imaging techniques through complex media and coherent control of waves in photonic systems.