On-chip control of the coherence matrix of four-mode partially coherent light: rank, entropy, and modal Stokes parameters

TL;DR

This paper demonstrates on-chip manipulation of four-mode partially coherent light, enabling control over coherence properties and matrix reconstruction, advancing integrated photonics for optical information processing.

Contribution

It introduces a scalable on-chip platform using Mach-Zehnder interferometers to control and reconstruct high-dimensional coherence matrices of partially coherent light.

Findings

Successful on-chip control of coherence rank and entropy.

Implementation of unitary transformations for coherence matrix shaping.

Tomographic reconstruction of the coherence matrix via modal Stokes parameters.

Abstract

Partially coherent light offers salutary capabilities in optical information processing that cannot be matched by coherent light. To date, this `coherence advantage' has been confirmed in proof-of-principle optical communications protocols using bulk optics. Taking full advantage of such opportunities necessitates processing multimode partially coherent light in integrated photonics platforms that alone provide the requisite stability for cascaded operations on a large scale. Here we demonstrate on-chip manipulation of four-mode partially coherent light described by a $4\times4$ Hermitian coherence matrix. Starting with generic maximally incoherent light, we utilize an on-chip hexagonal mesh of Mach-Zehnder interferometers to perform all the unitary and non-unitary tasks that are critical for realizing structured coherence: controlling the coherence rank (the number of non-zero eigenvalues of the coherence matrix); tuning the field entropy; molding the structure of the coherence matrix via $4\times4$ unitary transformations constructed out of sequences of $2\times2$ unitaries acting on pairs of modes; and tomographic reconstruction of the coherence matrix by measuring the modal Stokes parameters associated with Kronecker-Pauli matrices. These results confirm the scalability of utilizing $2\times2$ on-chip building blocks for the synthesis and reconstruction of high-dimensional coherence matrices, and provide a decisive step towards large-scale on-chip manipulation of massively moded partially coherent light for applications in optical information processing.