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arXiv:2601.09802

Programmable on-chip synthesis and reconstruction of partially coherent two-mode optical fields

Amin Hashemi, Abbas Shiri, Bahaa E. A. Saleh, Andrea Blanco‐Redondo, Ayman F. Abouraddy

Published Jan 14, 2026• 2 citations
arXivHTMLPDF

Abstract

Partially coherent light is typically studied in the context of freely propagating continuous fields. Recent developments have indicated the existence of a `coherence advantage' in multimode optical communications, where partially coherent light outperforms coherent light. However, exploiting partial coherence in such applications requires manipulating multimode field coherence in programmable on-chip platforms. We present here the first example of on-chip synthesis and characterization of two-mode optical fields in an integrated on-chip hexagonal mesh of Mach-Zehnder interferometers. Starting with incoherent two-mode light, we adjust the degree of coherence on the chip with non-unitary transformations, construct $2\times2$ unitary transformations to synthesize prescribed coherence matrices, and reconstruct the coherence matrices via measurements of the spatial Stokes parameters. These results indicate the possibility of deploying programmable photonics for producing large-dimensional structured partially coherent light for applications in communications, cryptography, sensing, and spectroscopy.

DOI
10.48550/arxiv.2601.09802

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Partially coherent light is typically studied in the context of freely propagating continuous fields. Recent developments have indicated the existence of a `coherence advantage' in multimode optical communications, where partially coherent light outperforms coherent light. However, exploiting partial coherence in such applications requires manipulating multimode field coherence in programmable on-chip platforms. We present here the first example of on-chip synthesis and characterization of two-mode optical fields in an integrated on-chip hexagonal mesh of Mach-Zehnder interferometers. Starting with incoherent two-mode light, we adjust the degree of coherence on the chip with non-unitary transformations, construct 2×22\times22×2 unitary transformations to synthesize prescribed coherence matrices, and reconstruct the coherence matrices via measurements of the spatial Stokes parameters. These results indicate the possibility of deploying programmable photonics for producing large-dimensional structured partially coherent light for applications in communications, cryptography, sensing, and spectroscopy.
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 4×44\times44×4 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 4×44\times44×4 unitary transformations constructed out of sequences of 2×22\times22×2 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 2×22\times22×2 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.
Recent advances in optical imaging and communication increasingly involve high-dimensional, partially coherent light, creating a growing need for scalable tools to measure and manipulate coherence. Here, we demonstrate the automatic separation of spatially partially coherent light into "coherence modes" -- its orthogonal and mutually incoherent components. To make this separation possible, we exploit variational processing in layered self-configuring interferometer architectures in a silicon photonic circuit. This process formally finds and measures the eigenvectors and eigenvalues of the coherency matrix, hence measuring the partially coherent state, while leaving it intact and separated after optimization. Furthermore, we show that mutually incoherent beams, if spatially orthogonal, can be automatically separated even if they are completely overlapped, hence separating unknown laser beams based only on their mutual incoherence. Our experiment finds and separates the two strongest coherence modes starting from a nine-mode sampling of the partially or fully overlapping fields from two independent lasers. The method requires a number of physical components that scales linearly with the rank rrr of the coherency matrix and operates through a sequence of rrr in situ gradient-based optimizations enabled by electronic drive frequency multiplexing of interferometer phase shifters. We benchmark its performance against a mixture-based tomographic method, also implemented on chip. These results establish a scalable framework for programmable coherence analysis and control in imaging, communication, and photonic information processing.
Structured coherence -- partially coherent light spanned by a finite number of modes -- is emerging as a powerful tool in optical communications, computation, cryptography, and spectroscopy. Key to these prospects is the recent development of on-chip processing of structured coherence, in which large meshes of interferometers implement unitary and non-unitary transformations on the Hermitian coherence matrix representing multimode partially coherent light. Two related critical tasks for the applications of structured coherence are the reconstruction of an unknown coherence matrix and its diagonalization. Stokes tomography has been utilized in reconstructing the coherence matrix, whereas variational processing has been employed in its diagonalization. We show here that Stokes tomography can also be exploited in the on-chip diagonalization of an unknown coherence matrix, which we verify for two-mode and four-mode structured coherence in an integrated hexagonal mesh of Mach-Zehnder interferometers. This photonic circuit implements a predetermined sequence of configurations to estimate the generalized Stokes parameters, which -- in a final step -- inform a reconfiguration of the photonic circuit that diagonalizes the coherence matrix. The field is thus left in a coherent-mode representation comprising uncorrelated, orthogonal modes whose weights correspond to the eigenvalues of the original coherence matrix. Moreover, the integrated photonic circuit can be configured to provide the original field alongside its diagonalized counterpart at the circuit output. We verify the diagonalization procedure for coherence matrices of different coherence rank, entropy, and structure. Finally, we dispel the common notion that O(N^2) steps are required for reconstructing an N x N coherence matrix and show that only O(N) steps are needed.
Programmable linear optical interferometers are a core primitive in optical signal processing, quantum information processing, and photonic computing. Existing photonic-integrated implementations realize arbitrary MMM-mode unitaries using Mach--Zehnder-interferometer meshes whose footprint and accumulated loss scale with O(M2)O(M^2)O(M2) optical components. Here we analyze and experimentally demonstrate a programmable architecture for implementing linear optical transformations directly on spatially tiled free-space {\em pixel modes} using multi-plane light conversion (MPLC). In this architecture, MMM spatial modes arranged on a transverse lattice undergo a unitary transformation and are mapped to MMM output modes of identical geometry through a sequence of programmable phase masks separated by free-space propagation segments. Numerical simulations show that arbitrary MMM-mode unitaries can be compiled to a desired high fidelity using a number of phase planes that scales approximately linearly with MMM. Using a spatial-light-modulator-based MPLC, we experimentally demonstrate programmable interferometers acting on up to 161616 spatial pixel modes, including tunable beamsplitters, Hadamard unitaries, spatial permutations, and partial unitaries on select subsets of modes. These results establish MPLC-based pixel-mode interferometers as a promising architecture for programmable linear optics with applications in classical and quantum optical interconnects, photonic switching, and quantum information processing.
General-purpose programmable photonic processors provide a versatile platform for integrating diverse functionalities on a single chip. Leveraging a two-dimensional hexagonal waveguide mesh of Mach-Zehnder interferometers, these systems have demonstrated significant potential in microwave photonics applications. Additionally, they are a promising platform for creating unitary linear transformations, which are key elements in quantum computing and photonic neural networks. However, a general procedure for implementing these transformations on such systems has not been established yet. This work demonstrates the programming of universal unitary transformations on a general-purpose programmable photonic circuit with a hexagonal topology. We detail the steps to split the light on-chip, demonstrate that an equivalent structure to the Mach-Zehnder interferometer with one internal and one external phase shifter can be built in the hexagonal mesh, and program both the triangular and rectangular architectures for matrix multiplication. We recalibrate the system to account for passive phase deviations. Experimental programming of 3x3 and 4x4 random unitary matrices yields fidelities > 98% and bit precisions over 5 bits. To the best of our knowledge, this is the first time that random unitary matrices are demonstrated on a general-purpose photonic processor and pave the way for the implementation of programmable photonic circuits in optical computing and signal processing systems.
General-purpose programmable photonic processors offer a flexible foundation for integrating various functionalities within a single chip. A two-dimensional hexagonal waveguide mesh of Mach Zehnder interferometers has been shown to have great potential in the field of microwave photonics. Additionally, they are a promising platform for the creation of unitary linear transformations, which are key elements in photonic neural networks, In this article, we expand the portfolio of available applications for recirculating bricks mesh architecture to quantum technologies. We will show that a single programmable optical system is capable of performing various functions depending on the requirements. In particular, we will focus in this work on boson sampling, a task that best demonstrates quantum advantage, as well as on tasks that enable the determination of photon indistinguishability, which plays a key role in photonic quantum technologies. We will also show that, in addition to spatial modes, the same optical system can be equally well-suited for work on temporal modes through the implementation of an appropriate number of loops.