Programmable pixel-mode linear interferometers using multi-plane light conversion

Programmable linear optical interferometers are a core primitive in optical signal processing, quantum information processing, and photonic computing. Existing photonic-integrated implementations realize arbitrary $M$-mode unitaries using Mach–Zehnder-interferometer meshes whose footprint and accumulated loss scale with $O(M^2)$ optical components. Here we analyze and experimentally demonstrate a programmable architecture for implementing linear optical transformations directly on spatially tiled free-space pixel modes using multi-plane light conversion (MPLC). In this architecture, $M$ spatial modes arranged on a transverse lattice undergo a unitary transformation and are mapped to $M$ output modes of identical geometry through a sequence of programmable phase masks separated by free-space propagation segments. Numerical simulations show that arbitrary $M$-mode unitaries can be compiled to a desired high fidelity using a number of phase planes that scales approximately linearly with $M$. Using a spatial-light-modulator-based MPLC, we experimentally demonstrate programmable interferometers acting on up to $16$ spatial pixel modes, including tunable beamsplitters, Hadamard unitaries, spatial permutations, boosted-Bell-measurement unitaries, 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.

💡 Research Summary

The paper introduces a new architecture for programmable linear optical interferometers that operates directly on free‑space, spatially tiled “pixel” modes using Multi‑Plane Light Conversion (MPLC). Conventional integrated photonic platforms implement arbitrary M‑mode unitaries with meshes of Mach‑Zehnder interferometers (MZIs), requiring O(M²) tunable beamsplitters and phase shifters, which leads to large footprints and accumulated loss as the mode count grows. In contrast, the proposed MPLC‑based pixel‑mode interferometer uses a sequence of K programmable phase masks separated by free‑space propagation distances. Each mask consists of a P×P array of phase‑only pixels; the optical field propagates between masks according to Rayleigh‑Sommerfeld diffraction.

The authors formulate the problem as a unitary mapping between input pixel modes ϕₘ(x,y) (Gaussian or hard‑circular profiles centered on a square lattice with spacing b) and identical‑shaped output modes ψₘ(x′,y′). The target transformation is a unitary matrix U such that â_out = U â_in. To compile a given U into a set of phase masks, they employ a wave‑front‑matching (WFM) algorithm that iteratively propagates forward and backward superpositions of the input and desired output modes, updating the phase at each plane to minimize a cost function based on two performance metrics: average transmissivity (¯η) and average crosstalk (¯ε).

Numerical simulations explore a range of unitaries—variable‑transmissivity two‑mode beamsplitters, real and complex Hadamard matrices, spatial permutations, and boosted Bell‑state‑measurement (BSM) circuits—on systems of 2, 4, 8, and 16 modes. A key finding is that the number of required phase planes K scales approximately linearly with the number of modes M (K ≈ c M), rather than quadratically as in MZI meshes. For example, achieving ¯η ≥ 0.95 and ¯ε ≤ 0.005 for a complex Hadamard unitary requires K ≈ 1.2 M. The simulations also identify design windows: a mode‑spacing ratio b/σ ≥ 2 (σ is the mode‑field radius) yields a plateau in both η and ε, indicating sufficient isolation between neighboring pixel modes; and a phase‑mask pixel size Δ ≤ 0.3 σ maintains high performance, matching the resolution of commercial spatial light modulators (SLMs).

Experimentally, the authors implement the architecture with a 532 nm laser, a Gaussian mode field diameter σ = 350 µm, and an SLM‑based MPLC containing 10–13 phase planes. They demonstrate programmable interferometers acting on up to 16 pixel modes, realizing tunable beamsplitters, 4‑mode Hadamard transforms, 8‑ and 16‑mode complex Hadamard matrices, arbitrary spatial permutations, and boosted BSM unitaries that exceed the 50 % success probability of conventional linear‑optical Bell measurements. The experimental results closely match the simulated performance, confirming the feasibility of the approach.

The paper highlights several advantages of the MPLC pixel‑mode platform: (1) full programmability via software‑controlled phase values without hardware reconfiguration; (2) direct compatibility with free‑space emitters such as atomic arrays, quantum dots, or VCSEL arrays, reducing coupling loss; (3) a footprint and loss budget governed by diffraction physics rather than waveguide geometry, offering potential compactness for large‑M systems. Limitations include the refresh rate and diffraction efficiency of current SLMs, and the need to optimize the inter‑plane propagation distance w for specific applications. The authors suggest that future work could replace SLMs with faster electro‑optic phase arrays to enable real‑time reconfiguration.

In summary, the study demonstrates that MPLC can serve as a powerful, scalable alternative to MZI‑based meshes for programmable linear optics. By achieving linear scaling of required optical elements with mode count, maintaining low loss and crosstalk, and providing flexible interfacing with free‑space quantum emitters, this architecture opens pathways for high‑dimensional quantum information processing, optical neural‑network accelerators, and large‑scale spatial‑division multiplexing in both classical and quantum photonic systems.