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arXiv:2607.14759

Local Variance-Based Calibration of Programmable Photonic Interferometer Meshes

Gökhan Elmas, Igor A. Litvin, Janis Nötzel

physics.opticsquant-phSubmitted Jul 16, 2026• Announced Jul 17, 2026
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Abstract

Programmable photonic interferometer meshes enable reconfigurable linear optical transformations, but their performance depends critically on accurate calibration of Mach-Zehnder interferometers and phase shifters. Conventional methods often require node isolation, dedicated routing paths, orthogonal training states, reference channels, or prior phase-voltage characterization, which become increasingly difficult in large thermally tuned meshes. We introduce a local variance-based self-calibration method using intensity-only measurements. Controlled phase perturbations are applied, and calibration points are identified from minima of the measured output-power variance. For Mach-Zehnder interferometers, the variance follows a characteristic |sin(theta)| dependence, allowing bar and cross operating points to be found without conventional node isolation. For phase shifters, balanced interference produces a complementary |cos(phi)| variance signature, enabling quadrature calibration through the same statistical principle. We validate the method experimentally on an 8 x 8 silicon nitride programmable photonic processor using a fully automated two-stage procedure. Starting from random phase settings, all Mach-Zehnder interferometers are calibrated first, followed by phase-shifter calibration under balanced-interference conditions. As a system-level test, we implement an embedded 4 x 4 Hadamard transformation on the 8 x 8 processor using a Clements decomposition. These results establish local output variance as a simple calibration observable for programmable photonic meshes. The method is compatible with discrete random phase ensembles and requires neither conventional node isolation nor orthogonal training fields, making it a practical calibration primitive for scalable self-stabilizing photonic processors.

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Programmable photonic interferometer meshes enable reconfigurable linear optical transformations, but their performance depends critically on accurate calibration of Mach-Zehnder interferometers and phase shifters. Conventional methods often require node isolation, dedicated routing paths, orthogonal training states, reference channels, or prior phase-voltage characterization, which become increasingly difficult in large thermally tuned meshes.
We introduce a local variance-based self-calibration method using intensity-only measurements. Controlled phase perturbations are applied, and calibration points are identified from minima of the measured output-power variance. For Mach-Zehnder interferometers, the variance follows a characteristic |sin(theta)| dependence, allowing bar and cross operating points to be found without conventional node isolation. For phase shifters, balanced interference produces a complementary |cos(phi)| variance signature, enabling quadrature calibration through the same statistical principle.
We validate the method experimentally on an 8 x 8 silicon nitride programmable photonic processor using a fully automated two-stage procedure. Starting from random phase settings, all Mach-Zehnder interferometers are calibrated first, followed by phase-shifter calibration under balanced-interference conditions. As a system-level test, we implement an embedded 4 x 4 Hadamard transformation on the 8 x 8 processor using a Clements decomposition.
These results establish local output variance as a simple calibration observable for programmable photonic meshes. The method is compatible with discrete random phase ensembles and requires neither conventional node isolation nor orthogonal training fields, making it a practical calibration primitive for scalable self-stabilizing photonic processors.
We present an efficient calibration and programming methodology in the presence of imperfections and uncertainties for Mach-Zehnder interferometer (MZI)-based optical processors, utilizing the diagonal optical path properties. This approach enables direct phase monitoring of MZI phase shifters, inherently suppressing calibration errors caused by spurious scattered light originating from non-diagonal blocks and eliminating the need for computationally intensive calibration/programming schemes. We experimentally validate these properties using a 4 × 4 interferometric mesh fabricated on a silicon-on-insulator platform, demonstrating that the calibration remains unaffected by phase-setting uncertainties in preceding or succeeding blocks on a diagonal path. We also present a benchmarking procedure to assess testbed fidelity, which is further used to confirm the effectiveness of our approach by programming two random weight matrices, where fine-tuning via the diagonal path reduces the mean error of matrix-vector multiplication by 79% compared to an offline calibration method. These results highlight diagonal path properties as a practical and scalable solution for calibrating and programming reconfigurable multiport interferometers.
Reconfigurable photonic processors suffer performance loss from fabrication tolerances, thermal drift, and other phase- and amplitude-error sources. We introduce an energy-aware calibration routine that simultaneously restores accuracy and minimizes heater power. After output-channel normalization, every Mach-Zehnder interferometer and external phase shifter is retuned by fitting measured transfer matrices to theory, halving the error in a 4 × 4 Hadamard-transform test. Three complementary optimizations-a global phase offset, selection of the lower-voltage branch for each SU(2) rotation, and permutation of matrix rows-substantially reduce total electrical power without degrading fidelity. This precision, power-conscious calibration removes a key obstacle to scalable, high-performance photonic computing systems.
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 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 photonic 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 3 × 3 and 4 × 4 random unitary matrices yields fidelities >98% and bit precisions over five 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.
Programmable photonic meshes provide a promising platform for analog matrix-vector multiplication, but their scalability is often limited by the large phase-shift ranges required in universal interferometer circuits. We introduce a perturbative programming method that operates the circuit near a fixed reference configuration and realizes the target transformation through interferometric subtraction, thereby reducing the required programmable phase excursion. We develop this approach for photonic matrix-vector multiplication architectures based on universal unitary meshes, and low-depth non-unitary constructions based on sums of unitaries. We identify favorable reference configurations through a local conditioning criterion, analyze the phase statistics obtained for random target matrices, and show that perturbative programming produces phase distribution shrinking as the matrix size increases. Identified reference point allows for the subtraction to be carried out electronically after detection, avoiding the interferometric subtraction loss. We further quantify the trade-off between reduced phase range and the intrinsic overhead introduced by the subtraction architecture, and show that for sufficiently lossy phase shifters the reduced phase range can compensate for this penalty. These results identify perturbative programming as a conditional but potentially useful route toward more scalable programmable photonic matrix processors.
Phase fluctuations between optical inputs limit programmable photonic processors because their output powers depend on coherent interference. We study the phase-drift penalty that arises when sine and cosine quadratures are measured sequentially rather than simultaneously. The analysis is motivated by measurements from an eight-mode programmable photonic processor, including 35 free-running recordings of 300 s acquired at approximately 125 samples per second per channel. These recordings provide an empirical route for estimating the phase-increment variance at a selected reconfiguration interval. The estimate is defined at the time of the second measurement. For fixed quadrature order, perturbation of the atan2 reconstruction gives eC→S=−δτsin⁡2φ0+O(δτ2)e_{C\to S}=-δ_τ\sin^2φ_0+O(δ_τ^2)eC→S​=−δτ​sin2φ0​+O(δτ2​) and eS→C=−δτcos⁡2φ0+O(δτ2)e_{S\to C}=-δ_τ\cos^2φ_0+O(δ_τ^2)eS→C​=−δτ​cos2φ0​+O(δτ2​). Writing Qτ=Var⁡(δτ)Q_τ=\operatorname{Var}(δ_τ)Qτ​=Var(δτ​), uniform phase averaging gives the first-order drift mean-square error 3Qτ/83Q_τ/83Qτ​/8. A phase-predicted ordering rule measures the locally less informative quadrature first and the more informative quadrature second. Its uniform first-order penalty is (3/8−1/π)Qτ(3/8-1/π)Q_τ(3/8−1/π)Qτ​, which is 84.9 percent below the fixed-order value. We also derive an increment-aware estimator from a local state-space model. Marginalizing the unknown phase increment increases the variance of a stale phase observation by QτQ_τQτ​, reducing its Fisher information from III to I/(1+IQτ)I/(1+IQ_τ)I/(1+IQτ​). For ideal balanced Poisson detection, the Fisher information of each quadrature equals its detected signal-photon number. This yields dimensionless architecture boundaries in spatial information and phase-increment variance. Nonlinear Monte Carlo simulations validate the perturbative laws, quantify robustness to prediction error, and compare simultaneous, fixed-order, increment-aware, and adaptive receivers under a common noise model.