Effective programming of a photonic processor with complex interferometric structure

TL;DR

The paper addresses programming reconfigurable photonic processors that implement complex interferometric transformations by reconstructing a digital model from calibration data. It introduces a matrix-parameterization $U(\vec{x}) = M_2 \times P(\vec{\varphi}) \times M_1$ with crosstalk represented by $A$ and bias $\vec{\Phi}_0$, and validates two data-driven approaches (calibration-based and ML-based) to predict and configure the chip’s unitary transformations. Across 100 random unitaries, the method achieves an average matrix fidelity around $0.996$, while broadband switching tests (7 wavelengths) show robust, high-fidelity predictions with $\geq 0.99$ mutual fidelity between measurement and model. The work demonstrates a scalable strategy to program non-conventional interferometric photonic architectures, enabling reliable optical information processing and motivating extensions toward Haar-random unitaries and universal interferometers.

Abstract

Reconfigurable photonics have rapidly become an invaluable tool for information processing. Light-based computing accelerators are promising for boosting neural network learning and inference and optical interconnects are foreseen as a solution to the information transfer bottleneck in high-performance computing. In this study, we demonstrate the successful programming of a transformation implemented using a reconfigurable photonic circuit with a non-conventional architecture. The core of most photonic processors is an MZI-based architecture that establishes an analytical connection between the controllable parameters and circuit transformation. However, several architectures that are substantially more difficult to program have improved robustness to fabrication defects. We use two algorithms that rely on different initial datasets to reconstruct the circuit model of a complex interferometer, and then program the required unitary transformation. Both methods performed accurate circuit programming with an average fidelity above 98%. Our results provide a strong foundation for the introduction of non-conventional interferometric architectures for photonic information processing.

Figures (12)

• Figure 1: Schematic photonic chip structure. The preparation part, consisting of three cascaded MZIs and a target complex interferometer consisting of two $4\times 4$ multiport couplers sandwiching three tunable phase shifters, are both in the same fused silica sample. Laser light is injected into the second input port of the chip. This allows for the preparation of an arbitrary optical distribution of light among the four input ports of the target interferometer. The MZIs in the interferometer can be individually calibrated using auxiliary waveguides that are weakly coupled to the output section of the preparation part of the interferometer. Auxiliary waveguides lie 35 $\mu$m below the main waveguide plane with preparation and target interferometers. Each auxiliary waveguide is only coupled to the corresponding waveguide of the preparation interferometer and only at its output region.
• Figure 2: a) Typical output optical power dependence $P_m(\varphi(x_j))$ in cases a) without crosstalk and b) with mutual crosstalk between adjacent phase-shifters. This illustration shows the numerical modeling of the calibration of the phase shifter $\varphi_1$ when coherent radiation is injected into the third input port of the target interferometer (see Fig. \ref{['fig:experimental setup']}). In the absence of crosstalk, all $P_m(\varphi(x_j))$ curves are sinusoidal with an equal period. However, in the presence of crosstalk, each $P_m(\varphi(x_j))$ becomes a complex and non-periodic curve. c) A schematic illustration of the digital model of the target interferometer and its parametrization. The chips' unitary transformation $U$ was decomposed in three blocks: two mode-mixing blocks $M_{1,2}$ and a phase shift layer $P(\vec{\varphi}(\vec{x}, \vec{\varphi}_0, A))$ between them. Both mode-mixing blocks $M_{1,2}$ were parameterized by a triangular mesh of MZIs Reck1994, which required 9 real parameters $t_j$ in the range $t_j \in [ 0, 2 \pi ]$. d) Mode-mixing unitary matrices $M_{1,2}$ obtained from the simultaneous approximation of all calibration data. e) The $\Phi_0$ vector of the bias phase shifts and the matrix of crosstalk $A$ obtained from the simultaneous approximation of the calibration data.
• Figure 3: Guidelines for the estimation of relations between the crosstalk elements $A = \{ \alpha_{ij} \}$.
• Figure 4: The results of the digital model of the optical chip quality testing. a) The Matrix fidelity between 100 measured unitaries on chip and the corresponding unitaries simulated using the chip's model. b) An example of a pair of measured-simulated unitaries with the lowest value of matrix fidelity $99.2\%$. All the other 99 pairs of measured-simulated unitaries have greater matrix-fidelity values. c) Graph of average optical port-to-port switching fidelities for different wavelengths of coherent radiation. d) Histograms of the power distribution at the output ports of the optical chip, reconfigured for one-to-one switching to a specific output, are shown for the first input port and three wavelengths.
• Figure 5: The fidelity distribution histograms for ML based model test. a) Testing the learning of artificial neural network on phase shifts-matrices ($\vec{\varphi}$-$U$) dataset. b) Testing the learning of artificial neural network on currents-matrices ($\vec{x}$ - $U$) dataset.