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.
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.
There has been an escalating demand for dynamically reconfigurable photonic structures to implement any linear optical transformation between the input and output ports. Such devices are often constructed as a mesh of reconfigurable Mach-Zehnder interferometers(MZIs). Consequently, the programmed MZIs can redistribute the light to implementarbitrary unitary transformations from an input vector of optical signals to an outputvector of coherent optical modes. These structures have been widely used as a promising hardware platform for fast and energy-efficient matrix multiplications in different applications, such as information processing, machine learning algorithms, neural networks(NNs), etc. Matrix multiplication is an essential but time- and energy-consuming operation in machine learning computations. The computational complexity of NNs necessitates well designed and implemented hardware accelerators for fast and energy-efficient data processing, which allows for scaling the structure to larger NNs in current and upcoming applications. Over the last few years, the considerable progress in silicon photonics has made it possible to fabricate multiport optical interferometric structures with small ootprints and high-power efficiency, which can be exploited as hardware accelerators, thanks to the inherent parallelism of optics. This Ph.D. thesis presents the theoretical and experimental analysis of multiport reconfigurable MZI-based optical processors. The optical processors are meshes of 2×2 reconfigurable MZIs. It is demonstrated how the optical transformation matrix of the optical processors is theoretically decomposed for a given application. The Reck-mesh-based optical processor is experimentally calibrated before programming the device for a given application. Additionally, the thesis includes the theoretical and measurement results of a single layer NN implemented by a 4×4 Reck-mesh-based optical processor. Finally, a novel phase-error- and loss-tolerant multiport field-programmable MZI-based optical processor for optical NNs is proposed. The new structure with a diamond mesh shape makes use of a set of additional MZIs compared to the commonly used Reck (triangular) mesh. The additional MZIs in the Diamond mesh make its topology more symmetric yielding higher phase error- and loss-tolerance, and also provide extra degrees of freedom in the optimization of ONN weight matrix during training. Furthermore, the better classification performance of the Diamond mesh compared to the Reck mesh is associated with the fact that the Diamond mesh is capable of excluding the light intensity that could have degraded the classification accuracy of the implemented ONNs. This is done by means of the tapered-out wave guides of the additional MZIs in the Diamond mesh, while the optimal light intensity is sent to its outputs for better classification. The demonstration of these analyses is significant as it can be used to implement any universal field-programmable photonic device as an optical processor, i.e., optical computational accelerator, which can be experimentally programmed to implement arbitrary linear optical transformation matrix for a given application. Additionally, the presented analytical results in this thesis can be used to enhance the classification performance of ONNs implemented by such structures. As a result of these analyses, the thesis proposes the Diamond-mesh-based optical processor as a promising candidate for large scale ONNs which outperforms the Reck-mesh-based ones in the presence of experimental imperfections
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 demonstrate a novel mesh of Mach-Zehnder interferometers (MZIs) for programmable optical processors. We thoroughly analyze the benefits and drawbacks of previously known meshes and compare our newly proposed mesh with these prior architectures, highlighting its unique features and advantages. The proposed mesh, referred to as Bokun mesh, is an architecture that merges the attributes of the prior topologies Diamond and Clements. Similar to Diamond, Bokun provides diagonal paths passing through every individual MZI enabling direct phase monitoring. However, unlike Diamond and similar to Clements, Bokun maintains a minimum optical depth leading to better scalability. Providing the monitoring option, Bokun's programming is faster improving the total energy efficiency of the processor. The performance of Bokun mesh enabled by an optimal optical depth is also more resilient to the loss and fabrication imperfections compared to architectures with longer depth such as Reck and Diamond. Employing an efficient programming scheme, the proposed architecture improves energy efficiency by 83% maintaining the same computation accuracy for weight matrix changes at 2 kHz.
Manufacturing errors introduce phase deviations in Mach–Zehnder interferometers (MZIs) that degrade the fidelity of optical processors. To address this issue, we employ a Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton method for phase calibration of a 4×4 reconfigurable MZI optical processor based on the Reck architecture. By optimizing the mapping from the target matrix to the optical network, the method determines the optimized phase parameters of 12 phase shifters. Thermo-optic simulations are further used to establish the relationship between the applied bias voltage and the induced phase shift, providing a link between the optimized phase parameters and the electrical driving conditions. Compared with Particle Swarm Optimization (PSO), Genetic Algorithms (GA), and Gradient Descent with Momentum (GDM), the BFGS method provides faster convergence and high calibration fidelity. These results demonstrate an efficient approach for phase calibration of programmable MZI optical processors.
Programmable linear optical processors (LOPs) can have widespread applications in computing and information processing due to their capabilities of implementing reconfigurable on-chip linear transformations. A conventional LOP that uses a mesh of Mach-Zehnder interferometers (MZIs) requires 2N+3 stages of phase shifters for $N\ifmmode\times\else\texttimes\fi{}N$ matrices. However, it is beneficial to reduce the number of phase-shifter stages to realize a more compact and lower-loss LOP, especially when long and lossy electro-optic phase shifters are used. In this work, we propose a structure for LOPs that can implement arbitrary matrices as long as they can be realized by previous MZI-based schemes. Through numerical analysis, we further show that the number of phase-shifter stages in the proposed structure can be reduced to N+2 and N+3 for a large number of random dense matrices and sparse matrices, respectively. This work contributes to the realization of compact, low-loss, and energy-efficient programmable LOPs.