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arXiv:2412.03951 · Journal of Lightwave Technology

Calibration of Cascaded Phase Shifters Using Pairwise Scan Method in Silicon Photonics Integrated Chip

Yan-Xiang Jia, Xuyang Wang, Yizhuo Hou, Yu Zhang, Yuqi Shi, Qiang Zhang, Jun Zou, Yongmin Li

Published Jan 2, 2025• 1 citation
arXivHTMLPDF

Abstract

Cascaded phase shifters (CPSs) based on silicon photonics integrated chips play important roles in quantum information processing tasks. Owing to an increase in the scale of silicon photonics chips, the time required to calibrate various CPSs has increased. We propose a pairwise scan method for rapidly calibrating CPSs by introducing equivalent Mach Zehnder Interferometer structures and a reasonable constraint of the initial relative phase. The calibration can be nearly completed when the scanning process is finished, and only a little calculation is required. To achieve better performance, the key components, thermal optical phase shifter and$2 \times 2$50/50 multimode interference coupler, were simulated and optimized to prevent thermal crosstalk and ensure a good balance. A 6-CPSs structure in a packaged silicon photonics chip under different temperature was used to verify the rapid pairwise scan method, and a fidelity of 99.97% was achieved.

DOI
10.1109/jlt.2024.3525039

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Cascaded phase shifters (CPSs) based on silicon photonics integrated chips play important roles in quantum information processing tasks. Owing to an increase in the scale of silicon photonics chips, the time required to calibrate various CPSs has increased. We propose a pairwise scan method for rapidly calibrating CPSs by introducing equivalent Mach Zehnder Interferometer structures and a reasonable constraint of the initial relative phase. The calibration can be nearly completed when the scanning process is finished, and only a little calculation is required. To achieve better performance, the key components, thermal optical phase shifter and2×22 \times 22×250/50 multimode interference coupler, were simulated and optimized to prevent thermal crosstalk and ensure a good balance. A 6-CPSs structure in a packaged silicon photonics chip under different temperature was used to verify the rapid pairwise scan method, and a fidelity of 99.97% was achieved.
With the development of research on integrated photonic quantum information processing, the integration level of the integrated quantum photonic circuits has been increasing continuously, which makes the calibration of the phase shifters on the chip increasingly difficult. For the calibration of multiple cascaded phase shifters that is not easy to be decoupled, the resources consumed by conventional brute force methods increase exponentially with the number of phase shifters, making it impossible to calibrate a relatively large number of cascaded phase shifters. In this work, we experimentally validate an efficient method for calibrating cascaded phase shifters that achieves an exponential increase in calibration efficiency compared to the conventional method, thus solving the calibration problem for multiple cascaded phase shifters. Specifically, we experimentally calibrate an integrated quantum photonic circuit with nine cascaded phase shifters and achieve a high-precision calibration with an average fidelity of 99.26%.
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.
The growing maturity of photonic integrated circuit (PIC) fabrication technology enables the high integration of an increasing number of optical components onto a single chip. With the incremental circuit complexity, the calibration of active phase shifters in a large-scale PIC becomes a crucial issue. The traditional one-by-one calibration techniques encounter significant hurdles with the propagation of calibration errors, and achieving the decoupling of all phase shifters for independent calibration is not straightforward. To address this issue, we propose a global calibration approach for large-scale PIC. Our method utilizes a custom network to simultaneously learn the nonlinear phase-current relations for all thermo-optic phase shifters on the PIC by minimizing the negative likelihood of the measurement datasets. Moreover, the reflectivities of all static beam splitter components can also be synchronizedly extracted using this calibration method. As an example, a quantum walk PIC with a circuit depth of 12 is calibrated, and a programmable discrete-time quantum walk is experimentally demonstrated. These results will greatly benefit the applications of large-scale PICs in photonic quantum information processing.
Interest in quantum computing is rapidly growing in the scientific community as such technology could be the key to enable intensive use of machine learning and big data algorithms. Quantum computers can be conceived from basic photonic elements, such as Mach-Zehnder interferometers (MZI), but they still need control mechanisms and sensing elements from traditional VLSI technology. In this study, we present an ongoing study on a potential architecture for these basic photonic circuits. We realized two Photonic Integrated Circuit (PIC) test structures embedding metallic thermistors as phase shifters and silicon photodiodes as output detectors. We present a complete characterization of the phase shifter elements for an effective on-chip PIC interaction. To induce a consistent phase shift still retaining coherence of light, we act on the phase-shifters by means of a closed-loop control. By controlling through Pulse-Width Modulation the phase shifters, we drive the path of photons accurately in the PIC, demonstrating the effectiveness of the proposed configuration for the management of a photonic chip.
Programmable photonic integrated circuits have mainly been developed based on the single wavelength channel operation of fundamental building blocks consisting of Mach-Zehnder interferometers (MZIs) with tunable phase shifters. We propose and study optical circuit models consisting of cascaded optical resonators that enable the independent operation of multiple wavelength channels in a more compact footprint than the conventional MZIs. By adopting experimental values reported for silicon micro-ring resonators, the fidelities of different types of 2×2 unitary transformations and higher-dimensional unitary transformations are examined by employing the Reck algorithm and the Clements algorithm.
We develop a geometric-phase framework for time-bin photonic qudits and propose a practical calibration and feed-forward algorithm for separating and compensating geometric (Pancharatnam-Berry), dynamical, and technical phase contributions. Working directly in the time-bin basis, we use a parallel-transport gauge so that geometric phases appear as experimentally identifiable interferometric offsets, while all phase contributions enter a bin-resolved diagonal transformation. We model state preparation by cascaded unbalanced Mach-Zehnder interferometers and give closed-form amplitudes for arbitrary splitting ratios and phases, noting that single-port monitoring requires post-selection and renormalization. We then give an interferometric tomography recipe based on adjacent-bin scans, with a Fourier-basis cross-check, and a multi-mode numerical case study that separates total, dynamical, and geometric phases and demonstrates feed-forward compensation. The protocol uses standard components, including tunable UMZIs, phase shifters or EOMs, and single-photon detectors, together with routine phase sweeps. It is intended for small to moderate dimensions, approximately d up to 10, and provides a scalable route toward phase-stable high-dimensional temporal encoding for quantum communication and photonic processing.