Global Optimization of Universal Unitary Photonic Integrated Circuits

Introduction

Universal unitary photonic integrated circuits (PICs) have the ability to perform arbitrary unitary transformations in the optical domain, making them highly valuable for applications in optical communication, deep learning, and quantum information processing. These circuits are built using Mach-Zehnder interferometers (MZIs) as the basic building blocks, with directional couplers (DCs) or multimode interferometer (MMI) couplers used to split the light within each MZI.

For ideal operation, each splitter in the MZIs requires a precise 50:50 splitting ratio. However, in practical fabricated devices, this ratio is highly sensitive to fabrication errors, posing a significant challenge in achieving high operational fidelity at the desired wavelength. Furthermore, the operational wavelength range is limited because the fidelity rapidly decreases when the wavelength deviates from the optimal value.

A common structure for these universal unitary PICs was proposed by Clements et al., as shown in Figure 1(a). For a device with N input and output ports, it requires N MZI stages to realize arbitrary N×N unitary matrices.

Figure 1: (a) Schematic structure of the universal unitary PIC proposed by Clements et al. (b) Structure proposed in this work, with an extra MZI stage added as an example. The number of MZI stages can be further increased.

In this work, the authors propose a method to compensate for fabrication errors by adding extra MZI stages and globally optimizing all the phase shifts using a simulated annealing algorithm [5]. They then experimentally demonstrate the feasibility of their method using a 4×4 universal unitary PIC fabricated on a silicon-on-insulator (SOI) platform.

Principle and Analysis

In a real device, the experimentally realized matrix U_exp deviates from the target matrix U due to hardware errors, and the fidelity can be calculated as:

By increasing the number of MZI stages and globally optimizing all the phase shifts using a simulated annealing algorithm, the fidelity can be improved when the splitting ratios deviate from the ideal 50:50 value.

The authors numerically analyzed the fidelities of 4×4 circuits with various stage numbers, assuming a control accuracy of 0.01 rad for all phase shifts, an average splitting ratio of r:100-r (where r is a variable between 0 and 100) with a standard deviation of 2, and 1000 Haar-random unitary matrices as target matrices. The results, shown in Figure 2, demonstrate that the average fidelity is significantly improved by the optimization, even without adding more stages (M = 4). Further improvements are obtained by increasing the stage number, although more stages also result in higher insertion loss, so a proper stage number must be chosen for a real device.

Figure 2: Average fidelities when various circuits are used to implement 1000 random target matrices.

Experimental Results

To experimentally demonstrate their method, the authors fabricated a 4×4 universal unitary PIC on an SOI platform, as shown in Figure 3(a). The waveguide core has dimensions of 440 × 220 nm^2, and thermo-optic phase shifters are used to tune the MZIs. The experimental setup, shown in Figure 3(b), involves injecting light into the input port, splitting it equally into 4 waveguides, modulating it with a 4-MZI array for vector generation, and measuring the optical powers at the 4 output ports using external photodetectors.

Figure 3: (a) A 4×4 universal unitary PIC fabricated on an SOI platform. No extra MZI stages are added. (b) Experimental setup. PC: polarization controller. PD: photodetector.

The authors first injected 1.55-μm-wavelength light into the circuit and optimized all the phase shifts to obtain two binary matrices (shown as insets in Figure 4). Then, keeping the phase conditions unchanged, they swept the wavelength from 1.5 to 1.6 μm and measured the fidelity at each wavelength.

Next, they used their proposed algorithm to optimize all the phase shifts at several wavelengths and measured the fidelities again. As shown in Figure 4, the fidelities were improved when the wavelength deviated from 1.55 μm, even without adding extra MZI stages to the circuit. The authors expect further improvement by adding extra MZI stages.

Figure 4: Measured fidelities for two binary matrices with and without global optimization, respectively. The optimization is performed at each wavelength.

Conclusion

In this work, the authors proposed a method to significantly improve the fidelity of universal unitary PICs by adding extra MZI stages and globally optimizing all the phase shifts using a simulated annealing algorithm. They demonstrated the feasibility of their method experimentally using a 4×4 universal unitary PIC fabricated on an SOI platform. This method may find applications in static scenarios where frequent reconfigurations are not necessary, allowing for improved performance in optical communication, deep learning, and quantum information processing applications.

Reference

[1] R. Tang, H. Tang, K. Ikeda, M. Okano, K. Toprasertpong, S. Takagi, and M. Takenaka, "Global Optimization of Universal Unitary Photonic Integrated Circuits," Department of Electrical Engineering and Information Systems, The University of Tokyo, Tokyo, Japan; National Institute of Advanced Industrial Science and Technology, Ibaraki, Japan, 2024, pp. 1-6, doi: 979-8-3503-9404-7/24/$31.00 ©2024 IEEE.