High-precision automated setting of arbitrary magnitude and phase of Mach-Zehnder interferometers for scalable optical computing

Abstract

Photonic technologies offer promising solutions to the power consumption, bandwidth constraints and latency limits of electronic hardware used in high-performance computing and artificial intelligence. Recently, many studies have proposed and successfully demonstrated photonic accelerators based on integrated meshes of Mach-Zehnder interferometers (MZIs), enabling matrix-vector multiplications directly in the optical domain. While being fast and energy efficient, these photonic architectures still struggle to get the required precision for such applications, because setting the complex coefficients of MZI tunable gates with a high accuracy is still an unsolved problem. This work demonstrates high-precision automated setting and stabilization of MZI-based optical gates with a resolution of 7.01 and 8.04 bits for the output power and phase, respectively. Demonstration is achieved on a multistage silicon photonic circuit comprising a coherent input vector generator, an MZI matrix-vector multiplier, and a coherent receiver for phase measurement. The proposed control strategy can configure the MZIs to any desired working point, without any prior calibration or complex algorithm for the correction of hardware non-idealities, and prevents the propagation of programming errors, thus allowing scalability towards optical processors of large size.

Figures (11)

• Figure 1: (a) Schematic of the MZI as a programmable 2x2 optical gate, with phase shifters $\phi$ and $\theta$. (b) Simulated power percentage and (c) phase difference at the output of the MZI with in-phase inputs of equal power, as a function of the phase shifts $\phi$ and $\theta$. The target working point, having $\phi = 1.8 \pi$ and $\theta = 0.15 \pi$, is highlighted by the green star. The red lines show the points sharing the same output power as the target, whereas the white lines highlight the points with the same phase difference. Two intersections are found, with the red dot indicating the wrong one.
• Figure 2: (a) Schematic of the MZI conceptually divided into two cascaded PS-coupler-sensor sections each with its control loop. The total power $P_T$ is measured with the two output photodetectors. (b) Simulation of the power ratio in position $B_2$ as a function of the $\phi$ shift. A phase shift $\phi = 1.8\pi$ corresponds to a $PR(B) = 0.2061$ with positive derivative. (c) Simulation of the power ratio in $C_1$ as a function of $\theta$, when $\phi = 1.8\pi$. A phase shift $\theta = 0.15\pi$ corresponds to a $PR(C) = 0.6836$ with positive derivative.
• Figure 3: (a) Schematic of the transparent photodetector. For a length L=65µm, the waveguide core is laterally extended and doped at its ends, to realize a transversal $p-i-n$ photodiode. (b) Measurement of the current of several photodetectors, as a function of the optical power. All curves are linear between 0 and -40, with a responsivity equal to 18nA/mW.
• Figure 4: (a) Microscope photograph and (b) schematic view of the PIC. The first interferometer serves as input vector generator, the MZI in the middle is the optical gate with the proposed control strategy and the last stage is a coherent receiver, used to analyze the phase difference at the gate output. The local feedback loops used to control the three heaters are highlighted with black arrows.
• Figure 5: Schematic view of the local feedback used in both the optical gate and the input vector generator.