Optical coprocessor based on spontaneous Brillouin scattering

TL;DR

The paper proposes an optical coprocessor based on a network of ring resonators coupled to a waveguide, leveraging spontaneous Brillouin scattering to pump anti-Stokes modes. The system's dynamics, captured by a Lindblad master equation, show that the stationary anti-Stokes intensity in the waveguide encodes a weighted sum of phonon occupancies, enabling matrix-vector multiplication. By using multiple copies and tuning coupling constants, the approach realizes both stochastic and positive matrices, with the potential for parallel computations across a frequency band. Parallelization across frequency channels could increase throughput by 10^2–10^4, offering a path toward energy-efficient, all-optical neural network accelerators that combine linear and non-linear Brillouin-based operations.

Abstract

Analog coprocessors for neural networks are an intensively developing field. They provide approximate results of computations for relatively low energy cost and at high speed. We show that a set of ring resonators with Brillouin interaction between photons and phonons, being coupled to a waveguide, can be used to implement matrix-vector multiplication. The input vector is formed by occupancies of the anti-Stokes optical modes pumped via spontaneous Brillouin scattering, i.e, scattering on thermal phonons. Brillouin scattering rates and coupling constants between ring resonators and the waveguide form the matrix. The system allows for parallel computations in frequency band.

Figures (4)

• Figure 1: Schematic representation of the system under consideration ($I_a=\langle\hat{a}_a^\dag \hat{a}_a\rangle$, $I_s=\langle\hat{a}_s^\dag \hat{a}_s\rangle$).
• Figure 2: Dynamics of the waveguide's anti-Stokes mode occupancy $I_a$ (solid line) and $\tilde{n} (\omega_\phi,T_{1,\cdots,N})$ (dashed line) for $N=50$, $\Omega_{k,a}/\omega_0$ being set randomly between $5\cdot 10^{-4}$ and $5\cdot 10^{-3}$, $\gamma_\phi=0.1\omega_0$, $\gamma_a=5\cdot 10^{-4}\omega_0$, $n_k(\omega_\phi)$ being set randomly between $0.1$ and $2.0$, $(I_a/\omega_0)|_{t=0}=0$, $\omega=\omega_0$.
• Figure 3: Dynamics of the waveguide's anti-Stokes mode occupancy $I_a$ (solid line) and $\tilde{n} (\omega_\phi,T_{1,\cdots,N})$ (dashed line) for $N=50$, $\Omega_{k,a}/\omega_0$ being set randomly between $5\cdot 10^{-3}$ and $5\cdot 10^{-2}$, $\gamma_\phi=0.1\omega_0$, $\gamma_a=5\cdot 10^{-4}\omega_0$, $n_k(\omega_\phi)$ being set randomly between $0.1$ and $2.0$, $(I_a/\omega_0)|_{t=0}=0$, $\omega=\omega_0$.
• Figure 4: Dynamics of the waveguide's anti-Stokes mode occupancy $I_a$ (solid line) and value $4 \sum_k \Omega_{k,a}^2 n_k (\omega_\phi) / \gamma_a^2$ (dashed line) for $N=50$, $\Omega_{k,a}/\omega_0$ being set randomly between $10^{-5}$ and $10^{-4}$, $\gamma_\phi=10^{-3}\omega_0$, $\gamma_a=10^{-1}\omega_0$, $n_k(\omega_\phi)$ being set randomly between $0$ and $2$, $(I_a/\omega_0)|_{t=0}=0$, $\omega=\omega_0$.