A Microring as a Reservoir Computing Node: Memory/Nonlinear Tasks and Effect of Input Non-ideality

TL;DR

This work demonstrates a compact photonic reservoir computing system based on a silicon microring in an add-drop configuration, using time-multiplexed virtual nodes and offline ridge regression to study memory and nonlinearity in both linear (AND/OR) and nonlinear (XOR) tasks. By varying bitrate, detuning, and input power, the authors map bit-error-rate performance and identify that the microring can provide fading memory up to about $2$ bits and, when memory is supplied, nonlinear activation enhances the computation of nonlinear tasks like XOR, with the free-carrier and thermo-optic nonlinearities playing key roles. A critical finding is that the apparent reservoir performance must be carefully compared to the input-only regression due to input non-ideality from modulators and detection; RB maps quantify when the reservoir actually improves task performance. The study highlights how intrinsic microring dynamics enable both memory and nonlinearity in a minimal photonic element, offering guidance for designing scalable, energy-efficient photonic RC hardware and for strategies to extend memory through encoding or hybrid architectures.

Abstract

The nonlinear response of an optical microresonator is used in a time multiplexed reservoir computing neural network. Within a virtual node approach combined with an offline training through ridge regression, we solved linear and nonlinear logic operations. We analyzed the nonlinearity of the microresonator as a memory between bits and/or as a neural activation function. This is made possible by controlling both the distance between bits subject to the logical operation and the number of bits supplied to the ridge regression. We show that the optical microresonator exhibits up to two bits of memory in linear tasks and that it allows solving nonlinear tasks providing both memory and nonlinearity. Finally, we demonstrate that the virtual node approach always requires a comparison of the reservoir's performance with the results obtained by applying the same training process on the input signal.

Figures (8)

• Figure 1: Sketch representing the three cases on which we tested the logical operations. $n_1$ indicates the distance between the bits on which the logical operation (LO) is performed and $n_2$ is the number of bits provided to the ridge regression in the training procedure. Note that the flow of bits is such that the past bits ($\bm{b}_{j-n_1}^i$) are processed by the microresonator before the present bit ($\bm{b}_{j}^i$), i.e. the bit flow is inverted with respect to the time flow which is indicated in the figure.
• Figure 2: (\ref{['fig:uring']}) Sketch of the microring resonator in the add-drop configuration. (\ref{['fig:spectrum']}) Normalized transmission spectrum around the resonance frequency. The detuning is the frequency difference between the laser frequency and the microring resonat frequency of 193.5. (\ref{['fig:setup']}) Diagram of the experimental setup. CWTL: Continuous Wave Tunable Laser, AWG: Arbitrary Waveform Generator, EOM: Electro-Optic Modulator, PD: Photodetector, PC: polarization control, VOA: Variable Optical Attenuator, EDFA: Erbium Doped Optical Amplifier, BPF: Band Pass Filter, Pc: Personal computer.
• Figure 3: Maps as a function of the frequency detuning and input bitrate for AND 1 with 2 R-bit and $N_v^d = 5$. (top) BER estimation from the RC network at the power which ensures the best network performances; (middle) the power at which the $\textrm{BER}^{b}_{\textrm{out}}$ values in the first panel are achieved; (bottom) the ratio between $\textrm{BER}^{b}_{\textrm{in}}$ and $\textrm{BER}^{b}_{\textrm{out}}$. All the values are given in a logarithmic scale.
• Figure 4: Same maps of \ref{['fig:AND1_2Rb_5Nv']} for AND 1 with 1 R-bit and $N_v^d = 5$.
• Figure 5: Same maps of \ref{['fig:AND1_2Rb_5Nv']} for AND 2 with 1 R-bit and $N_v^d = 5$.