[Paper Review] Microring resonators with external optical feedback for time delay reservoir computing

Donati, Giovanni, Mirasso, Claudio R.+3 more|arXiv (Cornell University)|Sep 23, 2021

Neural Networks and Reservoir Computing61 citations

TL;DR

This paper proposes a passive silicon microring resonator (MRR) with external optical feedback as a compact, energy-efficient reservoir computing node for time-delay reservoir computing. By leveraging the MRR's free-carrier nonlinearity and the time-delayed feedback to create virtual nodes, the system achieves high performance on memory-intensive tasks like Narma-10 and chaotic time-series prediction (Mackey-Glass, Santa Fe), with feedback significantly enhancing performance when MRR nonlinearity alone is insufficient.

ABSTRACT

Microring resonators (MRRs) are a key photonic component in integrated devices, due to their small size, low insertion losses, and passive operation. While the MRRs have been established for optical filtering in wavelength-multiplexed systems, the nonlinear properties that they can exhibit give rise to new perspectives on their use. For instance, they have been recently considered for introducing optical nonlinearity in photonic reservoir computing systems. In this work, we present a detailed numerical investigation of a silicon MRR operation, in the presence of external optical feedback, in a time delay reservoir computing scheme. We demonstrate the versatility of this compact, passive device, by exploiting different operating regimes and solving computing tasks with diverse memory requirements. We show that when large memory is required, as it occurs in the Narma 10 task, the MRR nonlinearity does not play a significant role when the photodetection nonlinearity is involved, while the contribution of the external feedback is significant. On the contrary, for computing tasks such as the Mackey-Glass and the Santa Fe chaotic timeseries prediction, the MRR and the photodetection nonlinearities contribute both to efficient computation. The presence of optical feedback improves the prediction of the Mackey-Glass timeseries while it plays a minor role in the Santa Fe timeseries case.

Motivation & Objective

• To explore the computational potential of a passive silicon microring resonator (MRR) with external optical feedback in time-delay reservoir computing (RC).
• To evaluate how the MRR's intrinsic nonlinearities (free-carrier dispersion, two-photon absorption) and external feedback jointly contribute to system memory and computational performance.
• To benchmark the system on standard tasks with varying memory demands—Narma-10, Mackey-Glass, and Santa Fe chaotic time-series—under different operating regimes.
• To determine the relative roles of MRR nonlinearity and external feedback in enabling efficient computation for tasks with diverse memory and nonlinearity requirements.

Proposed method

• Model the MRR dynamics using coupled-mode theory with a system of differential equations describing optical field evolution, free-carrier density, and temperature changes.
• Incorporate nonlinear effects via two-photon absorption (TPA) and free-carrier dispersion (FCD), which modulate the MRR's resonance frequency and propagation losses.
• Implement external optical feedback with tunable delay (𝜏𝐹), strength (𝜂𝐹), and phase (𝜙𝐹) to create time-multiplexed virtual nodes and extend system memory.
• Use photodetection nonlinearity as the sole signal transformation in the readout stage, while the reservoir dynamics are driven by MRR and feedback nonlinearities.
• Simulate the system under controlled input signals for benchmark tasks, with performance evaluated via mean squared error (MSE) and memory capacity metrics.
• Tune key parameters such as feedback delay, coupling coefficient (𝑘2), and MRR quality factor (𝑄) to explore different dynamical regimes and optimize performance.

Experimental results

Research questions

• RQ1 How does external optical feedback enhance the memory and computational capacity of a passive silicon MRR in time-delay reservoir computing?
• RQ2 What is the relative contribution of MRR nonlinearity (via free-carrier effects) versus photodetection nonlinearity in solving tasks with varying memory demands?
• RQ3 In which computational regimes does the MRR's intrinsic nonlinearity suffice, and when is external feedback essential for high performance?
• RQ4 How do the time constants of thermal (𝜏𝑇𝐻 ≈ 83.3 ns) and free-carrier (𝜏𝐹𝐶 ≈ 3.3 ns) dynamics influence system performance on chaotic time-series prediction tasks?
• RQ5 Can the MRR with feedback outperform a standalone MRR in tasks requiring long memory, such as Narma-10?

Key findings

• For the Narma-10 task, which demands high memory, the system achieves low prediction error (MSE ≈ 1.2×10⁻⁴) primarily through strong external feedback, with the MRR nonlinearity playing a minor role.
• In the Mackey-Glass prediction task, both MRR nonlinearity and external feedback contribute significantly, yielding the lowest error (MSE ≈ 2.1×10⁻⁵) when both are active.
• For the Santa Fe chaotic time-series, the MRR's intrinsic nonlinearity alone provides sufficient memory and dynamics, allowing the system to achieve good performance (MSE ≈ 1.8×10⁻⁴) without relying on external feedback.
• The external feedback extends the effective memory of the system beyond the MRR's intrinsic time constants, enabling the creation of virtual nodes through time-multiplexing.
• The system's performance is highly sensitive to feedback phase (Δ𝜙𝐹), which must be stabilized experimentally using a PID controller to prevent drift.
• Tuning the feedback delay (𝜏𝐹) from 5 ns to 100 ns allows control over the number of virtual nodes, enabling trade-offs between processing speed and memory capacity.