Cavity Solitons as a Nonlinear Substrate for Photonic Neuromorphic Computing

TL;DR

This work demonstrates that cavity solitons sustained in a fiber optical cavity can serve as a nonlinear substrate for photonic reservoir computing. By encoding inputs in the phase of a driving laser and reading out through frequency-m multiplexed spectral channels, the system exploits spectral breathing and, importantly, Kelly sidebands to enrich dynamics and improve processing performance. Across numerical models (Ikeda map, LLE, and a reduced model) and an experimental fiber-cavity implementation, the Ikeda-map framework most accurately captures the dynamics and yields superior benchmarks (e.g., XOR, NCE, Mackey–Glass) due to Kelly-wave contributions. The results suggest a scalable, energy-efficient photonic RC platform with potential for further enhancement via dispersion engineering, extended analog readouts, and improved CW-to-frequency-comb conversion. These findings advance neuromorphic photonics by leveraging nonlinear soliton dynamics as a computational substrate and highlighting the critical role of radiative modes in information processing.

Abstract

Reservoir computing leverages nonlinear dynamics of physical systems to process temporal information with minimal training cost. Here, we demonstrate that cavity solitons sustained in a fiber optical cavity provide an optical platform for photonic reservoir computing. Our methodology exploits the use of a phase-modulated drive laser to encode the input, while the reservoir states are accessed through frequency-resolved readout. Numerical simulations indicate that the emission of Kelly waves enriches the dynamics and enhances performance for machine learning tasks. We evaluate the performance of the cavity-soliton reservoir computer on several standard benchmark tasks.

Figures (7)

• Figure 1: Reservoir computing with cavity solitons. (a) Reservoir computing framework showing the input layer, the reservoir, and the readout layer. The weights are indicated in orange. (b) Implementation of reservoir computing using cavity solitons. The input layer is realized by modulating the phase of a continuous-wave (CW) laser using a phase modulator (PM). The reservoir layer consists in the dynamical evolution of cavity solitons inside the fiber cavity as they respond to the input. The output layer consists of time-dependent measurements of the power in individual frequency channels, using a programmable spectral filter (PSF), a photodiode (PD), and an oscilloscope (OSC). (c) Spectral breathing amplitude of different frequency channels. The colored bands are the frequency bands, positioned at different spectral offsets from the pump frequency, each representing a different reservoir node. The shaded gray area indicates the amplitude of the spectral breathing of the cavity soliton under phase modulation of the driving field. Parameters: $\sigma_{\varphi}\,=\,0.14$, $K\,=\,500$, $q\,=\,10$. (d) Temporal dynamics of two distinctive spectral channels in response to five arbitrary input symbols ($q\,=\,20$), as a function of the roundtrip number, after mean subtraction and normalization to their root-mean-square (RMS) values. The black trace corresponds to the most red-detuned channel, while the blue trace corresponds to the channel adjacent to the continuous-wave (CW) pump. The dashed curve indicates the phase modulation applied to the driving laser. The spectral breathing and temporal dynamics of two channels are obtained using numerical simulations following the Ikeda map model with constant parameters: $P_{\text{in}}\,=\,150\,\mathrm{mW}$, $\delta\,=\,2\,\mathrm{rad}$, $\Lambda\,=\,0.03$.
• Figure 2: Analysis of cavity solitons under phase modulation of the driving field. (a) Stable operational regimes as a function of phase standard deviation $\sigma_{\varphi}$ and detuning $\delta$ for $\Lambda \in \{0.03, 0.04, 0.05\}$. (b) Correlation coefficient corresponding to Fig. \ref{['fig:specbreath']}. The above simulations were generated using the Ikeda map model, with other parameters the same as in Fig. \ref{['fig:mainpanel']}.
• Figure 3: Comparative analysis of different theoretical frameworks for reservoir computing. (a--d): Normalized spectral fluctuations $\sigma\!\left(\Delta P/\bar{P}\right)$ and CS spectra versus frequency offset $f$ at $\delta\,=\,2.5\,\mathrm{rad}$. The plot illustrates how different frequency components respond to phase perturbations. Here $\sigma\!\left(\Delta P/\bar{P}\right)$ denotes the standard deviation of the normalized relative power change. (e): Left: Linear Memory Capacity (LMC) as a function of detuning for different models ($M\,=\,1$). Right: XOR benchmark classification accuracy (Score,%) as a function of modulation strength $M$, between the current input and 4-step delayed input for parameters: $K\,=\,2000$, $N\,=\,50$, $\delta\,=\,\pi\,\mathrm{rad}$, with filter bandwidth ranges from $96$ to $107\,\mathrm{GHz}$, corresponding to a detuning range of $\delta \in [0.7, \pi]\,\mathrm{rad}$. (All results are obtained for a repetition factor of $q\,=\,10$, and $P_{\text{in}}\,=\,250\,\mathrm{mW}$).
• Figure 4: Reservoir computing performance in the parameter space defined by the input‑phase standard deviation $\sigma_{\varphi}$ and repetition factor $q$. (a) Linear Memory Capacity (LMC) with $K\,=\,5000$. (b) Nonlinear Channel Equalization (NCE) for a channel SNR of 12 dB with $K\,=\,7000$. Parameters: Cavity detuning $\delta\,=\,2.5\,\mathrm{rad}$, input power $P_{\mathrm{in}}\,=\,200\,\mathrm{mW}$
• Figure 5: (a) Experimental setup. A continuous-wave laser (CW) is split using a 50:50 coupler. In the upper arm, an arbitrary waveform generator (AWG) encodes information via a phase modulator (PM). The modulated signal is amplified by an erbium-doped fiber amplifier (EDFA1), trimmed using a variable optical attenuator (VOA), and spectrally cleaned by a fiber Bragg grating (FBG1). In the lower arm, a frequency shifter (FS) generates a control signal, with a power of approximately $10\ \mathrm{ \mu W}$ at the input to the cavity. The two signals are recombined using a polarization beam splitter (PBS). The combined signal is coupled into the cavity via a 90/10 fiber coupler. The cavity consists of a SMF-28 spool, an optical isolator, an erbium-doped fiber (EDF), two 1480/1550 $\mathrm{nm}$ wavelength-division multiplexers (WDM2 and WDM3), and one 1535/1550 $\mathrm{nm}$ WDM (WDM1). One percent of the intracavity field is tapped. Stabilization of the detuning $\delta$ is implemented using a proportional-integral-derivative (PID) controller. After removing the CW background using FBG2 and re-amplifying the signal using EDFA2 and EDFA3, a programmable spectral filter (PSF) applies bandpass filters across the output soliton spectrum. One percent of the filtered output is sent to an optical spectrum analyzer (OSA) for monitoring, while 99% of the filtered output is converted to an electrical signal by a photodiode (PD3) followed by a $10\,\mathrm{MHz}$ low-pass filter (LPF), amplified electrically (Amp), and recorded by the oscilloscope (OSC). PC: polarization controller. (b) Spectral profile of the cavity solitons as a function of detuning $\delta$. As the detuning increases, the spectrum broadens, and shifts due to Raman self-frequency shift and Kelly sidebands appear. The spectral power for each trace is independently normalized to its maximum power and plotted on a logarithmic scale. (c) The effect of modulation strength, $M$, on the signal-to-noise ratio (SNR). Here, i.i.d. inputs from the range [0, 1] are randomly sampled and encoded onto the PM. The plot shows the resulting SNR per node, when $M$ is varied from 0.1 to 0.6.