This study investigates an innovative approach to optical reservoir computing using fiber Rayleigh backscattering. A frequency-modulated Rayleigh scattering random reservoir structure is proposed to improve the modeling capability for complex data by expanding the feature space dimensions. The work also introduces a compensatory deep reservoir structure, where a second Rayleigh scattering-based reservoir learns the prediction residuals from the first-stage reservoir, further enhancing the overall prediction accuracy. The objective of this research is to explore the potential of optical reservoir computing in chaotic system prediction tasks, emphasizing its high-dimensional mapping and memory properties, which could enable long-term accurate predictions in complex scenarios.

The methodology involved theoretical analysis, simulation modeling, and experimental validation. The frequency modulation technique was employed to modulate the input signals and created a diverse set of dynamic features. The Rayleigh scattering in optical fibers was leveraged to naturally perform high-dimensional random mapping of the input signals, while a second reservoir compensated for prediction residuals. The entire system was modeled and validated using simulations of chaotic time series predictions, particularly using the Rössler chaotic system as a benchmark. Furthermore, experiments were conducted to verify the feasibility of the proposed optical deep reservoir computing system in a practical environment.

The theoretical derivations, simulations, and experimental results demonstrated that the Rayleigh scattering-based optical reservoir computing system could effectively capture chaotic dynamics, with the mean squared error (MSE) for chaotic sequence prediction reaching the order of 10^-3. The frequency modulation approach significantly enhanced the system’s capability to distinguish between different input data, which resulted in improved prediction accuracy in long-term forecasting tasks. The compensatory deep reservoir structure further improved prediction accuracy by focusing on learning the residual errors from the primary reservoir. Experimental results showed a notable improvement in prediction performance compared to conventional optical phase-modulated reservoirs, with a decrease in MSE by one order of magnitude after introducing the deep reservoir structure.

This research introduces a frequency-modulated optical deep reservoir computing approach, which improves the feature space and dynamic range of input signals while maintaining low system complexity. The incorporation of fiber Rayleigh scattering as a natural high-dimensional mapping tool, combined with the nonlinear detection provided by photodetectors, enables effective prediction of chaotic sequences. The introduction of the compensatory deep reservoir structure enhances prediction performance without significantly increasing hardware cost. These findings indicate that the proposed optical deep reservoir computing system holds significant potential for applications in complex chaotic system modeling, high-precision time series prediction, and other optical information processing tasks.