1. Introduction

Reservoir computing (RC) is a computational model that simulates brain information processing [1–3]. It has achieved success in areas such as time series prediction and pattern classification [4–6]. RC uses randomly connected networks to transform input signals into high-dimensional representations, which are then processed by readout layers to generate outputs. Advanced optical computing systems are actively exploring various areas, including high-speed optical neural networks [7,8], efficient photonic spiking neuron [9,10], and brain-inspired photonic synapses [11]. These neuromorphic photonic systems are inherently suited for AI operations toward faster, smarter, and more energy-efficient, and are very promising options for the development of new photonic AI processors. Compared to the neuromorphic photonic system solutions mentioned above, RC also performs excellently, making it a popular choice in neural computing applications [12–14]. However, constructing an efficient RC with sufficient physical complexity as computational resources remains a hardware challenge.

The reservoir layer (RL) is a stationary nonlinear system comprised of dynamical processes in a RC system. To address the physical complexity, some researchers propose a single nonlinear node and a delay loop as an alternative to multi-node networks. These nonlinear time-delayed dynamical systems possess high dimensionality and short-term memory properties, along with the concept of a dynamic RL. Consequently, time-delayed optical RC systems have generated a number of recent studies [15–24]. For example, in 2012, Paquot et al. proposed an optoelectronic RL architecture using modulators and delay lines for tasks such as channel equalization and speech recognition [21]. In 2015, based on a coherently-driven passive fiber optic cavity, Vinckier et al. showcased an all-optical RL architecture, which enabled a straightforward, high-performance, and energy-efficient computation [22]. Guo et al. introduced a time-delayed RL that utilizes a vertical cavity surface emitting laser (VCSEL) system with optical injection and feedback [23,24]. In 2019, they simulated two parallel RC systems using two polarization-resolved modes of VCSEL capable of effectively parallel predicting two independent chaotic time series [23]. Later, in 2023, they experimentally achieved high-performance modulation format recognition in a VCSEL-based RC system [24]. Time-delayed optical RC systems offer intelligent information processing capabilities, but they are constrained by the tradeoff between network size and modulation rate. In order to enhance the network capacity, it is necessary to scale up the RC system. However, this approach indicates that increasing the length of the feedback loop will reduce the processing speed required to achieve this capacity. This constraint arises from the data transmission speed fed to the RL since surpassing the time delay could potentially impact the signal quality of all virtual nodes [25]. To mitigate this inherent drawback, researchers have proposed spatiotemporal RC, utilizing photonics integrated circuits as the RL [26,27]. Nonetheless, these architectures are currently limited to only a few tens of nodes, and are thus inadequate for processing complex tasks such as image classification due to significant link loss. Moreover, recent experiments have successfully achieved all-optical spatially distributed photonic RC with diffractive optical elements, enabling the architecture to handle more complex tasks with thousands of nodes [28,29]. In 2023, Phang introduces a novel photonic RC (PhRC) architecture that eliminates the requirement for a physical feedback system by demonstrating the virtual generation of feedback through the inherent physical processes, utilizing the back-propagating Stokes laser and slow-phonon wave [30]. Therefore, given the challenges of adaptability and versatility, it is valuable to explore PhRC structures capable of achieving high-speed, high-performance, and parallel operations.

More importantly, the linear readout layer in the RC system, which also plays a vital role, has not received sufficient attention. The majority of its operations are carried out through numerical simulation offline. It is thus necessary to use a high-speed analog-to-digital converter (ADC) in the backend, which unavoidably restricts the real-time processing speed of the entire RC system and adds complexity to the system. Limited attempts have been made to implement this concept in hardware and explore its full potential [31]. Fortunately, a new study (Ma et al.) has successfully implemented an analog readout layer using an optical readout system based on Mach-Zehnder interferometers, eliminating the need for ADC [32]. The processing delay of their system solely relies on the 1 nanosecond delay of the optical path, avoiding any additional delay or power consumption. Additionally, Zhang et al. propose an adaptive active PhRC architecture utilizing the Kalman filter, enabling a readout system proficient in mitigating the inherent long-term drift associated with readout weights [33]. Indeed, the analog readout layer is currently attracting research attention, despite the challenges associated with large-scale linear regression operations.

In this paper, we propose a fully-analog feedforward photonic RC (FF-PhRC) system, using optical fiber to construct an all-optical RL. Unlike traditional RL structures that rely on time-delayed loop, our system takes advantage of the pulse broadening effect caused by dispersion in optical fiber, resulting in a short-term “fading memory” property. To further enhance the system's capabilities, by combining the multiplication property of the Mach-Zehnder modulator (MZM) with the temporal integration property of the distributed feedback-laser diode (DFB-LD), we succeed in designing an optoelectronic readout layer capable of real-time multiplication and addition operations on the reservoir output states. This new design not only reduces the burden on the back-end digital domain but also improves the system's overall performance. To validate the effectiveness of our proposed FF-PhRC system, we conduct proof-of-concept experiments on two tasks. The first task involves predicting the Mackey-Glass time series, where our FF-PhRC achieves a high normalized root mean square error (NRMSE) accuracy of 0.23 within the analog domain. The second task involves classification tasks using the FF-PhRC, where we evaluate its performance on benchmark datasets such as the temporal spoken digit dataset and the pattern MNIST image dataset, and achieve recognition accuracies of 96% and 93.4%, respectively. Furthermore, our FF-PhRC system operates at a rate of 10 GHz per wavelength in a wavelength division multiplexing (WDM) system, enabling multiple task processing. In brief, our proposed system has the potential for further improvement in spatiotemporal, parallel, and high-speed aspects, which makes it a promising and beneficial addition to the existing system.

2. Principle of the photonic FF-PhRC

As shown in Fig. 1(a), the RC system is a recurrently-connected nonlinear dynamic system driven by one or multiple input signals. Thousands of internal nodes are randomly connected with fixed connection weights, effectively capturing the temporal characteristics of the input signals. The current state of the reservoir is determined by the combination of the inputs and the previous states of the reservoir nodes, which can be regarded as the output of the RL. The output is then passed through a linear readout layer to obtain the final output. Here, different from the time-delayed RC systems based on a feedback structure, we propose a novel method to achieve short-term memory by using the fiber dispersion effect, where under the impact of chromatic dispersion, signals with different frequencies experience pulse broadening during signal transmission. This pulse broadening effect can be employed to form an RL that features a fading memory, as illustrated in Fig. 1(b). When an optical pulse enters the dispersion fiber, the output pulse undergoes significant broadening depending on adjacent inputs. This broadening reveals the intertemporal correlation among the time-series signals, presenting the correlation relationship among virtual nodes in adjacent time slots. Signal dispersion in fiber can alter signal shape at varying frequencies, leading to a short-term memory effect during pulse sequence transmission.

 

Fig. 1. A Fully-analog Feedforward Photonic Reservoir Computing (FF-PhRC) system. (a) A schematic diagram of the RC system, which consists of a nonlinear dynamical RL and a linear readout layer. (b) A temporal diagram of the optical pulse undergoing dispersion effects during transmission through an optical fiber, demonstrating the fiber as a RL. (c) The general structure and principles of the FF-PhRC model. The input layer of the RC model, enclosed by the yellow line at the top, mainly performs data preprocessing. The blue window in the middle consists of an all-optical RL primarily composed of electro-optic modulator and optical fiber, while the red window on the right serves as the readout layer and performs the linear classification task for output signals. (d) The control input signal of the modulator. A pulse train contains pulses with different repetition rates before driving an electro-optic modulator and (e) the output signal measured after the reservoir layer. The measured reservoir state readout at the output channel presents that the network’s transfer function is nonlinear and exhibits short-term temporal correlations due to pulse broadening effects caused by dispersion. The pulse width of a pulse is defined using a full width at half maximum (FWHM).

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The schematic diagram of the FF-PhRC in Fig. 1(c) is composed of an input layer, an RL, and a readout layer. In the input layer, the input signal is discretized into a sequence, denoted as u(n), through periodic sampling, where n is the sampling index. Each u(n) is multiplied by a generated mask M(t) to produce the modulated signal S(t). The value of M(t) is randomly chosen as 0 or 1 at the virtual node spacing, which is defined as an interval of θ. The mask controls the allocation of input information, assigning different weights and dynamic characteristics to the nodes. The primary function of the RL is to map the input signal to a high-dimensional state space. In the RL, the signal S(t) from the input layer is modulated onto the light by an electro-optic modulator and then transmitted through an optical fiber. Our proposed fiber-based RL exhibits a short-term memory, implying that the response to the current input signal in the RL is not only impacted by the current input signal but also previous and succeeding signals in the RL, thus enhancing its computation diversity and adaptability.

In the readout layer, the state of the virtual nodes is determined by the amplitude of the output waveform after being sampled at a time interval of θ. The output of the RC system is represented by the state of the reservoir, Xi (i = 1, 2, …, n, where n is the number of virtual nodes). For example, at a pulse repetition frequency of 10 GHz, the reservoir's output waveform state can be expressed mathematically as:

Equation (1) shows that the output at time k of the RL, x(k), is influenced not only by the current input u(k), but also by the preceding inputs at k-1 and k-2, and the succeeding inputs at k + 1 and k + 2. The function f() is linked to the MZM that produces a nonlinearity of cos²(·). Gi (i = -2, -1, 1, 2) reflects the degree of the respective signal's superimposition on the current signal due to the pulse broadening effect. It is worth mentioning that we set the bias point of the MZM at one-third of Vpi to ensure that the signal power can operate properly in the nonlinear region of the MZM, thus realizing the trade-off between signal performance and nonlinear effects. The temporal characteristic of the RL is well-suited to meet its requirements since adjacent inputs impact output x(k) of the system, thus generating a memory feature based on temporal correlation. By performing linear regression, we analyze the response state of the nodes to obtain the output of the system. The linear regression can be expressed as:

We analyze the temporal dynamic characteristics of an optical fiber with a dispersion coefficient (D = -997.9 ps/nm) and losses (α = 3.6 dB) by observing the output response. Figure 1(d) illustrates the input state of pulse signals with varying frequencies, and Fig. 1(e) displays the corresponding waveform signal after transmission through the optical fiber. When the pulse repetition rate is 4 GHz, no interference occurs due to wide pulse spacing and inadequate pulse broadening to impact the adjacent signals. However, as the pulse repetition rate increases to 6.5 GHz, the pulse broadening increases, and the peak values of the three output pulses gradually rise due to the overlap of adjacent signals, leading to signal distortion. When the pulse repetition rate increases to 10 GHz, pulse broadening becomes more prominent. As a result, the higher frequency components of a narrower pulse signal experience greater phase variations, causing them to lag far behind the lower frequency component. At this point, the broadened waveform of the first pulse is superimposed on the waveforms of the latter two pulses, resulting in a double-peak pulse in the time domain. In summary, our results demonstrate the impact of dispersion on optical fibers and the rich temporal dynamics of pulses, suggesting the suitability of optical fibers as the basis for all-optical RL system hardware.

3. Photonic implementation of FF-PhRC for real-time prediction of chaotic time-series signals

To evaluate the performance of FF-PhRC for chaotic signal prediction, we have selected the Mackey-Glass chaotic system, which has been widely used as a benchmark task in various RC studies. The Mackey-Glass system is defined by

To evaluate the performance of the all-optical RL and the analog readout layer in a WDM system, as depicted in Fig. 2, we first test a time-series signal of length 1200, divided into two halves for training and validation purposes. Then, we use a 4-channel laser diode (Alnair, TLG-200) with a narrow linewidth serving as the driving laser to produce a carrier linewidth of 10 kHz for each laser diode. In the third step, a WDM system is established using four distinct wavelengths (C32(1551.72 nm), C33(1550.92 nm), C34(1550.12 nm), and C35(1549.32 nm)) of light waves, which are multiplexed via a 4:1 optical multiplexer. Subsequently, we perform a preprocessing mask operation, encoding masked time-series data onto the amplitude of the pulse trains with a repetition frequency of 10 GHz.

 

Fig. 2. An FF-PhRC system for chaotic signal prediction. The up side shows the steps for training the time-series signal, while the down side illustrates the testing process. Together, they form the real-time prediction process for FF-PhRC. The experimental setup for the FF-PhRC based on wavelength division multiplexing (WDM) is shown in the middle. CW: continuous wave; WDM: wavelength division multiplexing; MZM: Mach-Zehnder modulator; SMF: single-mode fiber; EDFA: erbium-doped fiber amplifier; VDL: variable delay line; VOA: variable optical attenuator; PD: photodetector

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An arbitrary waveform generator (Keysight AWG 8196A) is then employed to drive the masked pulse waveforms into the MZM, which converts the electrical signal into an optical signal while performing the electric-optical nonlinear function of cos² node in the RL. The pulse trains propagate through the fiber-based RL and are then affected by the dispersion, capturing temporal characteristics and mapping them to the reservoir state. The signal is subsequently amplified using an Erbium-doped fiber amplifier (EDFA) and separated through DWDM to extract the combined signal. Our readout technique uses linear regression, which involves two processes: training and testing. Due to the WDM architecture, the signals at the C32-C35 wavelengths have similar shapes after wavelength division demultiplexing. Therefore, during the training process, we only need to train on one of the wavelengths (C35) and then use the photodetector (PD) to acquire the corresponding waveform signals, which is then digitalized offline to obtain the training w^out with an oscilloscope (Keysight UXR0334A) with a receiving bandwidth of 33 GHz. The w^out formula is expressed as:

In the testing process, the w^out obtained from the training process is applied to the readout layer. To ensure the alignment of the output, we add adjustable delay lines after each wavelength since signals at different wavelengths are affected by dispersion after passing through the fiber, which results in delayed outputs. Additionally, we encode the weight vector w^out onto the optical power of each wavelength by adjusting the attenuation value of the variable optical attenuator to perform spectrum shaping. For the chaotic signal prediction task, the mask length (ML), which determines the required number of wavelengths, is set at 4. We use a PD to detect the weighted signals at different wavelengths and combine them to achieve the interleaving of time and wavelength, thereby realizing the matrix multiplication between X^test and w^out. Finally, the output waveform is obtained by digitizing the signal using an oscilloscope. In this way, by using WDM technology, we enable real-time prediction of time-series signals. It is worth mentioning that since the FF-PhRC system poses no constraint on the length of the input prediction data, it can effectively manage large-scale data streams, the only limitation being the length of ML required, i.e., the total number of wavelengths.

We then use the NRMSE to assess the deviation between the estimated value, denoted by y'(k + 1), and the actual value, denoted by y(k + 1). With an NRMSE value of 0.06, our simulated FF-PhRC exhibits excellent predictive performance, as depicted in Fig. 3(a). In terms of the experimentally observed predictive capability of our FF-PhRC system, the noise in the analog circuit does not have a significant impact on it, proved by the NRMSE value of our fully-analog FF-PhRC (0.23). The experimental results demonstrate that the trained FF-PhRC system can predict Mackey-Glass variables in real-time at a rate of 10 GHz, as presented in Fig. 3(b). The spatial traces of y(k + 1) and y'(k + 1) corresponding to the simulation and experiment are depicted in Fig. 3(c) and 3(d), respectively. Here, a detailed simulation process is provided in the Appendix.

 

Fig. 3. Demonstration of Mackey-Glass time-series prediction with the FF-PhRC system. (a) The simulation prediction is conducted using the identical setup as the experiment. (b) The prediction result was obtained from experimental data collected from the FF-PhRC system. (c) and (d) show the respective phase space plots for the simulation and the experiment, respectively. The true (black) and RC system's predicted output (red) are plotted. (e) shows the variation of NRMSE accuracy of the prediction with mask length under different pulse rates. (f) Trend chart of NRMSE prediction accuracy with changing sampling virtual node number.

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We investigate the effect of ML on the performance of FF-PhRC by conducting simulations on predicted NRMSE accuracy at different pulse rates. Our simulations include three different pulse rates according to the broadening properties of the experiments: 10 GHz pulse rate (represented by black squares), 6.5 GHz pulse rate (represented by red triangles), and 4 GHz pulse rate (represented by blue circles). Figure 3(e) portrays the trends of predictive accuracy for signals with three different pulse rates. For each parameter value, we calculate an average of 30 simulation results and display their standard deviation in a vertical line. Our findings demonstrate that the system's predictive performance gradually improves with the increase in ML. Furthermore, the system reaches its optimal level and becomes stable when ML reaches 10. These results highlight the importance of sufficient ML to achieve good predictive performance. We also compare the three different signal rates and find that the black squares and red triangles exhibit better performance in the prediction task by generating more complex dynamic responses in the RL process, which is attributable to the temporal correlation between past and present signals. In contrast, even with longer ML, the blue circles’ curve lacks temporal correlation between previous and current signals. Consequently, its predicted NRMSE performance remains at approximately 0.145, which is half a magnitude lower than that of the black squares and red triangles.

To examine the impact of the number of virtual nodes, we vary the number of virtual nodes sampled from the RL to the output layer while keeping the ML at 4, and then resultant trends of the predictive accuracy are being presented in Fig. 3(f). It can be observed that the predictive accuracy increases with an increase in the number of sampling virtual nodes but eventually tends to saturate. Moreover, a comparison of the 6.5 GHz repetition input pulse with the 10 GHz repetition input pulse indicates that using a 6.5 GHz frequency sampling suffices to maintain a predictive accuracy of around 0.1 for a 10 GHz repetition input pulse.

4. Photonic implementation of the WDM-based FF-PhRC for classification tasks

In the RC model, the role of the mask serves the same purpose as the input connection weights. By breaking the system's symmetry, masks enable RL to exhibit more complex internal dynamics and nonlinear capabilities [34,35]. To effectively deal with dependencies in image data and improve the efficiency and accuracy of the classification task, the RC model requires stronger nonlinear capabilities. Increasing the length of the mask is thus a viable solution as this can yield sufficient diversity [35]. In the architecture of Fig. 2, since the number of wavelengths corresponds to the mask length, and the hardware architecture of the readout layer does not support the mask length. To achieve this goal, we make modifications to the readout layer of the FF-PhRC system designed for classification tasks. Specifically, a MZM has been utilized to implement the signal and weight multiplication, while the temporal pulse-shaping property of the DFB-LD is used to complete the summing operation of long data streams [36]. The experimental setup for the FF-PhRC system as a classification task is illustrated in Fig. 4(a), where the same optical source device in time prediction is used except that there are two channels and that the C34 and C35 bands are adjusted. The electrical signal is obtained by modulating the masked signal at a frequency of 10 GHz. It is worth mentioning that because of the independent nature of each waveform and the hardware channel constraints, we use two AWG (Keysight, M8196A and Keysight, M8195A) devices to control the electrical carrier signals of the C34 and C35 bands. Finally, the generated WDM signal is transmitted through a fiber-based RL, and subsequently experiences a gain of 20 dB using an EDFA, followed by wavelength demultiplexing by a DWDM. Similar to the time-series prediction task, we divide the analog readout layer into training and testing phases. In the training phase, we add a PD at each wavelength to convert the optical signal to an electrical signal, and then digitize the resulting signal using an oscilloscope (OSC, Keysight, UXR0334A) to obtain the reservoir state waveform of each wavelength. We then use the ridge regression method from processed data sample signals to obtain w^out. For example, we use the following ridge regression:

 

Fig. 4. Illustration of classification tasks performed with the FF-PhRC system. (a) Experimental setup of the FF-PhRC system. (b) Flowchart of the classification process for spoken data. (c) Flowchart of the classification process for MNIST data.

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In the testing phase, the following steps are executed: The w^out are mapped to the amplitude of a 10-Gbaud pulse sequence to convert output weights to amplitude values. The pulse sequence is modulated onto an optical carrier using a MZM, which can multiply the time series signal to obtain the output result. A direct current (DC) block is then applied to remove the DC component from the signal for further processing. The pulse shaping property of a DFB-LD is utilized to compress the information of the entire data stream (∼2µs) into a single pulse. After the intensity of output waveform is detected using a PD, the detected signal is passed through a 50 MHz low-pass filter (LPF) to remove high-frequency noise. Finally, an output waveform is obtained by digitizing the signal using an oscilloscope. The maximum amplitude of the generated waveform represents the result of the matrix multiplication.

To demonstrate the effectiveness of our proposed FF-PhRC method, we have chosen two benchmark classification tasks, the spoken digit dataset and the image MNIST dataset, depicted in Figs. 4(b) and (c), respectively. Before processing the spoken dataset in the NIST TI46 database, the raw acoustic wave signal is preprocessed and converted to a sequence of 50-dimensional vectors using the Lyon passive ear model. Each dimension of the vector sequence corresponds to a sub-sequence of length 40, which is padded with zeros if it is shorter. The scalar input of the RL, Xⁱⁿ, is obtained by multiplying the cochleagram matrix X with a random matrix W of size 64 × M, where the binary values (-1 and 1) are randomly assigned. Next, the matrix Xⁱⁿ is unfolded into one-dimensional time-series data and loaded onto the wavelength C34, as depicted in Fig. 4(b). When preprocessing MNIST image data, we apply mask processing to enhance image features and improve recognition accuracy. Unlike mask processing method of time-series signal, it uses convolution-based mask operations for the two-dimensional image data. To increase the diversity of convolution calculations and improve recognition accuracy, we use a randomly assigned matrix as the convolution kernel and employ 320 convolution kernels. The size of the convolution kernel is empirically set to 21 × 21 but can be adjusted according to the specific situation. By applying random convolution operation to the input image, we obtain a new feature representation of the image, which is then loaded into wavelength C35 in one-dimensional data format. We then combine the optical input of C34 and C35 wavelengths with WDM technology, which are then passed through the fiber-based RL to obtain the response output, as shown in Fig. 4(c).

For the spoken data, we select 500 samples from five different female speakers. These samples consist of utterances of the digits from 0 to 9, with 10 repetitions each. We randomly select 450 samples for training and 50 samples for testing. From the training samples w^out is derived, with a simulation accuracy of 98%, as shown in Fig. 5(a). In the experiment, although the calculation performance is slightly reduced due to link noise interference, our FF-PhRC system can still correctly recognize 48 spoken signals, with a word error rate of 4%, as shown in Fig. 5(b). In addition, our proposed RC system has the ability to process two different tasks simultaneously. To demonstrate the versatility of the system's processing capabilities, we also perform classification using the MNIST image dataset. Specifically, the training set consists of 3000 images, and the recognition accuracy is calculated using a set of 500 images that are not included in the training set. Through simulation using a digital FF-PhRC system, we achieve a recognition accuracy of 94.6%, as illustrated in Fig. 5(c). In contrast, during experimental testing using the FF-PhRC system, we obtain a classification accuracy of 93.4%. The corresponding confusion matrix is shown in Fig. 5(d). Although our experimental hardware has some limitations and can only demonstrate the feasibility of dual-wavelength inputs, our FF-PhRC system is independent and flexible at each wavelength, and thus has the ability to support more channels and can be applied to the C-band of telecommunications. Our experimental results thus demonstrate the potential of using WDM technology for ultra-wideband parallel processing.

 

Fig. 5. Demonstration of classification tasks performed with FF-PhRC system. For the spoken dataset, the left figures (a) and (b) show the confusion matrices obtained from simulation and experiment, respectively, where darker colors indicate higher recognition scores. The right figures display the classification results obtained from the MNIST dataset using the FF-PhRC system, where (c) and (d) are the confusion matrices for simulation and experiment, respectively.

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The distinctions between all-optical and optoelectronic implementations of RC rely on the specific types of RL utilized. In comparison with conventional RC models shown in Table 1, our FF-PhRC model demonstrates significant advantages in terms of speed and task performance. Regarding the future potential of photonic RC, the remarkable capabilities of analog optical computing technology are evident in its ability to achieve high speed, facilitate data parallelization, and complete multitasking processing.

Table 1. Performance comparison of state-of-the-art photonic RC implementations

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5. Discussion and conclusion

In this paper, we present a novel FF-PhRC system that is universal and flexible, based on fiber-based RL architecture principles. We have validated the proposed system through theoretical, simulation, and experimental analyses. With the fading memory feature of pulse broadening, we map the RC algorithm onto physical optical fibers in theoretical analysis, and results show that our system can effectively solve practical recognition tasks such as time-series prediction and handwritten digit recognition. While optical links suffer from performance degradation due to noise, the FF-PhRC system still performs well in fully-analog computing. One of the key features of our system is a flexible weight updating strategy that can be adjusted during optimization. This enhances the system's adaptability and allows for effective handling of diverse data and tasks, leading to optimized performance.

However, it is important to note that the classification performance of our system has not yet reached optimal levels, leaving room for further improvements. Although limited by the computer's memory resources during the training process, using a larger training dataset is a potential area for improving network performance. Additionally, the system can parallel process the same classification task to achieve multiple masks in multiple channels, thereby enhancing network performance. Another potential area is increasing the frequency of repeated pulse input, which enables the pulse effects to become more pronounced and the RL to have richer temporal features at higher rates, thus contributing to better performance of the system. This property can eliminate the need to construct numerous individual nodes, making the FF-PhRC system ideal for real-time processing. More importantly, in order to maintain the trade-off between the signal-to-noise quality of the signal and the classification result, EDFA has been introduced while increasing the power consumption of the system. Therefore, reducing the power consumption of the system in the future is a worthwhile consideration.

Our proposed FF-PhRC system offers real-time processing of large-scale readout networks, making it a promising alternative to delay-based RC methods. While it may not perform as well as computer-based digital processing in classification tasks, it still achieves excellent outcomes. Future progress in algorithm and experimental advancements, particularly in dense WDM technology, can further exploit the potential of fiber interconnectivity, improving model richness and system performance. This opens up exciting prospects for the FF-PhRC system in optical computing, intelligent information processing, and communication fields, with potential applications in chaotic signal prediction, spoken analysis, and image recognition. Due to its computational principles, our approach has the capability to seamlessly integrate into existing communication networks or local area networks.