A Silicon Photonic Neural Network for Chromatic Dispersion Compensation in 20 Gbps PAM4 Signal at 125 km and Its Scalability up to 100 Gbps

TL;DR

This work demonstrates a silicon photonic neural network implementing an 8-tap time-delayed complex perceptron to pre-compensate chromatic dispersion for IM-DD PAM4 transmissions. The device uses amplitude and phase weights on 8 delayed optical taps, summed optically to realize a transversal optical FIR, with a nonlinear end-stage detection. Training via PSO and Adam optimizes the tap weights to maximize eye-diagram aperture, achieving CD compensation up to 125 km at 10 Gbaud PAM4 and showing scalability toward higher speeds. Experimental comparisons with a tunable dispersion compensator show competitive performance, while practical limitations like insertion loss and fabrication-induced parameter variations are discussed. The results indicate a viable path toward fully optical CD compensation with potential improvements via on-chip amplification and electro-optic enhancements for future high-bandwidth applications.

Abstract

A feed-forward photonic neural network (PNN) is tested for chromatic dispersion compensation in Intensity Modulation/Direct Detection optical links. The PNN is based on a sequence of linear and nonlinear transformations. The linear stage is constituted by an 8-tap time-delayed complex perceptron implemented on a Silicon-On-insulator platform and acting as a tunable optical filter. The nonlinear stage is provided by the square modulus of the electrical field applied at the end-of-line photodetector. The training maximizes the separation between the optical levels (i.e. the eye diagram aperture), with consequent reduction of the Bit Error Rate. Effective equalization is experimentally demonstrated for 20 Gbps 4-level Pulse Amplitude Modulated signal up to 125 km. An evolutionary algorithm and a gradient-based approach are tested for the training and then compared in terms of repeatability and convergence time. The optimal weights resulting from the training are interpreted in light of the theoretical transfer function of the optical fiber. Finally, a simulative study proves the scalability of the layout to larger bandwidths, up to 100 Gbps.

Figures (13)

• Figure 1: (a) Layout of the 8-channel time-delayed complex perceptron (PNN device). The input signal $x(t)$ propagates through a cascade of y-branches and spiralized optical paths producing 8 time-delayed copies hosted in as many parallel waveguides. The spirals are available in 3 lengths $L_A = 7.10$ mm, $L_B = 3.55$ mm, and $L_C = 1.77$ mm, corresponding to an added propagation time respectively of $\Delta t_A = 100$ ps, $\Delta t_B = 50$ ps, and $\Delta t_C = 25$ ps. The delayed copies are then applied with an amplitude and a phase weight via a series of a Mach-Zehnder interferometer (MZI) and a phase shifter (PS) hosted in each channel. These are controlled via current-driven micro-heaters placed on top of the waveguides. Finally, the output signal is obtained by complex-summing the weighted copies via a $1\times 8$ combiner realized with a cascade of y-branches. (b) Simplified experimental setup. The modulated optical signal is sent to the PNN device used as a pre-compensator for CD effect. The processed signal propagates then through a fiber span with variable lengths, between 0 km and 125 km with steps of 25 km. Two fast photodiodes connected to an oscilloscope (OSC) acquire respectively the input (RX1) and output (RX2) traces, then send them to the computer for loss function evaluation. A DC current generator drives the weights applied by the PNN device.
• Figure 2: Illustration of the one-sample separation loss function $\mathcal{L}_1(k)$ evaluation. The current representation refers to $k=N_{sps}/2$, and any reference to it in subscripts or superscripts has been omitted for clarity. The left panel presents a time trace of the output signal $y$ (blue line) as acquired by RX2, with 8 samples per symbol (blue dots), and the software-generated target signal (black line). The sub-sampling of $y$ at the $k$-th sample generates $y_k$, whose samples (large colored circles) are grouped into $\{y\}_{k,n}$ depending on the expected level $n$, with $n=0,\dots,3$. Samples in each group are distinguished by color (red, green, purple, yellow) and populate the corresponding distributions presented in the central panel. The left and right tails' position $E_L[n]$ and $E_R[n]$ for each distribution enter in the definition of $\mathcal{L}_1$ (see \ref{['eq:s1']}), while the thresholds $T_{n,n+1}$ (see \ref{['eq:threshold']}) produce a digitized version of $y_k$. For the sake of clarity, the visual representation is limited to the quantities referred to the two central levels. The right panel analyzes a single distribution ($n=3$ characterized by its mean value $I_n$ and its standard deviation $\sigma_n$. The value of $E_L[n]$ ($E_R[n]$) results from the average position of the leftmost (rightmost) 10% of the population, both represented by orange bars.
• Figure 3: Optimal amplitude weights $a_i$ with $i=1,\dots,8$ obtained after the training of the PNN in Full configuration (8 amplitude and 7 phase weights) for channel equalization at (a) 25 km, (b) 50 km, (c) 75 km, (d) 100 km, and (e) 125 km. The boxes below each diagram report the sum of the aperture levels $\Sigma_{i=1}^{N=8} a_i$ for that transmission scenario and the related insertion losses, IL.
• Figure 4: Comparison between different training strategies performed with PSO. (a) BER values measured after the training performed in full configuration with $\mathcal{L}_1$ (blue line), in PO configuration with $\mathcal{L}_1$ (orange line), and in PO configuration with $\mathcal{L}_2$ (yellow line) as a function of the fiber length. Each value results from the average over 20 measurements with the error bars corresponding to 68% credible interval for the associated Poisson distribution. (b-c) Eye diagrams at the receiver after the training performed in PO configuration with (b) $\mathcal{L}_1$ and (c) $\mathcal{L}_2$ respectively.
• Figure 5: (a-c) BER versus Power at the receiver profiles for propagation in (a) 25 km, (b) 75 km), and (c) 125 km. The unequalized (black stars) and equalized (colored circles) are compared with the Back-to-Back performance (BTB, black circles). The training procedures have been performed with the PSO and BER values obtained as an average over 50 acquisitions and their error bars represent the 68% credible interval for the corresponding Poisson distribution. (d-f) Unequalized eye diagrams for (d) 25 km, (e) 75 km, and (f) 125 km propagation. (g-i) Equalized eye diagrams for (g) 25 km, (h) 75 km, and (i) 125 km propagation.