Nov 12 min read

PAM4 Signal Regeneration using Silicon Photonics Optical Neural Networks

Introduction

Optical communication systems are increasingly adopting higher-order modulation formats like 4-level pulse amplitude modulation (PAM4) to increase data rates over existing fiber infrastructure. However, fiber chromatic dispersion and other impairments degrade the PAM4 signal, requiring signal regeneration. This tutorial discusses using an optical neural network (ONN) based on silicon photonics for regenerating PAM4 signals.

Optical Neural Networks

Neural networks running on electronic hardware face limitations like speed, scalability, and high power consumption. Optical neural networks (ONNs) implemented using integrated photonics can run AI/machine learning algorithms more efficiently. Different ONN designs utilize diffractive gratings, metasurfaces, or Mach-Zehnder interferometers (MZIs) for matrix/vector operations.

Proposed ONN Architecture

The proposed ONN architecture is based on a regression model using cascaded MZI meshes to regenerate degraded PAM4 signals, as shown in Figure 1.

Figure 1: (a) ONN model architecture for PAM4 regeneration; (b) Single MZI switch; (c) Electro-optic nonlinear activation function

A single MZI acts as a 2x2 matrix performing the transformation in Equation 1, with tunable phase shifts θ and φ.

The MZIs are arranged in a Reck mesh structure to realize a fully-connected neural network operation matrix (Equation 2), relating the input X and output Y (Equation 3).

Nonlinear activation is achieved via an electro-optic structure (Figure 1c) with a directional coupler, photodetector, electrical amplifier, and MZI (Equation 4).

During training, the mean squared error between the input degraded PAM4 signal (after fiber transmission) and the target PAM4 signal is minimized using an adaptive optimizer. This yields the optimal phase shift values for regenerating the signal.

Simulation Setup

Figure 2 shows the simulation setup in OptSim. A 40 Gbaud PAM4 signal at 1550nm is generated using a Mach-Zehnder modulator (MZM) and propagated through different fiber spans. The signal after the fiber and the original signal from the MZM are used as training data to optimize the ONN model in Python. The trained ONN phase values are then applied in OptSim to regenerate the fiber-degraded PAM4 signal.

Results and Discussion

Figure 3 plots the bit error rate (BER) of the 40 Gbaud PAM4 signal after propagating through different fiber lengths with and without the proposed ONN regenerator. The ONN can regenerate the signal up to 18km fiber propagation while meeting the soft-decision forward error correction (SD-FEC) threshold of BER < 2.4×10^-2 up to 12km.

Figure 3: BER of 40 Gbaud PAM4 signal through SSMF with and without ONN processing

The regenerative capability is visualized in the eye diagrams in Figure 4, showing the severely distorted 40 Gbaud PAM4 signal after 10km fiber transmission (a) and its regenerated form after ONN processing (b).

Figure 4: 40 Gbaud PAM4 eye diagrams (a) After 10km SSMF; (b) After 10km SSMF with ONN processing

Conclusion

This work proposes and simulates a silicon photonics optical neural network for regenerating PAM4 signals degraded by fiber transmission. By training an MZI-based ONN regression model, the 40 Gbaud PAM4 signal quality can be significantly improved to meet forward error correction requirements after up to 12km fiber propagation. The all-optical ONN avoids optical-electrical-optical conversions, enabling efficient high-speed PAM4 regeneration. Further work can explore extending this approach to higher baud rates.

Reference

T.-Y. Hung, C.-C. Wang, C.-W. Chow, Y.-C. Chang, and C.-H. Yeh, "PAM4 Signal Regenerator Using Mach-Zehnder Interferometer Based Optical Neural Network (ONN)," Department of Photonics, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan; Department of Photonics, Feng Chia University, Seatwen, Taichung 40724, Taiwan, 2024, pp. 1-6, doi: 979-8-3503-9404-7/24/$31.00 ©2024 IEEE.