20-GHz bandwidth optical activation function based on a semiconductor laser

Optical neural networks usually execute the linear multiply-accumulate operation in the optical domain, whereas the nonlinear activation function is mostly implemented in the digital or electrical domain. Here, we demonstrate a broadband activation function operated in the optical domain. The optical activation function (OAF) is achieved using a semiconductor laser with optical injection, which is operated in the unstable-locked regime beyond the Hopf bifurcation. The operation bandwidth of the OAF reaches as high as 20 GHz, which is limited by the relaxation oscillation resonance frequency of the semiconductor laser. The OAF mimics a ReLU function for modulation frequencies below 5 GHz, and resembles an ELU function for frequencies above 5 GHz.