# A complete, parallel and autonomous photonic neural network in a semiconductor multimode laser

## AG Optoelektronik und Quantenbauelemente

Neural networks are one of the disruptive computing concepts of our time. However, they fundamentally differ from classical, algorithmic computing. These differences result in equally fundamental, severe and relevant challenges for neural network computing using current computing substrates. Neural networks urge for parallelism across the entire processor and for a co-location of memory and arithmetic, i.e. beyond von Neumann architectures. Parallelism in particular made photonics a highly promising platform, yet until now scalable and integratable concepts are scarce. Here, we demonstrate for the first time how a fully parallel and fully implemented photonic neural network can be realized by spatially multiplexing neurons across the complex optical near-field of a semiconductor multimode laser. Discrete spatial sampling defines ∼90 nodes on the surface of a large-area vertical cavity surface emitting laser that is optically injected with the artificial neural networks input information. Importantly, all neural network connections are realized in hardware, and our processor produces results without pre- or post-processing. Input and output weights are realized via the complex transmission matrix of a multimode fiber and a digital micro-mirror array, respectively. We train the readout weights to perform 2-bit header recognition, a 2-bit XOR logical function and 2-bit digital to analog conversion, and obtain $\lt0.9 \times 10^{-3}$ and 2.9 × 10−2 error rates for digit recognition and XOR, respectively. Finally, the digital to analog conversion can be realized with a standard deviation of only 5.4 × 10−2. Crucially, our proof-of-concept system is scalable to much larger sizes and to bandwidths in excess of 20 GHz.