The optical domain is a promising field for the physical implementation of neural networks, due to the speed and parallelism of optics. Extreme learning machines (ELMs) are feed-forward neural networks in which only output weights are trained, while internal connections are randomly selected and left untrained. Here we report on a photonic ELM based on a frequency-multiplexed fiber setup. Multiplication by output weights can be performed either offline on a computer or optically by a programmable spectral filter. We present both numerical simulations and experimental results on classification tasks and a nonlinear channel equalization task.

We propose a novel method to perform plenoptic imaging at the diffraction limit by measuring second-order correlations of light between two reference planes, arbitrarily chosen, within the tridimensional scene of interest. We show that for both chaotic light and entangledphoton illumination, the protocol enables to change the focused planes, in post-processing, and to achieve an unprecedented combination of image resolution and depth of field. In particular, the depth of field results larger by a factor 3 with respect to previous correlation plenoptic imaging protocols, and by an order of magnitude with respect to standard imaging, while the resolution is kept at the diffraction limit. The results lead the way towards the development of compact designs for correlation plenoptic imaging devices based on chaotic light, as well as high-SNR plenoptic imaging devices based on entangled photon illumination, thus contributing to make correlation plenoptic imaging effectively competitive with commercial plenoptic devices.1This is not the case in so called Plenoptic 2.0, where the microlenses create redundant images of the scene of arXiv:2007.12033v2 [physics.optics] 4 Aug 2020 interest [25] and propagation direction is obtained by a sort of triangulation, with the effect of improving the depth of field while further sacrificing the image resolution

Reservoir computing is a brain-inspired approach for information processing, well suited to analog implementations. We report a photonic implementation of a reservoir computer that exploits frequency domain multiplexing to encode neuron states. The system processes 25 comb lines simultaneously (i.e., 25 neurons), at a rate of 20 MHz. We illustrate performances on two standard benchmark tasks: channel equalization and time series forecasting. We also demonstrate that frequency multiplexing allows output weights to be implemented in the optical domain, through optical attenuation. We discuss the perspectives for high-speed, high-performance, low-footprint implementations.

In a recent work, we reported on an Extreme Learning Machine (ELM) implemented in a photonic system based on frequency multiplexing, where each wavelength of the light encodes a different neuron state. In the present work, we experimentally demonstrate the parallelization potentialities of this approach. We show that multiple frequency combs centered on different frequencies can copropagate in the same system, resulting in either multiple independent ELMs executed in parallel on the same substrate or a single ELM with an increased number of neurons. We experimentally tested the performances of both these operation modes on several classification tasks, employing up to three different light sources, each of which generates an independent frequency comb. We also numerically evaluated the performances of the system in configurations containing up to 15 different light sources.

Reservoir Computers (RC) are brain-inspired algorithms that use partially untrained recurrent neural networks where only output connections are tuned. RCs can perform signal-analysis tasks such as distortion compensation. We recently demonstrated a photonic RC in which neurons are encoded in a frequency comb, untrained interconnections are realized by phase modulation, and trained output connections are realized by spectral filters. Here, we present a further development of this scheme in which the same substrate is used to implement two RCs simultaneously. The two RCs can either be used in parallel on different tasks, or in series, thereby implementing a "deep" RC.