Abstract
The propagation of light in nonlinear optical media has been widely used as a tabletop platform for emulating quantum-like phenomena due to their similar theoretical description to quantum fluids. These fluids of light are often used to study two-dimensional phenomena involving superfluid-like flows, yet turbulent regimes still remain underexplored. In this work, we study the possibility of creating two-dimensional turbulent phenomena and probing their signatures in the kinetic energy spectrum. To that end, we emulate and disturb a fluid of light with an all-optical defect using the propagation of two beams in a photorefractive crystal. Our experimental results show that the superfluid regime of the fluid of light breaks down at a critical velocity at which the defect starts to exert a drag force on the fluid, in accordance with the theoretical and numerical predictions. Furthermore, in this dissipative regime, nonlinear perturbations are excited on the fluid that can decay into vortex structures and thus precede a turbulent state. Using the off-axis digital holography method, we reconstructed the complex description of the output fluids and calculated the incompressible component of the kinetic energy. With these states, we observed the expected power law that characterizes the generated turbulent vortex dipole structures. The findings enclosed in this manuscript align with the theoretical predictions for the vortex structures of two-dimensional quantum fluids and thus may pave the way to the observation of other distinct hallmarks of turbulent phenomena, such as distinct turbulent regimes and their associated power laws and energy cascades.

Abstract
Extreme learning machines (ELMs) are a versatile machine learning technique that can be seamlessly implemented with optical systems. In short, they can be described as a network of hidden neurons with random fixed weights and biases, that generate a complex behaviour in response to an input. Yet, despite the success of the physical implementations of ELMs, there is still a lack of fundamental understanding about their optical implementations. This work makes use of an optical complex media to implement an ELM and introduce an ab-initio theoretical framework to support the experimental implementation. We validate the proposed framework, in particular, by exploring the correlation between the rank of the outputs, H, and its generalization capability, thus shedding new light into the inner workings of optical ELMs and opening paths towards future technological implementations of similar principles.

Abstract
Reservoir computing is a versatile approach for implementing physically Recurrent Neural networks which take advantage of a reservoir, consisting of a set of interconnected neurons with temporal dynamics, whose weights and biases are fixed and do not need to be optimized. Instead, the training takes place only at the output layer towards a specific task. One important requirement for these systems to work is nonlinearity, which in optical setups is usually obtained via the saturation of the detection device. In this work, we explore a distinct approach using a photorefractive crystal as the source of the nonlinearity in the reservoir. Furthermore, by leveraging on the time response of the photorefractive media, one can also have the temporal interaction required for such architecture. If we space out in time the propagation of different states, the temporal interaction is lost, and the system can work as an extreme learning machine. This corresponds to a physical implementation of a Feed-Forward Neural Network with a single hidden layer and fixed random weights and biases. Some preliminary results are presented and discussed. © Published under licence by IOP Publishing Ltd.

Abstract
Easily accessible through tabletop experiments, paraxial fluids of light are emerging as promising platforms for the simulation and exploration of quantumlike phenomena. In particular, the analogy builds on a formal equivalence between the governing model for a Bose-Einstein condensate under the mean-field approximation and the model of laser propagation inside nonlinear optical media under the paraxial approximation. Yet, the fact that the role of time is played by the propagation distance in the analog system imposes strong bounds on the range of accessible phenomena due to the limited length of the nonlinear medium. In this Letter, we present an experimental approach to solve this limitation in the form of a digital feedback loop, which consists of the reconstruction of the optical states at the end of the system followed by their subsequent reinjection exploiting wavefront shaping techniques. The results enclosed demonstrate the potential of this approach to access unprecedented dynamics, paving the way for the observation of novel phenomena in these systems.

Abstract
This communication explores an optical extreme learning architecture to unravel the impact of using a nonlinear optical media as an activation layer. Our analysis encloses the evaluation of multiple parameters, with special emphasis on the efficiency of the training process, the dimensionality of the output space, and computing performance across tasks associated with the classification in low-dimensionality input feature spaces. The results enclosed provide evidence of the importance of the nonlinear media as a building block of an optical extreme learning machine, effectively increasing the size of the output space, the accuracy, and the generalization performances. These findings may constitute a step to support future research on the field, specifically targeting the development of robust general-purpose all-optical hardware to a full-stack integration with optical sensing devices toward edge computing solutions.

Abstract
Lately, the field of optical computing resurfaced with the demonstration of a series of novel photonic neuromorphic schemes for autonomous and inline data processing promising parallel and light-speed computing. We emphasize the Photonic Extreme Learning Machine (PELM) as a versatile configuration exploring the randomness of optical media and device production to bypass the training of the hidden layer. Nevertheless, the implementation of this framework is limited to having the output layer performed digitally. In this work, we extend the general PELM implementation to an all-optical configuration by exploring the amplitude modulation from a spatial light modulator (SLM) as an output linear layer with the main challenge residing in the training of the output weights. The proposed solution explores the package pyTorch to train a digital twin using gradient descent back-propagation. The trained model is then transposed to the SLM performing the linear output layer. We showcase this methodology by solving a two-class classification problem where the total intensity reaching the camera predicts the class of the input sample.