The Game of Light

In memoriam: John Horton Conway

In 1970 an article by Martin Gardner appeared in Scientific American disclosing for the first time a “game” invented by John H. Conway: a matrix of ones and zeros changes with time according to simple rules inspired by biology. Cells (ones) survive or die because of overpopulation, or starvation. The simple rules surprisingly generate a variety of binary animals, named gliders, blocks, and spaceships, among others. By pen and paper, Conway demonstrated that complex dynamics spontaneously emerge in the game. Ultimately, Conway’s Game of Life turned out to be a universal Turing machine, and it is the most famous example of Cellular Automaton.

I was deeply inspired by the possibility of generating complexity with simple rules, like many others before me. In more than 50 years, Conway’s Game of Life inspired generations of scientists. “Life” is at the inner core of ideas that pervade nowadays machine learning, evolutionary biology, quantum computing, and many other fields. It also connects to the work of Wolfram and the development of Mathematica.

I was intrigued by the interaction between light and complexity and I wanted to combine the Game of Life with electromagnetic fields. I report below my original post on the topic (dating back to 2008). The article was rejected by many journals and finally published in a book dedicated to the 50 years of the GOL ( Game of Life Cellular Automata, Springer 2010).

The Enlightened Game of Life (EGOL)

The link between light and the development of complex behavior is as subtle as evident. Examples include the moonlight triggered mass spawning of hard corals in the Great Barrier, or the light-switch hypothesis in evolutionary biology, which ascribes the Cambrian explosion of biodiversity to the development of vision. Electromagnetic (EM) radiation drastically alters complex systems, from physics (e.g., climate changes) to biology (e.g., structural colors or bioluminescence). So far the emphasis has been given to bio-physical, or digital, models of the evolution of the eye with the aim of understanding the environmental influence on highly specialized organs. In this manuscript, we consider the way the appearance of photosensitivity affects the dynamics, the emergent properties and the self-organization of a community of interacting agents, specifically, of cellular automata (CA).

Quick and dirty implementation of the EGOL in a Python Notebook

https://github.com/nonlinearxwaves/gameoflife.git

Optimal noise in Ising machines

Ising machines are novel computing devices for the energy minimization of Ising models. These combinatorial optimization problems are of paramount importance for science and technology, but remain difficult to tackle on large scale by conventional electronics. Recently, various photonics-based Ising machines demonstrated ultra-fast computing of Ising ground state by data processing through multiple temporal or spatial optical channels. Experimental noise acts as a detrimental effect in many of these devices. On the contrary, we here demonstrate that an optimal noise level enhances the performance of spatial-photonic Ising machines on frustrated spin problems. By controlling the error rate at the detection, we introduce a noisy-feedback mechanism in an Ising machine based on spatial light modulation. We investigate the device performance on systems with hundreds of individually-addressable spins with all-to-all couplings and we found an increased success probability at a specific noise level. The optimal noise amplitude depends on graph properties and size, thus indicating an additional tunable parameter helpful in exploring complex energy landscapes and in avoiding trapping into local minima. The result points out noise as a resource for optical computing. This concept, which also holds in different nanophotonic neural networks, may be crucial in developing novel hardware with optics-enabled parallel architecture for large-scale optimizations.

arXiv:2004.02208

Published in Nanophotonics

Noise-enhanced spatial-photonic Ising machine

Topological photonic crystal fibers and ring resonators

With an exact recursive approach, we study photonic crystal fibers and resonators with topological features induced by Aubry–Andre–Harper cladding modulation. We find nontrivial gaps and edge states at the interface between regions with different topological invariants. These structures show topological protection against symmetry-preserving local perturbations that do not close the gap and sustain strong field localization and energy concentration at a given radial distance. As topological light guiding and trapping devices, they may bring about many opportunities for both fundamentals and applications unachievable with conventional devices.

Laura Pilozzi et al. Optics Letters 45, 1415 (2020)

Spin-orbit coupling in graphene-based nanostructures with broken rotational symmetry

Spin and angular momenta of light are important degrees of freedom in nanophotonics which control light propagation, optical forces and information encoding. Typically, optical angular momentum is generated using q-plates or spatial light modulators. Here, we show that graphene-supported plasmonic nanostructures with broken rotational symmetry provide a surprising spin to orbital angular momentum conversion, which can be continuously controlled by changing the electrochemical potential of graphene. Upon resonant illumination by a circularly polarized plane wave, a polygonal array of indium-tin-oxide nanoparticles on a graphene sheet generates scattered field carrying electrically-tunable orbital angular momentum. This unique photonic spin-orbit coupling occurs due to the strong coupling of graphene plasmon polaritons and localised surface plasmons of the nanoparticles and leads to the controlled directional excitation of graphene plasmons. The tuneable spin-orbit conversion pave the way to high-rate information encoding in optical communications, electric steering functionalities in optical tweezers, and nanorouting of higher-dimensional entangled photon states.

Ciattoni et al in arXiv:2002.12058

Theory of neuromorphic computing by waves

Machine-learning by rogue waves, dispersive shocks, and solitons

We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layer model, with an encoding input layer, a wave layer, and a decoding readout, behaves as a conventional neural network in approximating mathematical functions, real-world datasets, and universal Boolean gates. The rank of the transmission matrix has a fundamental role in assessing the learning abilities of the wave. For a given set of training points, a threshold nonlinearity for universal interpolation exists. When considering the nonlinear Schroedinger equation, the use of highly nonlinear regimes implies that solitons, rogue, and shock waves do have a leading role in training and computing. Our results may enable the realization of novel machine learning devices by using diverse physical systems, as nonlinear optics, hydrodynamics, polaritonics, and Bose-Einstein condensates. The application of these concepts to photonics opens the way to a large class of accelerators and new computational paradigms. In complex wave systems, as multimodal fibers, integrated optical circuits, random, topological devices, and metasurfaces, nonlinear waves can be employed to perform computation and solve complex combinatorial optimization.

ArXiv:1912.07077