Related papers: Predicting ultrafast nonlinear dynamics in fibre o…
Ultrafast lasers ($< 500$ fs) have enabled laser-matter interactions at intensities exceeding $10^{18} \rm{Wcm}^{-2}$ with only millijoules of laser energy. However, as pulse durations become shorter, larger spectral bandwidths are…
The properties of pulse propagation in a nonlinear fiber including linear damped term added in the usual nonlinear Schr\"odinger equation is analyzed analytically. We apply variational modified approach based on the lagrangian that describe…
Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations -- including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single…
We investigate the potential of supervised machine learning to propagate a quantum system in time. While Markovian dynamics can be learned easily, given a sufficient amount of data, non-Markovian systems are non-trivial and their…
A new method for finding solutions of the nonlinear Shr\"{o}dinger equation is proposed. Comutative multiplicative group of the nonlinear transformations, which operate on stationary localized solutions, enables a consideration of fractal…
We propose a mathematical framework to systematically explore the propagation properties of a class of continuous in time nonlinear neural network models comprising a hierarchy of processing areas, mutually connected according to the…
Metaoptics are thin, planar surfaces consisting of many subwavelength optical resonators that can be designed to simultaneously control the amplitude, phase, and polarization to arbitrarily shape an optical wavefront much in the same manner…
Deep neural networks have achieved remarkable breakthroughs by leveraging multiple layers of data processing to extract hidden representations, albeit at the cost of large electronic computing power. To enhance energy efficiency and speed,…
The propagation of light-pulse with negative group-velocity in a nonlinear medium is studied theoretically. We show that the necessary conditions for these effects to be observable are realized in a three-level $\Lambda$-system interacting…
The brain cortex, which processes visual, auditory and sensory data in the brain, is known to have many recurrent connections within its layers and from higher to lower layers. But, in the case of machine learning with neural networks, it…
We propose a novel method for learning convolutional neural image representations without manual supervision. We use motion cues in the form of optical flow, to supervise representations of static images. The obvious approach of training a…
The macroscopic response of short fiber reinforced composites is dependent on an extensive range of microstructural parameters. Thus, micromechanical modeling of these materials is challenging and in some cases, computationally expensive.…
The existence regimes and dynamics of soliton molecules in dispersion-managed (DM) optical fibers have been studied. Initially we develop a variational approximation (VA) for description of periodic dynamics of a soliton molecule within…
Latent variable models have been widely applied for the analysis of time series resulting from experimental neuroscience techniques. In these datasets, observations are relatively smooth and possibly nonlinear. We present Variational…
Building on the scientific understanding and technological infrastructure of single-mode fibers, multimode fibers are being explored as a means of adding new degrees of freedom to optical technologies such as telecommunications, fiber…
Training recurrent neural networks (RNNs) is a hard problem due to degeneracies in the optimization landscape, a problem also known as vanishing/exploding gradients. Short of designing new RNN architectures, previous methods for dealing…
We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse…
Simple fiber optic communication systems can be implemented using energy modulation of isolated time-limited pulses. Fundamental solitons are one possible solution for such pulses which offer a fundamental advantage: their shape is not…
We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a defocusing nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…