Related papers: Self-trapping and stable localized modes in nonlin…
The ground state of the Holstein molecular crystal model in one dimension is studied using the Global-Local variational method, analyzing in particular the total energy, kinetic energy, phonon energy, and interaction energy over a broad…
The Kerr nonlinearity allows for exact analytic soliton solutions in 1+1D. While nothing excludes that these solitons form in naturally-occurring real-world 3D settings as solitary walls or stripes, their observation has previously been…
We consider non-stationary localized oscillations of an infinite Bernoulli-Euler beam. The beam lies on the Winkler foundation with a point inhomogeneity (a concentrated spring with negative time-varying stiffness). In such a system with…
Waveguide arrays offer enormous potential to design circuit elements essential to fabricate optical devices capable to processing information codified by light. In this work we study the existence and stability of localized beams in one…
In this article we study the spectral, linear and nonlinear stability of stationary shock profile solutions to the Lax-Wendroff scheme for hyperbolic conservation laws. We first clarify the spectral stability of such solutions depending on…
We propose and demonstrate theoretically a method to achieve and design optical nonlinear responses through a light-mediated spatial hybridization of different standard nonlinearities. The mechanism is based on the fact that optical…
Spontaneous symmetry breaking in nonlinear systems provides a unified method to understand vastly different phenomena, ranging from Higgs mechanism [1] and superconductivity [2] to ecological stability [3] and genome generation [4].…
We investigate the properties of localized waves in systems governed by nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g.,…
We introduce a mechanism of stable spatiotemporal soliton formation in a multimode fiber laser. This is based on spatially graded dissipation, leading to distributed Kerr-lens mode-locking. Our analysis involves solutions of a generalized…
We theoretically study the effect of pulse trapping inside one-dimensional photonic crystal with relaxing cubic nonlinearity. We analyze dependence of light localization on pulse intensity and explain its physical mechanism as connected…
Electromagnetic localization and existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the…
We present a two-dimensional photonic crystal design with a microcavity of four defect dielectric rods with eigenfrequencies residing in the propagating band of directional waveguide. In the linear case for tuning of material parameters of…
We predict that spatial self-trapping of light can occur in soft matter encompassing a wide class of new materials such as colloids, foams, gels, fractal aggregates etc. We develop a general nonlocal theory that allows to relate the…
We investigate the use of guided modes bound to defects in photonic crystals for achieving double resonances. Photoluminescence enhancement by more than three orders of magnitude has been observed when the excitation and emission…
Production of entangled photon pairs is important in secure communication systems, quantum computing, and fundamental physics experiments. Achieving efficient generation of such photon pairs with low-loss parametric oscillators is a key…
We report the existence and properties of localized modes described by nonlinear Schroedinger equation with complex PT-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one…
Nonlinear optical phenomena are typically local. Here we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms…
We study localized modes on a single Ablowitz-Ladik impurity embedded in the bulk or at the surface of a one-dimensional linear lattice. Exact expressions are obtained for the bound state profile and energy. Dynamical excitation of the…
Photonic topological insulators and self-induced nonreciprocity based on nonlinear effects in asymmetric structures have garnered increased attention due to their potential applications in quantum information technologies and advanced…
We generalize the concept of nonlinear periodic structures to systems that show arbitrary spacetime variations of the refractive index. Nonlinear pulse propagation through these spatiotemporal photonic crystals can be described, for shallow…