Search results for "Nonlinear"
showing 10 items of 3684 documents
Watch-hand-like optical rogue waves in three-wave interactions
2015
11 págs.; 6 figs.; OCIS codes: (190.3100) Instabilities and chaos; (190.5530) Pulse propagation and temporal solitons; (190.4410) Nonlinear optics, parametric processes.
Peculiarities of coherent optical oscillation in Sn_2P_2S_6 crystals
2010
We show analytically and numerically that the unusual photorefractive nonlinear response of Sn2P2S6 crystals leads to a variety of new features of coherent optical oscillation. In addition to the explanation of the known peculiarities, new features are predicted.
Generalized complex Swift-Hohenberg equation for optical parametric oscillators
1997
A generalized complex Swift-Hohenberg equation including diffraction and nonlinear resonance terms is derived for spatially extended nondegenerate optical parametric oscillators (OPOs) with flat end mirrors. For vanishing pump detuning this equation becomes the complex Swift-Hohenberg (SH) equation valid also for lasers. Nevertheless the similarities between OPOs and lasers are limited, since the diffractive character of OPOs is lost when the diffraction coefficients of signal and idler fields are equal. This manifests, e.g., in the absence of advection by traveling waves (TWs), a clear difference with lasers. When pump detuning is nonzero a nonlinear resonance develops, as it occurs in deg…
Bi-color spatial solitons in linearly uncoupled planar waveguides
2004
We report on the observation of spatial optical simultons in a novel geometry consisting of two partially overlapped, linearly uncoupled planar waveguides in lithium niobate obtained by reverse proton exchange. Two orthogonally polarized modes are coupled through an off-diagonal tensor element of the quadratic nonlinearity, giving rise to second harmonic generation and mutual trapping via cascading. This phenomenon demonstrates a balance between diffraction and self-focusing for two orthogonal modes of different waveguides, and occurs at room temperature in longitudinally uniform waveguides.
Thermalization of the dispersive three-wave interaction
2007
We investigate the role of dispersion effects on the long-term evolution of the nonlinear three-wave interaction. We show that the three waves exhibit, as a general rule, an irreversible evolution towards a thermodynamic equilibrium state in which they propagate with identical velocities. As a result of this thermalization process, the three-wave system is driven away from spatio-temporal resonance, so that the equilibrium state does not satisfy the (phase-matching) resonant conditions of energy and momentum conservation for the averaged frequencies. Moreover, we show that the interplay between temporal dispersion and spatial diffraction leads to the emergence of a peculiar equilibrium stat…
Experimental approach to transverse wave-number selection in cavity nonlinear optics
2004
Spontaneous transverse pattern formation is experimentally studied in a ${\text{BaTiO}}_{3}$ photorefractive oscillator under degenerate four-wave mixing conditions. A near self-imaging resonator of high Fresnel number and quasi-one-dimensional in the transverse plane is used. A fine control technique of the cavity detuning, $\ensuremath{\Omega}$, is described. It allows a precise study of the relation of $\ensuremath{\Omega}$ with the transverse wave number ${k}_{\ensuremath{\perp}}$ of the roll patterns selected by the system. The law ${k}_{\ensuremath{\perp}}^{2}=\ensuremath{-}\ensuremath{\Omega}∕a$ is verified, which evidences that wave-number selection is mainly dictated by the cavity …
Diffraction-free beams with elliptic Bessel envelope in periodic media
2007
We report on discrete, nondiffracting, paraxial beams with a Bessel spatial envelope in 1D periodic structures of dielectric media. Anisotropy of the envelope profile is demonstrated to behave in the same manner as extraordinary waves in uniaxial crystals.
Multipole solitary wave solutions of the higher-order nonlinear Schrödinger equation with quintic non-Kerr terms
2013
We consider a high-order nonlinear Schrodinger (HNLS) equation with third- and fourth-order dispersions, quintic non-Kerr terms, self steepening, and self-frequency-shift effects. The model applies to the description of ultrashort optical pulse propagation in highly nonlinear media. We propose a complex envelope function ansatz composed of single bright, single dark and the product of bright and dark solitary waves that allows us to obtain analytically different shapes of solitary wave solutions. Parametric conditions for the existence and uniqueness of such solitary waves are presented. The solutions comprise fundamental solitons, kink and anti-kink solitons, W-shaped, dipole, tripole, and…
The multiple slope discontinuity beam element for nonlinear analysis of RC framed structures
2018
The seismic nonlinear response of reinforced concrete structures permits to identify critical zones of an existing structure and to better plan its rehabilitation process. It is obtained by performing finite element analysis using numerical models classifiable into two categories: lumped plasticity models and distributed plasticity models. The present work is devoted to the implementation, in a finite element environment, of an elastoplastic Euler–Bernoulli beam element showing possible slope discontinuities at any position along the beam span, in the framework of a modified lumped plasticity. The differential equation of an Euler–Bernoulli beam element under static loads in presence of mul…
The Soliton Concept in Lattice Dynamics
1996
In previous chapters we have considered nonlinear waves in the macroworld. We have examined different systems which provide the simplest examples of onedimensional systems or devices, where the localized waves or pulses called solitons can be simply and coherently created, easily observed, and manipulated on a macroscopic scale. At the microscopic level the localized nonlinear wave modes have a spatial extension ranging from less than a few microns to a few angstroms. These excitations, which correspond to large-amplitude atomic or molecular motions, are mainly created by thermal processes, sometimes by some external stimulus; their experimental manifestation is indirect; their observation …