Self-defocusing Kerr Media Research Articles

Local dynamic behavior of dark beams in self-defocusing Kerr media

We study the local dynamic behavior of dark beams in self-defocusing Kerr media. In this, we are encouraged by the interesting results obtained in Refs. [1,2], although these papers are concerned with the bright beams in self-focusing Kerr media. Similar to these papers, we are interested in the two-dimensional (2D) necklace ring beams, but under certain circumstances. Different from these papers, we are interested in the dark necklace beams in self-defocusing media. When the dimensionless ring radius L is far greater than the ring thickness w, the 2D defocusing nonlinear Schrödinger equation in cylindrical coordinates can be simplified to the standard 1D defocused nonlinear Schrödinger (NLS) equation. Then, an approximate solution of the 1D NLS equation can be constructed by different means, for example by a simple combination of exponential and trigonometric functions. In general, such a necklace solution can be described by two parameters: the ring radius L and the topological charge m. Hence, we study the local dynamic behavior of dark beams with different topological charges m and different ring radii L when they are much larger that the ring thickness w. Different spatial distributions of dark beams are obtained for m zero, positive integer, and half-integer. We use direct numerical simulation to confirm the validity of our analytical approximate solution. Our results show that the structure of dark beams can be well controlled by adjusting the ring radius and the topological charge. Our procedure provides a new method for dealing with high-dimensional nonlinear equations of different origin.

One-dimensional -symmetric eigenmodes in k-wave number Scarf II potential with defocusing nonlinearity

The stationary states and dynamical evolution of one-dimensional eigenmodes in self-defocusing nonlinear Kerr medium under transverse parity-time () symmetric k-wave number Scarff-II potential have been analysed. We study the effect of the coefficient of the imaginary component of the -symmetric potential on the eigenvalue spectra of the ground and first excited states in linear and nonlinear models. Symmetric eigenmodes with real eigenvalues are obtained in the unbroken regime in both models. The linear stability analysis shows that the solutions are stable in the unbroken regime. The stable propagation of the solutions in linear and nonlinear media supported by -symmetric k-wave number Scarff-II potential is also investigated. The comparison of the solutions in the presence and the absence of nonlinearity reveals that in the self-defocusing Kerr medium nonlinearity suppresses the region of -symmetry. The influence of the width of the complex k-wave number Scarff-II potential and the depth of the real potential function on the -symmetry breaking have also been analysed.

Spatiotemporal optical vortex solitons: Dark solitons with transverse and tilted phase line singularities

Vortex solitons (dark solitons) are described in self-defocusing Kerr media whose phase line singularity is not parallel to the propagation direction, but is perpendicular or tilted almost arbitrary angles, depending on the medium linear dispersion. These solitons broaden the so-called spatiotemporal optical vortices recently observed in experiments to the nonlinear realm, opening new perspectives in practical applications of optical vortices.

TM Standing Wave Solution of Maxwell Equations in a Self-Defocusing Kerr Media and its Application to a Thin-Film Waveguide

We applied the dielectric function method to solve analytically L-NL-L structure problems with negative Kerr nonlinearity. A damped wave in linear and a periodic standing wave in non-linear media had to be matched at boundaries. We gave a formulation of boundary conditions that did not explicitly include a film thickness. The boundary-value of a dielectric function can be expressed through the constant of non-trivial integral of motion. Using it, one generates a family of matched solutions satisfying boundary conditions. Then arbitrary film thickness can be checked against this family of solutions in search of matches. As a result, all fitted solutions are determined straightforwardly.

Localized Airy Wave Packets in a Self-Defocusing Kerr Medium

Families of vortex-like and Gaussian-like localized Airy wave packets, propagating in a self-defocusing Kerr medium, are discovered. Their propagation is described by the cylindrical Korteweg–de Vries (CKdV) equation, reduced from the nonlinear Schrodinger equation by utilizing the reductive perturbation technique. The CKdV equation is solved using the Hirota bilinear method to obtain analytical Airy wave packet families of different order. In particular, we focus on the distribution of optical intensity via numerical simulations of the Airy wave packet solutions, obtained for different initial phases and amplitudes, at given propagation distances. In distinction to the usual ring solitons, the Airy wave packets display a novel internal structure, which reveals novel nonlinear phenomena during the propagation of packets.

Peregrine solitons and algebraic soliton pairs in Kerr media considering space–time correction

Abstract Exact unified rational solutions describing a family of Peregrine solitons as well as related algebraic soliton pairs in either self-focusing or self-defocusing Kerr media are presented, with distinct defining regimes and an explicit relationship for those of opposite nonlinearity. The active role of the space–time correction effect that plays in these soliton species is highlighted, leading to unique dynamics such as the persistence of Peregrine solitons in a defocusing Kerr medium, the availability of giant peak amplitude for the bright–bright soliton pair, and the existence of so-called bright–dark soliton pair. The evolution dynamics of the algebraic two-soliton state toward a spliced single soliton is also discussed.

Analog of gravitational force in hyperbolic metamaterials

Subwavelength confinement of light in nonlinear hyperbolic metamaterials due to formation of spatial solitons has attracted much recent attention because of its seemingly counterintuitive behavior. In order to achieve self-focusing in a hyperbolic wire medium, a nonlinear self-defocusing Kerr medium must be used as a dielectric host. Here we demonstrate that this behavior finds a natural explanation in terms of the analog of gravity. A wave equation describing the propagation of extraordinary light inside hyperbolic metamaterials exhibits (2+1)-dimensional Lorentz symmetry. The role of time in the corresponding effective three-dimensional Minkowski space-time is played by the spatial coordinate aligned with the optical axis of the metamaterial. Nonlinear optical Kerr effect ``bends'' this space-time resulting in effective gravitational force between extraordinary photons. In order for the effective gravitational constant to be positive, a negative self-defocusing Kerr medium must be used as a host. If gravitational self-interaction is strong enough, the spatial soliton may collapse into a black hole analog.

Optical vortex bullets in inhomogeneous dispersive nonlinear fibers

We investigate the possibility of forming spatiotemporal vortex solitons (optical vortex bullets) in inhomogeneous dispersive nonlinear optical fibers using a graded-index Kerr medium as an example. We use a variational approach to solve the multidimensional inhomogeneous nonlinear Schrodinger equation and show that vortex solitons can be stabilized under certain conditions in self-defocusing Kerr medium. Optical vortex results from the phase singularity in a light wave, which the energy flow rotates around the vortex core in a given direction. However, we show that vortex solitons become bistable in self-focusing Kerr medium, depending on pulse energy.

Theoretical and experimental investigations of spatial optical dark soliton filamentization in nonlocal self-defocusing Kerr medium

In this paper, the spatial optical dark soliton filamentization in a nonlocal self-defocusing Kerr medium is investigated. Theoretically, starting from nonlocal nonlinear theoretical model, we examine the influences of the degree of nonlocality and the attenuation constant on the formation of dark soliton filaments by numerical simulation method. We find that when the input background optical intensity is determined, the greater the degree of nonlocality, the farther the initial point of the formation of dark filaments is and the less the number of dark filaments decreases with the increase of the degree of nonlocality; when the ratio of the background optical intensity to the critical optical intensity is fixed, the degree of nonlocality can hardly influence the number of dark filaments and the number of dark filaments under nonlocality is equal to that under locality. Besides, when the input background optical intensity is determined, the number of dark filaments decreases with the increase of the attenuation constant. Experimentally, by changing the concentration of dye solution and the ellipticity of background light, we discuss the influences of the concentration of sample and the ellipticity of background light on the formation of dark soliton filaments respectively and find that when the input background average optical intensity is determined, the number of dark filaments decreases with the increases of the concentration of sample and the ellipticity of background light; when the ratio of the background average optical intensity to the critical optical intensity is fixed, the concentration of sample can hardly influence the number of dark filaments. Besides, the phenomenon of optical shock wave is found in our experiment.

Induced focusing due to counter-propagation of a pair of bright and dark optical beams in self-defocusing Kerr media

We present two-dimensional numerical simulations of a nonlinear optical system made of a bright probe and a dark pump beam that counter propagate in a thin slice of self-defocusing Kerr media, simultaneously. The numerical results show that although the medium is self-defocusing to both pump and probe beam, a profile compression occurs under some conditions, and the weak bright probe beam is focused due to cross-phase modulation. The influence of the characteristics of beams and medium length on the probe beam compression is also investigated.

Induced focusing from co-propagation of a pair of bright–dark optical beams in self-defocusing Kerr media

Explored is the induced focusing in the bright-probe-and-dark-pump geometry in a two-dimensional self-defocusing Kerr medium. It is numerically simulated that a bright probe beam and a dark pump beam co-propagate in the medium. The numerical results show that under some conditions the weak probe beam can be induced to focus due to cross-phase modulation by the intense dark pump beam. Further simulations show that the strongest focusing can be obtained by choosing suitable propagation parameters. The effect of the finite bright background on the induced focusing is also discussed.

Weak-wave advancement in nearly collinear four-wave mixing

We identify a new four-wave mixing process in which two nearly collinear pump beams produce phase-dependent gain into a weak bisector signal beam in a self-defocusing Kerr medium. Phase matching is achieved by weak-wave advancement caused by cross-phase modulation between the pump and signal beams. We relate this process to the inverse of spatial modulational instability and suggest a time-domain analog.

Dynamical behaviour of unbounded spatial solitons in self-defocusing media with small χ(5) self-focusing nonlinearity

A numerical study is made on dynamics of unbounded bright/dark spatial soliton (UBSS/DSS) in self-defocusing Kerr media with small χ (5) self-focusing nonlinearity. Induced by the non-soliton part in the initial condition, soliton scattering process is followed by uneven energy redistribution between the scattered wavepackets with the additional radiation taking part in. Enhanced by the χ (5) self-focusing effect with modification of the cubic defocusing nonlinearity, the resultant propagation of the coupled UBSS/DSS channels presents a striking contrast in brightness/blackness. Stable propagation of such soliton pair requires exacting physical conditions composed of appropriate ratio of cubic-quintic nonlinearity and initial repulsive force of sufficient strength matched with fitting input light power.

Influence of the Kerr-medium type on the wave’s reflection states at a nonlinear interface for different angles of incidence

An analysis of a monochromatic plane wave’s reflection at a nonlinear interface is presented that constitutes a generalization and an extension of previous studies on this subject. We examine the influence of self-focusing and self-defocusing Kerr media on total and partial reflection states. We consider the whole range of angles of incidence and four types of media interfaces. In our model we do not apply the slowly varying amplitude approximation, and we give analytical real positive nonoscillating solutions to the nonlinear differential wave equations in total and partial reflection cases. For each case we also derive relations between the amplitude reflectance and input intensity, which indicate that in some situations the wave’s behavior at a nonlinear interface is governed by the nonlinear critical and the nonlinear characteristic angles. It is pointed out that the reflection states change bistably. We show, for different angles of incidence, the ranges in which the effective permittivity of nonlinear media can be changed via the incident intensity.

Oblique interactions of dark spatial solitons in self-defocusing media

The oblique interaction of two dark spatial soliton stripes propagating in a uniform self-defocusing Kerr medium is considered. Both positive and negative colliding phase shifts are possible, depending on the blackness of the dark solitons and the geometry of the interaction. The critical angle between the propagating directions of two solitons at which no phase shift occurs as a result of the interaction is 120°.

Influence of the cross-phase modulation effect on the polarization states of waves transmitted through a non-linear Fabry–Pe´rot cavity

An analysis of the influence of the cross-phase modulation effect on the polarization states of waves transmitted through a non-linear Fabry–Pe´rot resonator with a self- focusing and self-defocusing Kerr medium is presented. The case is considered of two plane waves with different wavelengths incident on a non-linear Fabry–Pe´rot cavity. It is shown that the polarization states of the transmitted waves change bistably or multistably and depend on the parameters of incident waves and the resonator.

OPTICAL DOMAIN WALLS IN ATOMIC VAPORS

We present a theoretical analysis of the recently discovered optical domain-wall solitons. We discuss the fundamental link which exists between diffractive spatial domain-wall solitons and the instability responsible for the self-filamentation of polarized laser beams in self-defocusing Kerr media. We show that the vector properties of the third-order nonlinear response of atomic vapors satisfy the conditions of occurrence of this instability and are therefore suited to the experimental observation of the spatial polarization domain-wall solitons.

Polarization-domain solitary waves of circular symmetry in Kerr media

We present a new class of dark circularly symmetric solitary wave in bulk, self-defocusing Kerr media. The waves comprise two orthogonally polarized fields mutually guiding each other and forming separate polarization domains. The stability of these new solutions and the dynamics of related structures are briefly investigated.

Stable black self-guided beams of circular symmetry in a bulk Kerr medium

We demonstrate the existence of a stable black self-guided beam of circular symmetry in a bulk self-defocusing Kerr medium. There are no gray or higher-order self-guided beams of circular symmetry. The stability of black beams of circular symmetry is in sharp contrast to analogous bright beams in a self-focusing medium, which are unstable. Black self-guided beams are ideal for all-optical devices in bulk material as they can induce a single-mode optical fiber to guide a (weak) signal beam.