Self-defocusing Nonlinear Media Research Articles

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.

Dissipative Vortex Solitons in Defocusing Media with Spatially Inhomogeneous Nonlinear Absorption**Supported by the National Natural Science Foundation of China under Grant No. 11705164 and the Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ16A040003

In this paper, by solving a complex nonlinear Schrödinger equation, radially symmetric dissipative vortex solitons are obtained analytically and are tested numerically. We find that spatially inhomogeneous nonlinear absorption gives rise to the stability of dissipative vortex solitons in self-defocusing nonlinear medium in the presence of constant linear gain. Numerical simulation reveals the interaction effect among linear gain and nonlinear loss in the azimuthal modulation instabilities of these vortices suppression. Apart from the uniform linear gain indeed affects the stability of vortex in this media, another noticeable feature of current setup is that the steep spatial modulation of the nonlinear absorption can suppress sidelobes effectively and support stable vortex solitons in situations with uniform linear gain. Under appropriate conditions, the vortex solitons can propagate stably and feature no symmetry breaking, although the beams exhibit radical compression and amplification as they propagate.

Multi-pole dark solitons in nonlocal and cubic-quintic nonlinear medium

In this paper, we mainly simulate the characteristics of the ground state dark soliton and the multipole dark soliton in the nonlocal and cubic-quintic nonlinear medium. Firstly, the influences of the degree of nonlocality on the amplitude and the width of the dark soliton in the self-defocusing cubic-and self-focusing quantic-nonlinear medium are studied. Secondly, we find the nonlinear parameters affecting the amplitude values of solitons, but the refractive index induced by the light beam is always a fixed value. The numerical results show that the ground state dark soliton can be propagated stably alone the z axis, and the stable states of the dipole soliton and the dark tri-pole and quadru-pole solitons are stable. However, some quadru-pole dark soliton is unstable after propagating the remote distance. Furthermore, we also discuss the characteristics of the ground state dark soliton and the dark dipole soliton in the local cubic-nonlinear and nonlocal quantic nonlinear media. Both the amplitude and the beam width of the dark ground state soliton and dark dipole soliton are also affected by the degree of nonlocality and nonlinearity. Two boundary values of the induced refractive index change with the variations of the three nonlinear parameters. The dark soliton and the dipole dark soliton are more stable in the self-focusing cubic nonlinear and the nonlocal self-defocusing quantic nonlinear medium than those in the self defocusing cubic nonlinear and nonlocal self-focusing quantic nonlinear medium. The powers of single dark soliton and dark tri-pole soliton decrease monotonically with the increase of propagation constant when the cubic-quintic nonlinearities are certain values and these degrees of nonlocalities are taken different values. Furthermore, we also analyze linear stabilities of various nonlocal spatial dark solitons. And we find that the dipole dark soliton is unstable when the propagation constant is in the region[-0.9,-1.0]. These properties of linear stabilities of other multi-pole dark solitons are the same as their propagation properties.

Dark spatiotemporal optical solitary waves in self-defocusing nonlinear media

Dark three-dimensional spatiotemporal solitons or the “dark light bullets” in the self-defocusing nonlinear media with equal diffraction and dispersion lengths are demonstrated analytically. Our results show that the main characteristic of the dark light bullets can be described by the cylindrical Korteweg–de Vries (CKdV) equation. The dark wave packets are composed of the single-layer and multilayer toroidal rings. For the multilayer rings, there exist small inner rings enclosed in a large ring-shaped toroidal structure, when one chooses different orders of the soliton solutions of the CKdV equation. The radius of dark ring solitons increases with the propagation distance. Present results provide a feasible method for controlling the fundamental structure of these beams in the self-defocusing nonlinear media.

Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations.

We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation. An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species. We discover that this type of Peregrine soliton, viable for both the focusing and defocusing Kerr nonlinearities, could exhibit an extra doubly localized chirp while keeping the characteristic intensity features of the original Peregrine soliton, hence the term chirped Peregrine soliton. The existence of chirped Peregrine solitons in a self-defocusing nonlinear medium may be attributed to the presence of self-steepening effect when the latter is not balanced out by the third-order dispersion. We numerically confirm the robustness of such chirped Peregrine solitons in spite of the onset of modulation instability.

Dynamical behavior of the bright incoherent spatial solitons in self-defocusing nonlinear media

We present a theory of bright incoherent photovoltaic (PV) solitons in self-defocusing nonlinear media by using a coherent density approach. It is shown that this theory model is effectively governed by an infinite set of coupled nonlinear Schrödinger equations, which are initially weighted with respect to the incoherent angular power spectrum of source. We then numerically study the particular case of spatially incoherent beam propagating in LiNbO3:Fe crystal with split-step Fourier method. Numerical simulations indicate that the ratio of PV constant κ is a key parameter to spatial compression as well as the possible dark and bright PV solitons. Besides, the formation of bright incoherent PV solitons is affected by intensity ratios rT and width of the source angular power spectrum θ0. Better coherent property is found at margins of bright incoherent soliton through the associated coherence length calculation. These results are in good agreement with recent experimental observations.

The surface solitons in media with uniform and Gaussian modulated potentials

We investigate the existence and stability of solitons in media with uniform and Gaussian modulated potentials, including linear case, and self-focusing and self-defocusing nonlinear cases. For linear case, the eigenvalues and eigenfunction for different modulated depths of Gaussian potentials are obtained numerically. For nonlinear cases, the existence and stability of fundamental and multipole solitons are studied in self-focusing and self-defocusing media. For a fixed modulated depth, the eigenvalue for fundamental or multipole linear modes is equal to the critical propagation constant bc of fundamental and multipole solitons existence. Fundamental solitons are stable in both the self-defocusing nonlinear media and the self-focusing nonlinear case. Multipole solitons are stable with the propagation constants close to bc both for self-focusing and self-defocusing nonlinearities.

Observation of surface dark solitons in nonlocal nonlinear media

We investigated surface dark solitons (SDSs) at the interface between a self-defocusing nonlocal nonlinear medium and a linear medium, both theoretically and experimentally. We demonstrate that fundamental and higher-order SDSs can exist when the linear refractive index of the self-defocusing medium is much greater than that of the linear medium. The fundamental and second-order solitons are observed at the interface between air and a weakly absorbing liquid.

The optical solitons in the Scarff parity-time symmetric potentials

We investigate the existence and stability of solitons in parity-time (PT) symmetric Scarff complex potentials, including linear case, and self-focusing and self-defocusing nonlinear cases. For linear case, the PT-breaking points, the eigenvalues and eigenfunction for different modulated depths of PT symmetry Scarff complex potential are obtained numerically. For nonlinear cases, the existence and stability of fundamental and multipole solitons are studied in self-focusing and self-defocusing media. For a fixed modulated depth, the eigenvalue for fundamental or multipole linear modes is equal to the critical propagation constant bc of fundamental and multipole solitons existence. Fundamental solitons are stable in the self-defocusing nonlinear media and low power region for the self-focusing nonlinear case. Multipole solitons are stable with the propagation constants close to bc both for self-focusing and self-defocusing nonlinearities.

Interaction between one-dimensional dark spatial solitons and semi-infinite dark stripes

In this work we numerically study the evolution and interaction of one-dimensional (1-D) dark spatial solitons and semi-infinite dark stripes (SIDSs) in a local self-defocusing Kerr nonlinear medium. The experimental results in the linear regime of propagation confirm that the SIDS bending and fusion with the infinite 1-D dark beam modeled for negative nonlinearity is due to the opposite phase semi-helicities of SID beam ends. Results for several interaction scenaria show that bending ends of the semi-infinite dark stripes splice to the 1-D dark beam to form structures resembling waveguide couplers/branchers. Well pronounced modulational stability of 1-D dark spatial solitons under strong symmetric background beam modulation from decaying SIDSs is predicted.

Observation of photorefractive surface waves in self-defocusing LiNbO_3:Fe crystal

Photorefractive (PR) surface waves (SWs) in self-defocusing LiNbO(3):Fe are studied theoretically and experimentally. We demonstrate that SWs can also be formed in a self-defocusing nonlinear medium and that the nonlocal nonlinearity (such as the diffusion component of PR nonlinearity in this Letter) is the essential cause. The forming process of PR SWs with a self-deflection course of light beams has been observed. The results indicate the possibility of concentrating light energy in self-defocusing media, taking advantage of SWs.

Nonlinear focusing and defocusing of partially coherent spatial beams

We consider the propagation of a partially coherent spatial beam in both self-focusing and self-defocusing nonlinear media. Using a Gaussian-Schell model, we derive an equation governing the width of highly incoherent beams as they propagate in both types of media and confirm its validity by using numerical simulations. Experiments performed in a biased photorefractive crystal match the predicted scaling.

Dark solitons in nonlocal media: variational analysis

The propagation of dark solitons is systematically investigated in a weakly nonlocal self-defocusing Kerr-type nonlinear medium. Based on the variational principle, we get an analytical solution of such nonlocal dark solitons. We also clearly give the expression describing the transverse velocity of the dark solitons. We find that the width of the dark solitons is related to the degree of nonlocality and the grayness of the solitons, that there exists a threshold of the degree of nonlocality for such nonlocal dark solitons, and that, as the degree of nonlocality increases, the solitons' velocity will decrease. We also demonstrate the stability of the nonlocal dark solitons.

自散焦介质中的光开关现象

A spatial optical switch phenomenon caused by the induced focusing of a weak probe beam occurring in self-defocusing nonlinear media is discussed theoretically. A weak beam is induced to focus when it copropagates with an intense pump beam under the conditions that the probe and pump beams peak at different positions and propagate in different directions. Due to the effect of cross-phase modulation, the weak beam can not only be focused but also be deflected. The phenomenon is discussed by numerically solving the coupled amplitude equations.

Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

Collisions of spatial solitons occurring in the nonlinear Schröinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through.

The circular and elliptic white-light dark spatial solitons in a photovoltaic self-defocusing nonlinear medium

We observed circular white-light dark spatial solitons in photovoltaic self-defocusing LiNbO3:Fe crystal using an ordinary incandescent lamp as light source (a line source) with the filament of the bulb parallel to the crystalline c axis. Besides the above condition, the formation of the elliptic soliton needs an additive condition that the crystalline c axis is parallel to the minor axis of dark elliptic spot.

Incoherent multi-gap optical solitons in nonlinear photonic lattices

We demonstrate numerically that partially incoherent light can be trapped in the spectral band gaps of a photonic lattice, creating partially incoherent multi-component spatial optical solitons in a self-defocusing nonlinear periodic medium. We find numerically such incoherent multi-gap optical solitons and discuss how to generate them in experiment by interfering incoherent light beams at the input of a nonlinear periodic medium.

Induced focusing from counter-propagation of two optical beams in self-defocusing media

In this paper, it is numerically simulated that two optical beams with one’s intensity much stronger than the other propagate simultaneously in opposite directions in a two-dimensional self-defocusing nonlinear medium. The results show that the weaker probe beam can be induced to focus due to cross-phase modulation from the stronger pump beam under certain conditions. The effects of the four parameters, that is, the specimen length, the initial transversal distance between the beam centers, the initial pump amplitude, and the initial probe amplitude, on the focusing of the probe beam are also discussed, and it is found that some of the parameters have optimum values which result in the strongest focusing.

Induced focusing due to two optical beams counterpropagating in self-defocusing nonlinear media*

In this paper,a research work is done on two optical beams co-propagating in opp osite directions in two-dimensional self-defocusing nonlinear media.Numerical re sults show that the probe beam can be induced to focus due to cross-phase modula tion by the pump beam under certain conditions.We also discuss the effect on the focusing of the probe beam from the four parameters:the specimen length,the ini tial amplitudes of the pump beam and the probe beam,and the initial transversal distance between the centers of the two beams.We find that some of them have opt imum values,which result in the strongest focusing.

NONLINEAR CUSP DIFFRACTION CATASTROPHE AND VORTEX QUADRUPOLES FROM A SMOOTH INITIAL BEAM

Vortex quadrupoles and a nonlinear optical cusp diffraction catastrophe were observed at the output face of a self-defocusing nonlinear medium. The initial beam had a smooth cross-sectional intensity profile, but was elongated to an aspect ratio of 2:1. The power-dependent evolution of the beam is described.