Stability of non-degenerate parametric soliton in quadratic media

The non-degenerate solitons due to three-wave mixing in a quadratic medium are analyzed. A new stability criterion for these solitons is found and verified numerically. The influence of the non-paraxial terms on the instability threshold is also discussed.     

Transfer matrix method for media with quadratic optical nonlinearity

A transfer matrix method is developed for media containing nonlinear layers. This method can be used to calculate the propagation of light, the electromagnetic field profile, and also second-harmonic generation in layered structures containing a layer exhibiting quadratic nonlinearity. Zh. Tekh. Fiz. 69, 116–117 (April 1999)     

Multiple soliton bound states and symmetry breaking in quadratic media

We present a study of the dynamics of multiple soliton bound states in diffractive media with second-order nonlinearity. A numerical stability analysis of these bound states reveals that wave propagation in quadratic materials exhibits spatial symmetry-breaking instabilities.     

Quasi-stable propagation of vortices and soliton clusters in saturable Kerr media with square-root nonlinearity

Analytical and numerical investigation of the propagation of optical beams in Kerr-like saturable photorefractive media is carried out, utilizing a novel model for the local isotropic part of the space-charge field generated in the medium. Using a variational technique, optimal propagation parameters for the most stable propagation of otherwise unstable single Gaussian, single vortex, and optical soliton cluster beams are determined. Analogy between a ring of identical weakly overlapping solitons and a vortex of the same topological charge is explored.     

Evolution of acoustic waves in microinhomogeneous media with quadratic elastic nonlinearity and relaxation

A nonlinear wave equation for the velocity “relaxator” is derived in the framework of the rheological model and the corresponding equation of state of a microinhomogeneous medium containing viscoelastic defects with quadratic nonlinear elasticity. The equation is qualitatively analyzed, and numerical solutions to it are presented for a stationary symmetric shock wave and the evolution of initially harmonic waves.     

Noise evolution and soliton internal modes in dispersion-managed fiber systems

We perform a linear stability analysis of the Ablowitz-Biondini equations to explain the dynamic evolution of the noise squeezing, caused by the interplay among optical solitons and noise components, of initially uncorrelated statistics in fiber systems with dispersion management.     

Stationary soliton states in couplers with saturable nonlinearity

We find the possible stationary states for nonlinear couplers formed from materials that have saturable nonlinearities. We also determine the effect of saturation on the asymmetric state bifurcation point and the energy required for switching.     

Internal modes of solitons in media with a saturable nonlinearity of the refractive index

The theoretical analysis and calculation of internal modes (eigenmodes of small perturbations) of 1D, 2D, and 3D optical solitons in transparent media with a saturable nonlinearity of the refractive index are performed. Corrections that are nonlinear in the amplitude of perturbations and lead to the radiative damping of internal modes are found. The damping is shown to become weaker with increasing dimensionality of a solition.     

Polymer-based microcavity with photoencoded quadratic nonlinearity

Functional electro-optic polymer thin films embedded in microcavity structures have been poled by an all-optical procedure based on the interference of multiphoton absorption processes. The photoinduced X((2)) tensor was then further addressed at modal resonance for the fundamental wavelength, leading to significant enhancement of the second-harmonic-generation efficiency. An order-of-magnitude enhancement, which is due to electric field resonant conditions inside the microcavity, has been probed by an optical parametric oscillator, in comparison with a single-path thin-film configuration. This configuration opens new perspectives in the realm of nonlinear photonic device processing.     

Tunable soliton self-bending in optical lattices with nonlocal nonlinearity

We address the phenomenon of soliton self-bending in Kerr-type nonlocal nonlinear media with an imprinted transverse periodic modulation of the linear refractive index. We show that the imprinted optical lattice makes possible to control the mobility of soliton by varying the depth and the frequency of the linear refractive index modulation.     

Efficiency of quadratic soliton generation

We report what is believed to be the first experimental demonstration of soliton content as a function of the intensity of input light for multicolor quadratic solitons. Experiments were conducted with spatial solitons excited with Gaussian beams in a bulk crystal cut for second-harmonic generation. The effects introduced by the finite crystal length and by the scheme employed to elucidate the soliton energy are highlighted.     

Accumulation of embedded solitons in systems with quadratic nonlinearity

Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multiwave systems with quadratic nonlinearity, families of which seem to emerge from a critical point in the parameter space, where the zero solution has a fourfold zero eigenvalue. In this paper, the existence of such solutions is studied in a three-wave model. An appropriate rescaling casts the system in a normal form, which is universal for models supporting ESs through quadratic nonlinearities. The normal-form system contains a single irreducible parameter epsilon, and is tantamount to the basic model of type-I second-harmonic generation. An analytical approximation of Wentzel-Kramers-Brillouin type yields an asymptotic formula for the distribution of discrete values of epsilon at which the ESs exist. Comparison with numerical results shows that the asymptotic formula yields an exact value of the scaling index, -65, and a fairly good approximation for the numerical factor in front of the scaling term.     

Evolutions of matter-wave bright soliton with spatially modulated nonlinearity

The evolution characteristics of a matter-wave bright soliton are investigated by means of the variational approach in the presence of spatially varying nonlinearity. It is found that the atom density envelope of the soliton is changed as a result of the spatial variation of the s-wave scattering length. The stable soliton can exist in appropriate initial conditions. The movement of the soliton depends on the sign and value of the coefficient of spatially modulated nonlinearity. These theoretical predictions are confirmed by the full numerical simulations of the one-dimensional Gross-Pitaevskii equation.     

Discrete soliton collisions in a waveguide array with saturable nonlinearity

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of mobile breathers with high power. Three main regimes are observed: breather fusion, breather reflection and breather creation. The last regime seems to be exclusive of systems with a saturable nonlinearity, and has been previously observed in continuous models. In some cases a “symmetry breaking” can be observed, which we show to be an numerical artifact.     

Optical soliton perturbation with quadratic-cubic nonlinearity by mapping methods

This paper reveals optical soliton solutions for the perturbed nonlinear Schrödinger’s equation that is studied with quadratic–cubic nonlinearity. The mapping methods are utilized to retrieve these solitons which are of bright, dark and singular type.     

Topological soliton perturbation for sine-Gordon equation with full nonlinearity

This Letter obtains the adiabatic parameter dynamics of topological solitons that are described by the fully nonlinear version of the perturbed sine-Gordon equation. The soliton perturbation theory is used to carry out the investigation.     

Gap soliton in a waveguide array with a saturating defocusing nonlinearity

We investigate radiation of the solitary waves in the first band gap of the waveguide array with a defocusing nonlinearities of different types (Kerr nonlinearity and saturating nonlinearity). We confirm recent findings that gap solitons (GSs) are unstable for their eigenfrequencies around the middle of the band gap for Kerr nonlinearity. The instability is mediated by four-wave mixing process and appears in the form of radiation of solitons into mode continua of the upper and lower bands. We find that this soliton radiation is reduced (and even suppressed completely) in case of a saturating nonlinearity, resulting in substantial stabilization of the GSs.     

Power controlled soliton stability and steering in lattices with saturable nonlinearity

Dynamical properties of discrete solitons in nonlinear Schr?dinger lattices with saturable nonlinearity are studied in the framework of the one-dimensional discrete Vinetskii-Kukhtarev model. Two stationary strongly localized modes, centered on site (A) and between two neighboring sites (B), are obtained. The associated Peierls-Nabarro potential is bounded and has multiple zeros indicating strong implications on the stability and dynamics of the localized modes. Besides a stable propagation of mode A, a stable propagation of mode B is also possible. The enhanced ability of the large power solitons to move across the lattice is pointed out and numerically verified.     

Birth of solitons in quadratic spatial soliton collisions

We demonstrate experimentally and theoretically the creation of a third soliton in two soliton collision processes in type I noncritically phase-matched KNbO3. The output pattern in the collision process is phase dependent, but the total energy and the relative ratio of the fundamental to the second harmonic in each soliton remain essentially unchanged to within experimental accuracy.