Quadratic solitary waves in a counterpropagating quasi-phase-matched configuration

We demonstrate the possibility of self-trapping of optical beams by use of quasi phase matching in a counterpropagating configuration in quadratic media. We also show the predominant stability of these spatial self-guided beams and estimate the power level required for their experimental observation.Comment: 3 pages, 4 figure

Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing

We demonstrate that weak parametric interaction of a fundamental beam with its third harmonic field in Kerr media gives rise to a rich variety of families of non-fundamental (multi-humped) solitary waves. Making a comprehensive comparison between bifurcation phenomena for these families in bulk media and planar waveguides, we discover two novel types of soliton bifurcations and other interesting findings. The later includes (i) multi-humped solitary waves without even or odd symmetry and (ii) multi-humped solitary waves with large separation between their humps which, however, may not be viewed as bound states of several distinct one-humped solitons.Comment: 9 pages, 17 figures, submitted to Phys. Rev.

Approximate solutions and scaling transformations for quadratic solitons

We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, 'almost exact', explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially-developed approach, based on analysis of the scaling properties. Additionally, we use these approximations to describe the linear tails of solitary waves which are related to the properties of the soliton bound states.Comment: 11 pages, 9 figures; submitted for publicatio

Solutions to the Optical Cascading Equations

Group theoretical methods are used to study the equations describing \chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the nice properties of soliton equations. Large families of explicit analytical solutions are obtained in terms of elliptic functions. In special cases, these periodic solutions reduce to localized ones, i.e., solitary waves. All previously known explicit solutions are recovered, and many additional ones are obtainedComment: 21 page

A remark on deformations of Hurwitz Frobenius manifolds

In this note we use the formalism of multi-KP hierarchies in order to give some general formulas for infinitesimal deformations of solutions of the Darboux-Egoroff system. As an application, we explain how Shramchenko's deformations of Frobenius manifold structures on Hurwitz spaces fit into the general formalism of Givental-van de Leur twisted loop group action on the space of semi-simple Frobenius manifolds.Comment: 10 page

Geoecological problems of urban land pollution in contact zones with iron ore production

The article is concerned with the issues of study heavy metal migration in the soils in close proximity to iron ore mining and processing facilities in the territory of Starooskol-Gubkin industrial are

Scientific rationale for inclusion of a new nature complex Belyj Kolodez (Russia, Belgorod Region) into the emerald network

The article shows that there are resources for extending the national list of potential Areas of Special Conservation Interest (ASCI's) of the Emerald network in densely populated and old-developed regions. The representativeness of the Belyj Kolodez nature complex (Russia, Belgorod region) is substantiated. Based on the survey of the territory, the types of priority habitats were identified according to the EUNIR classificatio

Three-Wave Modulational Stability and Dark Solitons in a Quadratic Nonlinear Waveguide with Grating

We consider continuous-wave (CW) states and dark solitons (DSs) in a system of two fundamental-frequency (FF) and one second-harmonic (SH) waves in a planar waveguide with the quadratic nonlinearity, the FF components being linearly coupled by resonant reflections on the Bragg grating. We demonstrate that, in contrast with the usual situation in quadratic spatial-domain models, CW states with the phase shift between the FF and SH components are modulationally stable in a broad parameter region in this system, provided that the CW wavenumber does not belong to the system's spectral gap. Stationary fundamental DSs are found numerically, and are also constructed by means of a specially devised analytical approximation. Bound states of two and three DSs are found too. The fundamental DSs and two-solitons bound states are stable in all the cases when the CW background is stable, which is shown by dint of calculation of the corresponding eigenvalues, and verified in direct simulations. Tilted DSs are found too. They attain a maximum contrast at a finite value of the tilt, that does not depend on the phase mismatch. At a maximum value of the tilt, which grows with the mismatch, the DS merges into the CW background. Interactions between the tilted solitons are shown to be completely elastic.Comment: 10 pages, 12 figures; Journal of Optics A, in pres

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, give rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s=1. There is no threshold necessary for the existence of these solitons. They are found to be stable against small perturbations if their energy exceeds a certain critical value, so that the stability domain occupies about 10% of the existence region of the solitons. We also demonstrate that the s=1 solitons are stable against very strong perturbations initially added to them. However, on the contrary to spatial vortex solitons in the same model, the spatiotemporal solitons with s=2 are never stable.Comment: latex text, 10 ps and 2 jpg figures; Physical Review E, in pres

Quadratic solitons in cubic crystals

Starting from the Maxwell's equations and without resort to the paraxial approximation, we derive equations describing stationary (1+1)-dimensional beams propagating at an arbitrary direction in an optical crystal with cubic symmetry and purely quadratic nonlinearity. The equations are derived separately for beams with the TE and TM polarizations. In both cases, they contain and cubic nonlinear terms, the latter ones generated via the cascading mechanism. The final TE equations and soliton solutions to them are quite similar to those in previously known models with mixed quadratic-cubic nonlinearities. On the contrary to this, the TM model is very different from previously known ones. It consists of four first-order equations for transverse and longitudinal components of the electric field at the fundamental and second harmonics. Fundamental-soliton solutions of the TM model are also drastically different from the usual "quadratic" solitons, in terms of the parity of their components. In particular, the transverse and longitudinal components of the electric field at the fundamental harmonic in the fundamental TM solitons are described, respectively, by odd and single-humped even functions of the transverse coordinate. Amplitudes of the longitudinal and transverse fields become comparable for very narrow solitons, whose width is commensurate to the carrier wavelength.Comment: Optics Communications, in pres