Related papers: Narrow light beams with linear polarization in a K…
For the nonlinear vector curl-curl equation describing a monochromatic light wave in a Kerr medium, an exact reduction is suggested which results in a system of four ordinary differential equations, of the first order each, for functions of…
A system of equations has been proposed for a monochromatic weakly nonlinear light wave in a Kerr medium. This system is equivalent up to the third order in electric field to the known equation $\mbox{curl}\,\mbox{curl}\, {\bf E}=k_0^2[{\bf…
Nonlinear losses accompanying Kerr self-focusing substantially impacts the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D+1 nonlinear Schrodinger equation which are…
We address the problem of existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of (2+1)-dimensional two-mode self-trapped beams, with…
We demonstrate a possibility to stabilize three-dimensional spatiotemporal solitons ("light bullets") in self--focusing Kerr media by means of a combination of dispersion management in the longitudinal direction (with the group-velocity…
Very narrow spatial bright solitons in (1+1)D and (2+1)D versions of cubic-quintic and full saturable models are studied, starting from the full system of the Maxwell's equations, rather than from the paraxial (NLS) approximation. For the…
We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As…
Using the numerical solution of the nonlinear Schr\"odinger equation and a variational method it is shown that (3+1)-dimensional spatiotemporal optical solitons, known as light bullets, can be stabilized in a layered Kerr medium with…
We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the…
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…
The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation with a periodic potential is demonstrated by means of the variational approximation (VA)…
Collisions of left- and right-polarized spatiotemporal optical solitons have been numerically simulated for a locally isotropic focusing Kerr medium with anomalous chromatic dispersion. The stable propagation of such ``light bullets'' in a…
We prove that spatial Kerr solitons, usually obtained in the frame of nonlinear Schroedinger equation valid in the paraxial approximation, can be found in a generalized form as exact solutions of Maxwell's equations. In particular, they are…
The existence and stability of stable bright solitons in one-dimensional (1D) media with a spatially periodical modulated Kerr nonlinearity are demonstrated by means of the linear-stability analysis and in direct numerical simulations. The…
We propose the modulation of dispersion to prevent collapse of planar pulsed beams which propagate in Kerr-type self-focusing optical media. As a result, we find a new type of two-dimensional spatio-temporal solitons stabilized by…
The optical Kerr micro-ring provides an ideal platform for the study of dissipative optical solitons. Dissipative solitons are localized waves produced by a precise equilibrium between dispersion and nonlinearity, as well as gain and loss.…
The Kerr nonlinearity allows for exact analytic soliton solutions in 1+1D. While nothing excludes that these solitons form in naturally-occurring real-world 3D settings as solitary walls or stripes, their observation has previously been…
We show analytically, numerically, and experimentally that a transversely stable one-dimensional [(1+1)D] bright Kerr soliton can exist in a 3D bulk medium. The transverse instability of the soliton is completely eliminated if it is made…
We study spatial vector solitons in a photonic crystal fiber (PCF) made of a material with the focusing Kerr nonlinearity. We show that such two-component localized nonlinear waves consist of two mutually trapped components confined by the…
We have observed the spatial interactions between two ultra-weak optical beams that are initially collinear and non-overlapping. The weak beams are steered towards each other by a spatially varying cross-Kerr refractive index waveguide…