We analyze the salient features of vortex-ring solitons supported by cylindrically symmetric medi... more We analyze the salient features of vortex-ring solitons supported by cylindrically symmetric media with nonlocal thermal nonlinearity. We discover the existence of a maximum allowed topological charge for such vortex solitons to be stable on propagation: Only vortex-ring solitons with topological charge m </= 2 are found to be stable. This remarkable result holds independently of the radius of the sample.
We introduce a novel type of surface waves that can be excited at the edge of annular guiding str... more We introduce a novel type of surface waves that can be excited at the edge of annular guiding structures created by several concentric rings. We demonstrate that such surface waves can rotate upon propagation and for high enough rotation frequencies they do not require any power thresholds for their existence.
We study the properties of bright and vortex solitons in thermal media with nonuniform thermal co... more We study the properties of bright and vortex solitons in thermal media with nonuniform thermal conductivity and homogeneous refractive index, whereby the local modulation of the thermal conductivity strongly affects the entire refractive index distribution. While regions where the thermal conductivity is increased effectively expel light, self-trapping may occur in the regions with reduced thermal conductivity, even if such regions are located close to the material boundary. As a result, strongly asymmetric self-trapped beams may form inside a ring with reduced thermal conductivity and perform persistent rotary motion. Also, such rings are shown to support stable vortex solitons, which may feature strongly noncanonical shapes.
Two-parameter families of chirped stationary three-dimensional spatiotemporal solitons in dispers... more Two-parameter families of chirped stationary three-dimensional spatiotemporal solitons in dispersive quadratically nonlinear optical media featuring type-I second-harmonic generation are constructed in the presence of temporal walk-off. Basic features of these walking spatiotemporal solitons, including their dynamical stability, are investigated in the general case of unequal group-velocity dispersions at the fundamental and second-harmonic frequencies. In the cases when the solitons are unstable, the growth rate of a dominant perturbation eigenmode is found as a function of the soliton wave number shift. The findings are in full agreement with the stability predictions made on the basis of a marginal linear-stability curve. It is found that the walking three-dimensional spatiotemporal solitons are dynamically stable in most cases; hence in principle they may be experimentally generated in quadratically nonlinear media.
We report on the existence and properties of breathing periodic cnoidal pulse trains propagating ... more We report on the existence and properties of breathing periodic cnoidal pulse trains propagating in dispersion managed systems with piecewise constant dispersion. Our numerical investigations show that the dispersion management enhances the robustness of the periodic cnoidal pulse trains in comparison to the pulse trains existing in a uniform medium. The concept might have direct applications to pulse trains generated by mode-locked fiber lasers.
We analyze the salient features of vortex-ring solitons supported by cylindrically symmetric medi... more We analyze the salient features of vortex-ring solitons supported by cylindrically symmetric media with nonlocal thermal nonlinearity. We discover the existence of a maximum allowed topological charge for such vortex solitons to be stable on propagation: Only vortex-ring solitons with topological charge m </= 2 are found to be stable. This remarkable result holds independently of the radius of the sample.
We introduce a novel type of surface waves that can be excited at the edge of annular guiding str... more We introduce a novel type of surface waves that can be excited at the edge of annular guiding structures created by several concentric rings. We demonstrate that such surface waves can rotate upon propagation and for high enough rotation frequencies they do not require any power thresholds for their existence.
We study the properties of bright and vortex solitons in thermal media with nonuniform thermal co... more We study the properties of bright and vortex solitons in thermal media with nonuniform thermal conductivity and homogeneous refractive index, whereby the local modulation of the thermal conductivity strongly affects the entire refractive index distribution. While regions where the thermal conductivity is increased effectively expel light, self-trapping may occur in the regions with reduced thermal conductivity, even if such regions are located close to the material boundary. As a result, strongly asymmetric self-trapped beams may form inside a ring with reduced thermal conductivity and perform persistent rotary motion. Also, such rings are shown to support stable vortex solitons, which may feature strongly noncanonical shapes.
Two-parameter families of chirped stationary three-dimensional spatiotemporal solitons in dispers... more Two-parameter families of chirped stationary three-dimensional spatiotemporal solitons in dispersive quadratically nonlinear optical media featuring type-I second-harmonic generation are constructed in the presence of temporal walk-off. Basic features of these walking spatiotemporal solitons, including their dynamical stability, are investigated in the general case of unequal group-velocity dispersions at the fundamental and second-harmonic frequencies. In the cases when the solitons are unstable, the growth rate of a dominant perturbation eigenmode is found as a function of the soliton wave number shift. The findings are in full agreement with the stability predictions made on the basis of a marginal linear-stability curve. It is found that the walking three-dimensional spatiotemporal solitons are dynamically stable in most cases; hence in principle they may be experimentally generated in quadratically nonlinear media.
We report on the existence and properties of breathing periodic cnoidal pulse trains propagating ... more We report on the existence and properties of breathing periodic cnoidal pulse trains propagating in dispersion managed systems with piecewise constant dispersion. Our numerical investigations show that the dispersion management enhances the robustness of the periodic cnoidal pulse trains in comparison to the pulse trains existing in a uniform medium. The concept might have direct applications to pulse trains generated by mode-locked fiber lasers.
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