Ginzburg-Landau equation bound to the metal-dielectric interface and transverse nonlinear optics with amplified plasmon polaritons

Using a multiple-scale asymptotic approach, we have derived the complex cubic Ginzburg-Landau equation for amplified and nonlinearly saturated surface plasmon polaritons propagating and diffracting along a metal-dielectric interface. An important feature of our method is that it explicitly accounts for nonlinear terms in the boundary conditions, which are critical for a correct description of nonlinear surface waves. Using our model we have analyzed filamentation and discussed bright and dark spatially localized structures of plasmons.Comment: http://link.aps.org/doi/10.1103/PhysRevA.81.03385

Looking at a soliton through the prism of optical supercontinuum

A traditional view on solitons in optical fibers as robust particle-like structures suited for informa- tion transmission has been significantly altered and broadened over the past decade, when solitons have been found to play the major role in generation of octave broad supercontinuum spectra in photonic-crystal and other types of optical fibers. This remarkable spectral broadening is achieved through complex processes of dispersive radiation being scattered from, emitted and transformed by solitons. Thus solitons have emerged as the major players in nonlinear frequency conversion in optical fibers. Unexpected analogies of these processes have been found with dynamics of ultracold atoms and ocean waves. This colloquium focuses on recent understanding and new insights into physics of soliton-radiation interaction and supercontinuum generation.Comment: http://rmp.aps.org/abstract/RMP/v82/i2/p1287_1 (some figures have been deleted due to space limits imposed by archive

Tricritical Behavior of Random Systems with Coupling to a Nonfluctuating Parameter

The influence of disordering upon the critical behavior of a system with hidden degrees of freedom is considered. It is shown that there is a tricritical behavior in the constrained system, while in the unconstrained system only phase transitions of the second order occur. © 1997 Elsevier Science B.V.I Partially supported by State Program “Actual Problems in Condensed Matter Physics: Neutron Studies” (Projects No. 96-104, 96-305) and Russian Foundation for Basic Researches (Project No. 97-02-17315), Russian Federation

Influence of Rare Regions on Quantum Phase Transition in Antiferromagnets with Hidden Degrees of Freedom

The effects of rare regions on the critical properties of quantum antiferromagnets with hidden degrees of freedom within the renormalization group is discussed. It is shown that for 'constrained' systems the stability range on the phase diagram remains the same as in the mean-field theory while for 'unconstrained' systems the stability range is effectively decreased

Stable multiple-charged localized optical vortices in cubic-quintic nonlinear media

The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and two-charged but also multiple-charged stable vortex solitons do exist. A vortex soliton occurs robust with respect to symmetry-breaking modulational instability in the self-defocusing regime provided that its radial profile becomes flattened, so that a self-trapped wave beam gets a pronounced surface. It is demonstrated that the dynamics of a slightly perturbed stable vortex soliton resembles an oscillation of a liquid stream having a surface tension. Using the idea of sustaining effective surface tension for spatial vortex soliton in a media with competing nonlinearities the explanation of a suppression of the modulational instability is proposed.Comment: 4 pages, 3 figures. Submitted to Journal of Optics A. The proceedings of the workshop NATO ARW, Kiev 2003 Singular Optics 200

Theory of radiation trapping by the accelerating solitons in optical fibers

We present a theory describing trapping of the normally dispersive radiation by the Raman solitons in optical fibers. Frequency of the radiation component is continuously blue shifting, while the soliton is red shifting. Underlying physics of the trapping effect is in the existence of the inertial gravity-like force acting on light in the accelerating frame of reference. We present analytical calculations of the rate of the opposing frequency shifts of the soliton and trapped radiation and find it to be greater than the rate of the red shift of the bare Raman soliton. Our findings are essential for understanding of the continuous shift of the high frequency edge of the supercontinuum spectra generated in photonic crystal fibers towards higher frequencies.Comment: Several misprints in text and formulas corrected. 10 pages, 9 figures, submitted to Phys. Rev.

Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries

We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys. JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves in the nonlinear Schr\"oedinger equation (NLS) can be generalised for models with two phase symmetries. MI of three-wave parametric spatial solitons due to group velocity dispersion (GVD) is investigated as a typical example of such models. We reveal a new branch of neck instability, which dominates the usual snake type MI found for normal GVD. The resultant nonlinear evolution is thereby qualitatively different from cases with only a single phase symmetry.Comment: 4 pages with figure

Instabilities of Higher-Order Parametric Solitons. Filamentation versus Coalescence

We investigate stability and dynamics of higher-order solitary waves in quadratic media, which have a central peak and one or more surrounding rings. We show existence of two qualitatively different behaviours. For positive phase mismatch the rings break up into filaments which move radially to initial ring. For sufficient negative mismatches rings are found to coalesce with central peak, forming a single oscillating filament.Comment: 5 pages, 7 figure

Macroscopic Zeno effect in Su-Schrieffer-Heeger photonic topological insulator

The quantum Zeno effect refers to slowing down of the decay of a quantum system that is affected by frequent measurements. Nowadays, the significance of this paradigm is extended far beyond quantum systems, where it was introduced, finding physical and mathematical analogies in such phenomena as the suppression of output beam decay by sufficiently strong absorption introduced in guiding optical systems. In the latter case, the effect is often termed as macroscopic Zeno effect. Recent studies in optics, where enhanced transparency of the entire system was observed upon the increase of the absorption, were largely focused on the systems obeying parity-time symmetry, hence, the observed effect was attributed to the symmetry breaking. While manifesting certain similarities in the behavior of the transparency of the system with the mentioned studies, the macroscopic Zeno phenomenon reported here in topological photonic system is far more general in nature. In particular, we show that it does not require the existence of exceptional points, and that it is based on the suppression of decay for only a subspace of modes that can propagate in the system, alike the quantum Zeno dynamics. By introducing controlled losses in one of the arms of a topological insulator comprising two closely positioned Su-Schrieffer-Heeger arrays, we demonstrate the macroscopic Zeno effect, which manifests itself in an increase of the transparency of the system with respect to the topological modes created at the interface between two arrays. The phenomenon remains robust against disorder in the non-Hermitian topological regime. In contrast, coupling a topological array with a non-topological one results in a monotonic decrease in output power with increasing absorption