Solitons in a medium with linear dissipation and localized gain

We present a variety of dissipative solitons and breathing modes in a medium with localized gain and homogeneous linear dissipation. The system posses a number of unusual properties, like exponentially localized modes in both focusing and defocusing media, the existence of modes in focusing media at negative propagation constant values, the simultaneous existence of stable symmetric and anti-symmetric localized modes when the gain landscape possesses two local maxima, as well as the existence of stable breathing solutions.Comment: 4 pages, 5 figures, to appear in Optics Letter

Disorder-induced soliton transmission in nonlinear photonic lattices

We address soliton transmission and reflection in nonlinear photonic lattices embedded into uniform Kerr nonlinear media. We show that by introducing disorder into the guiding lattice channels, one may achieve soliton transmission even under conditions where regular lattices reflect the input beam completely. In contrast, in the parameter range where the lattice is almost transparent for incoming solitons, disorder may induce a significant reflection.Comment: 5 pages, 4 figures, to appear in Optics Letter

Parametric amplification of random lattice soliton swinging

We consider the propagation of solitons in media with an imprinted transverse periodic or parabolic refractive index modulation when the modulation depth slightly fluctuates along the propagation direction. We find that, under suitable spectral resonance conditions, small transverse soliton oscillations may get parametrically amplified.Comment: 12 pages, 4 figures, to appear in Optics Letter

Wave patterns generated by a flow of two-component Bose-Einstein condensate with spin-orbit interaction past a localized obstacle

It is shown that spin-orbit interaction leads to drastic changes in wave patterns generated by a flow of two-component Bose-Einstein condensate (BEC) past an obstacle. The combined Rashba and Dresselhaus spin-orbit interaction affects in different ways two types of excitations---density and polarization waves---which can propagate in a two-component BEC. We show that the density and polarization "ship wave" patterns rotate in opposite directions around the axis located at the obstacle position and the angle of rotation depends on the strength of spin-orbit interaction. This rotation is accompanied by narrowing of the Mach cone. The influence of spin-orbit coupling on density solitons and polarization breathers is studied numerically.Comment: 5 pages, 3 figure

Dynamical light control in longitudinally modulated segmented waveguide arrays

We address light propagation in segmented waveguide arrays where the refractive index is longitudinally modulated with an out-of-phase modulation in adjacent waveguides, so that the coupling strength varies along propagation direction. Thus in resonant segments coupling may be inhibited hence light remains localized, while in detuned segments coupling results in complex switching scenarios that may be controlled by stacking several resonant and nonresonant segments. By tuning the modulation frequency and lengths of waveguide segments one may control the distribution of light among the output guides, including loca-lizing all light in the selected output channel.Comment: 12 pages, 4 figures, to appear in Europhysics Letter

Resonant mode conversion in the waveguides with an unbroken and broken PT-symmetry

We study resonant mode conversion in the PT-symmetric multimode waveguides, where symmetry breaking manifests itself in sequential destabilization (appearance of the complex eigenvalues) of the pairs of adjacent guided modes. We show that the efficient mode conversion is possible even in the presence of the resonant longitudinal modulation of the complex refractive index. The distinguishing feature of the resonant mode conversion in the PT-symmetric structure is a drastic growth of the width of the resonance curve when the gain/losses coefficient approaches a critical value, at which symmetry breaking occurs. We found that in the system with broken symmetry the resonant coupling between exponentially growing mode with stable higher-order one effectively stabilizes dynamically coupled pair of modes and remarkably diminishes the average rate of the total power growth.Comment: 4 pages, 6 figure

Stability of localized modes in PT-symmetric nonlinear potentials

We report on detailed investigation of the stability of localized modes in the nonlinear Schrodinger equations with a nonlinear parity-time (alias PT) symmetric potential. We are particularly focusing on the case where the spatially-dependent nonlinearity is purely imaginary. We compute the Evans function of the linear operator determining the linear stability of localized modes. Results of the Evans function analysis predict that for sufficiently small dissipation localized modes become stable when the propagation constant exceeds certain threshold value. This is the case for periodic and $\tanh$-shaped complex potentials where the modes having widths comparable with or smaller than the characteristic width of the complex potential are stable, while broad modes are unstable. In contrast, in complex potentials that change linearly with transverse coordinate all modes are stable, what suggests that the relation between width of the modes and spatial size of the complex potential define the stability in the general case. These results were confirmed using the direct propagation of the solutions for the mentioned examples.Comment: 6 pages, 4 figures; accepted to Europhysics Letters, https://www.epletters.net