Gap and out-gap breathers in a binary modulated discrete nonlinear Schr\"odinger model

We consider a modulated discrete nonlinear Schr\"odinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a 'forbidden' gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap -- discrete gap and out-gap breathers (DGBs and DOGBs) -- are investigated. Their linear stability is studied varying the system parameters from the continuous to the anti-continuous limit, and different types of oscillatory and real instabilities are revealed. It is shown, that generally DGBs in infinite modulated DNLS chains with hard (soft) nonlinearity do not possess any oscillatory instabilities for breather frequencies in the lower (upper) half of the gap. Regimes of 'exchange of stability' between symmetric and antisymmetric DGBs are observed, where an increased breather mobility is expected. The transformation from DGBs to DOGBs when the breather frequency enters the linear spectrum is studied, and the general bifurcation picture for DOGBs with tails of different wave numbers is described. Close to the anti-continuous limit, the localized linear eigenmodes and their corresponding eigenfrequencies are calculated analytically for several gap/out-gap breather configurations, yielding explicit proof of their linear stability or instability close to this limit.Comment: 17 pages, 12 figures, submitted to Eur. Phys. J.

Optical ratchets with discrete cavity solitons

We propose a setup to observe soliton ratchet effects using discrete cavity solitons in a one-dimensional array of coupled waveguide optical resonators. The net motion of solitons can be generated by an adiabatic shaking of the holding beam with zero average inclination angle. The resulting soliton velocity can be controlled by different parameters of the holding beam.Comment: 3 pages, 4 figures, submitted to Optics Letter

Quasiperiodic localized oscillating solutions in the discrete nonlinear Schr\"odinger equation with alternating on-site potential

We present what we believe to be the first known example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a non-integrable Hamiltonian lattice model. The model is a one-dimensional discrete nonlinear Schr\"odinger equation with alternating on-site energies, modelling e.g. an array of optical waveguides with alternating widths. The solution bifurcates from a stationary discrete gap soliton, and in a regime of large oscillations its intensity oscillates periodically between having one peak at the central site, and two symmetric peaks at the neighboring sites with a dip in the middle. Such solutions, termed 'pulsons', are found to exist in continuous families ranging arbitrarily close both to the anticontinuous and continuous limits. Furthermore, it is shown that they may be linearly stable also in a regime of large oscillations.Comment: 4 pages, 4 figures, to be published in Phys. Rev. E. Revised version: change of title, added Figs. 1(b),(c), 4 new references + minor clarification

Solitons and frequency combs in silica microring resonators: Interplay of the Raman and higher-order dispersion effects

The influence of Raman scattering and higher order dispersions on solitons and frequency comb generation in silica microring resonators is investigated. The Raman effect introduces a threshold value in the resonator quality factor above which the frequency locked solitons can not exist and, instead, a rich dynamics characterized by generation of self-frequency shift- ing solitons and dispersive waves is observed. A mechanism of broadening of the Cherenkov radiation through Hopf instability of the frequency locked solitons is also reported.Comment: 12 pages, 10 figure

Graphene plasmonic waveguides for mid-infrared supercontinuum generation on a chip

Using perturbation expansion of Maxwell equations with the nonlinear boundary condition, a generic propagation equation is derived to describe nonlinear effects, including spectral broadening of pulses, in graphene surface plasmon (GSP) waveguides. A considerable spectral broadening of an initial 100 fs pulse with 0.5 mW peak power in a 25 nm wide and 150 nm long waveguide is demonstrated. The generated supercontinuum covers the spectral range from 6 μm to 13 μm 

Topological edge states in equidistant arrays of Lithium Niobate nano-waveguides

We report that equidistant 1D arrays of thin-film Lithium Niobate nano-waveguides generically support topological edge states. Unlike conventional coupled-waveguide topological systems, the topological properties of these arrays are dictated by the interplay between intra- and inter-modal couplings of two families of guided modes with different parities. Exploiting two modes within the same waveguide to design a topological invariant allows us to decrease the system size by a factor of two and substantially simplify the structure. We present two example geometries where topological edge states of different types (based on either quasi-TE or quasi-TM modes) can be observed within a wide range of wavelengths and array spacings

Raman solitons in waveguides with simultaneous quadratic and Kerr nonlinearities

We analyse Raman-induced self-frequency shift in two-component solitons supported by both quadratic and cubic nonlinearities. Treating Raman terms as a perturbation, we derive expressions for soliton velocity and frequency shifts of the fundamental frequency and second harmonic soliton components. We find these predictions compare well with simulations of soliton propagation. We also show that Raman shift can cause two-component solitons to approach the boundary of their own existence and subsequently trigger soliton instabilities. In some cases these instabilities are accompanied by an almost complete transfer of power to the second harmonic, and emergence of a single-component Kerr solitonic pulse.Comment: 10 pages, 5 figure

Solitons near avoided mode crossings in χ(2) nanowaveguides

We present a model for $\chi^{(2)}$ waveguides accounting for three modes, two of which make an avoided crossing at the second harmonic wavelength. We introduce two linearly coupled pure modes and adjust the coupling to replicate the waveguide dispersion near the avoided crossing. Analysis of the nonlinear system reveals continuous wave (CW) solutions across much of the parameter-space and prevalence of its modulational instability. We also predict the existence of the avoided-crossing solitons, and study peculiarities of their dynamics and spectral properties, which include formation of a pedestal in the pulse tails and associated pronounced spectral peaks. Mapping these solitons onto the linear dispersion diagrams, we make connections between their existence and CW existence and stability. We also simulate the two-color soliton generation from a single frequency pump pulse to back up its formation and stability properties.Comment: 10 pages, 6 figure