29 research outputs found
Solitons in a system of three linearly coupled fiber gratings
We introduce a model of three parallel-coupled nonlinear waveguiding cores
equipped with Bragg gratings (BGs), which form an equilateral triangle. The
objective of the work is to investigate solitons and their stability in this
system. New results are also obtained for the earlier investigated dual-core
system. Families of symmetric and antisymmetric solutions are found
analytically, extending beyond the spectral gap in both the dual- and tri-core
systems. Moreover, these families persist in the case (strong coupling between
the cores) when there is no gap in the system's linear spectrum. Three
different types of asymmetric solitons are found in the tri-core system. They
exist only inside the spectral gap, but asymmetric solitons with nonvanishing
tails are found outside the gap as well. The symmetric solitons are stable up
to points at which two types of asymmetric solitons bifurcate from them. Beyond
the bifurcation, one type of the asymmetric solitons is stable, and the other
is not. Then, they swap their stability. In both the dual- and tri-core
systems, the stability region of the symmetric solitons extends far beyond the
gap, persisting in the case when the system has no gap at all. The whole
stability region of antisymmetric solitons is located outside the gap. Thus,
solitons in multi-core BGs can be observed experimentally in a much broader
frequency band than in the single-core one, and in a wider parameter range than
it could be expected.Comment: 20 text pages and 11 figure pages at the end of the document;
European Physical Journal D, in pres
Surface solitons in trilete lattices
Fundamental solitons pinned to the interface between three semi-infinite
one-dimensional nonlinear dynamical chains, coupled at a single site, are
investigated. The light propagation in the respective system with the
self-attractive on-site cubic nonlinearity, which can be implemented as an
array of nonlinear optical waveguides, is modeled by the system of three
discrete nonlinear Schr\"{o}dinger equations. The formation, stability and
dynamics of symmetric and asymmetric fundamental solitons centered at the
interface are investigated analytically by means of the variational
approximation (VA) and in a numerical form. The VA predicts that two asymmetric
and two antisymmetric branches exist in the entire parameter space, while four
asymmetric modes and the symmetric one can be found below some critical value
of the inter-lattice coupling parameter -- actually, past the symmetry-breaking
bifurcation. At this bifurcation point, the symmetric branch is destabilized
and two new asymmetric soliton branches appear, one stable and the other
unstable. In this area, the antisymmetric branch changes its character, getting
stabilized against oscillatory perturbations. In direct simulations, unstable
symmetric modes radiate a part of their power, staying trapped around the
interface. Highly unstable asymmetric modes transform into localized breathers
traveling from the interface region across the lattice without significant
power loss.Comment: Physica D in pres
Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices
We study spontaneous symmetry breaking in a system of two parallel
quasi-one-dimensional traps, equipped with optical lattices (OLs) and filled
with a Bose-Einstein condensate (BEC). The cores are linearly coupled by
tunneling. Analysis of the corresponding system of linearly coupled
Gross-Pitaevskii equations (GPEs) reveals that spectral bandgaps of the single
GPE split into subgaps. Symmetry breaking in two-component BEC solitons is
studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both
traps; the mixed situation, with repulsion in one trap and attraction in the
other (RA), is considered too. In all the cases, stable asymmetric solitons are
found, bifurcating from symmetric or antisymmetric ones (and destabilizing
them), in the AA and RR systems, respectively. In either case, bi-stability is
predicted, with a nonbifurcating stable branch, either antisymmetric or
symmetric, coexisting with asymmetric ones. Solitons destabilized by the
bifurcation tend to rearrange themselves into their stable asymmetric
counterparts. The impact of a phase mismatch, between the OLs in the two cores
is also studied. Also considered is a related model, for a binary BEC in a
single-core trap with the OL, assuming that the two species (representing
different spin states of the same atom) are coupled by linear interconversion.
In that case, the symmetry-breaking bifurcations in the AA and RR models switch
their character, if the inter-species nonlinear interaction becomes stronger
than the intra-species nonlinearity.Comment: 21 pages + 24 figs, accepted to Phys. Rev.
Trapping of two-component matter-wave solitons by mismatched optical lattices
We consider a one-dimensional model of a two-component Bose-Einstein
condensate in the presence of periodic external potentials of opposite signs,
acting on the two species. The interaction between the species is attractive,
while intra-species interactions may be attractive too [the system of the
right-bright (BB) type], or of opposite signs in the two components [the
gap-bright (GB) model]. We identify the existence and stability domains for
soliton complexes of the BB and GB types. The evolution of unstable solitons
leads to the establishment of oscillatory states. The increase of the strength
of the nonlinear attraction between the species results in symbiotic
stabilization of the complexes, despite the fact that one component is centered
around a local maximum of the respective periodic potential
Slow-light switching in nonlinear Bragg-grating coupler
We study propagation and switching of slow-light pulses in nonlinear couplers
with phase-shifted Bragg gratings. We demonstrate that power-controlled
nonlinear self-action of light can be used to compensate dispersion-induced
broadening of pulses through the formation of gap solitons, to control pulse
switching in the coupler, and to tune the propagation velocity.Comment: 3 pages, 4 figure
Two-Component Nonlinear Schrodinger Models with a Double-Well Potential
We introduce a model motivated by studies of Bose-Einstein condensates (BECs)
trapped in double-well potentials. We assume that a mixture of two hyperfine
states of the same atomic species is loaded in such a trap.The analysis is
focused on symmetry-breaking bifurcations in the system, starting at the linear
limit and gradually increasing the nonlinearity. Depending on values of the
chemical potentials of the two species, we find numerous states, as well as
symmetry-breaking bifurcations, in addition to those known in the
single-component setting. These branches, which include all relevant stationary
solutions of the problem, are predicted analytically by means of a two-mode
approximation, and confirmed numerically. For unstable branches, outcomes of
the instability development are explored in direct simulations.Comment: 17 pages, 12 figures, Physica D, in pres