5 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
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.
Three-Wave Modulational Stability and Dark Solitons in a Quadratic Nonlinear Waveguide with Grating
We consider continuous-wave (CW) states and dark solitons (DSs) in a system
of two fundamental-frequency (FF) and one second-harmonic (SH) waves in a
planar waveguide with the quadratic nonlinearity, the FF components being
linearly coupled by resonant reflections on the Bragg grating. We demonstrate
that, in contrast with the usual situation in quadratic spatial-domain models,
CW states with the phase shift between the FF and SH components are
modulationally stable in a broad parameter region in this system, provided that
the CW wavenumber does not belong to the system's spectral gap. Stationary
fundamental DSs are found numerically, and are also constructed by means of a
specially devised analytical approximation. Bound states of two and three DSs
are found too. The fundamental DSs and two-solitons bound states are stable in
all the cases when the CW background is stable, which is shown by dint of
calculation of the corresponding eigenvalues, and verified in direct
simulations. Tilted DSs are found too. They attain a maximum contrast at a
finite value of the tilt, that does not depend on the phase mismatch. At a
maximum value of the tilt, which grows with the mismatch, the DS merges into
the CW background. Interactions between the tilted solitons are shown to be
completely elastic.Comment: 10 pages, 12 figures; Journal of Optics A, in pres