686 research outputs found
On integrable discretization of the inhomogeneous Ablowitz-Ladik model
An integrable discretization of the inhomogeneous Ablowitz-Ladik model with a
linear force is introduced. Conditions on parameters of the discretization
which are necessary for reproducing Bloch oscillations are obtained. In
particular, it is shown that the step of the discretization must be
comensurable with the period of oscillations imposed by the inhomogeneous
force. By proper choice of the step of the discretization the period of
oscillations of a soliton in the discrete model can be made equal to an integer
number of periods of oscillations in the underline continuous-time lattice.Comment: 6 pages, 1 figure, LaTe
Modes and exceptional points in waveguides with impedance boundary conditions
A planar waveguide with impedance boundary, composed of non-perfect metallic
plates, and with passive or active dielectric filling is considered. We show
the possibility of selective mode guiding and amplification when homogeneous
pump is added to the dielectric, and analyze differences in TE and TM mode
propagation. Such a non-conservative system is also shown to feature
exceptional points, for specific and experimentally tunable parameters, which
are described for a particular case of transparent dielectric.Comment: Optics Letters (2016
Coherent-perfect-absorber and laser for bound states in a continuum
It is shown that two fundamentally different phenomena, the bound states in
continuum and the spectral singularity (or time-reversed spectral singularity),
can occur simultaneously. This can be achieved, in particular, in a rectangular
core dielectric waveguide with embedded active (or absorbing) layer. In such a
system a two-dimensional bound state in a continuum is created in the plane of
a waveguide cross section and it is emitted or absorbed along the waveguide
core. The idea can be used for experimental implementation of a laser or a
coherent-perfect-absorber for photonic bound state that resides in a continuous
spectrum
Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons
We reveal the existence of continuous families of guided single-mode solitons
in planar waveguides with weakly nonlinear active core and absorbing
boundaries. Stable propagation of TE and TM-polarized solitons is accompanied
by attenuation of all other modes, i.e. the waveguide features properties of
conservative and dissipative systems. If the linear spectrum of the waveguide
possesses exceptional points, which occurs in the case of TM-polarization, an
originally focusing (defocusing) material nonlinearity may become effectively
defocusing (focusing). This occurs due to the geometric phase of the carried
eigenmode when the surface impedance encircles the exceptional point. In its
turn the change of the effective nonlinearity ensures the existence of dark
(bright) solitons in spite of focusing (defocusing) Kerr nonlinearity of the
core. The existence of an exceptional point can also result in anomalous
enhancement of the effective nonlinearity. In terms of practical applications
the nonlinearity of the reported waveguide can be manipulated by controlling
the properties of the absorbing cladding.Comment: Published versio
Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity
We study defect modes of a Bose-Einstein condensate in an optical lattice
with a localized defect within the framework of the one-dimensional
Gross-Pitaevskii equation. It is shown that for a significant range of
parameters the defect modes can be accurately described by an expansion over
Wannier functions, whose envelope is governed by the coupled nonlinear
Schr\"{o}dinger equation with a delta-impurity. The stability of the defect
modes is verified by direct numerical simulations of the underlying
Gross-Pitaevskii equation with a periodic plus defect potentials. We also
discuss possibilities of driving defect modes through the lattice and suggest
ideas for their experimental generation.Comment: 14 pages, 9 Figures, 1 Tabl
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