86 research outputs found
Discrete gap solitons in a diffraction-managed waveguide array
A model including two nonlinear chains with linear and nonlinear couplings
between them, and opposite signs of the discrete diffraction inside the chains,
is introduced. For [] nonlinearity, the model finds two different
interpretations in terms of optical waveguide arrays, based on the
diffraction-management concept. A straightforward discrete []
model, with opposite signs of the diffraction at the fundamental and second
harmonics, is introduced also. Starting from the anti-continuum (AC) limit,
soliton solutions in the model are found, both above the phonon
band and inside the gap. Solitons above the gap may be stable as long as they
exist, but in the transition to the continuum limit they inevitably disappear.
On the contrary, solitons inside the gap persist all the way up to the
continuum limit. In the zero-mismatch case, they lose their stability long
before reaching the continuum limit, but finite mismatch can have a stabilizing
effect on them. A special procedure is developed to find discrete counterparts
of the Bragg-grating gap solitons. It is concluded that they exist all the
values of the coupling constant, but are stable only in the AC and continuum
limits. Solitons are also found in the model. They start as
stable solutions, but then lose their stability. Direct numerical simulations
in the cases of instability reveal a variety of scenarios, including
spontaneous transformation of the solitons into breather-like states,
destruction of one of the components (in favor of the other), and
symmetry-breaking effects. Quasi-periodic, as well as more complex, time
dependences of the soliton amplitudes are also observed as a result of the
instability development.Comment: 18 pages, 27 figures, Eur. Phys. J. D in pres
-Symmetric Periodic Optical Potentials
In quantum theory, any Hamiltonian describing a physical system is mathematically represented by a self-adjoint linear operator to ensure the reality of the associated observables. In an attempt to extend quantum mechanics into the complex domain, it was realized few years ago that certain non-Hermitian parity-time () symmetric Hamiltonians can exhibit an entirely real spectrum. Much of the reported progress has been remained theoretical, and therefore hasn't led to a viable experimental proposal for which non Hermitian quantum effects could be observed in laboratory experiments. Quite recently however, it was suggested that the concept of -symmetry could be physically realized within the framework of classical optics. This proposal has, in turn, stimulated extensive investigations and research studies related to -symmetric Optics and paved the way for the first experimental observation of -symmetry breaking in any physical system. In this paper, we present recent results regarding -symmetric Optic
Nonlinear Schr\"odinger equation for a PT symmetric delta-functions double well
The time-independent nonlinear Schr\"odinger equation is solved for two
attractive delta-function shaped potential wells where an imaginary loss term
is added in one well, and a gain term of the same size but with opposite sign
in the other. We show that for vanishing nonlinearity the model captures all
the features known from studies of PT symmetric optical wave guides, e.g., the
coalescence of modes in an exceptional point at a critical value of the
loss/gain parameter, and the breaking of PT symmetry beyond. With the
nonlinearity present, the equation is a model for a Bose-Einstein condensate
with loss and gain in a double well potential. We find that the nonlinear
Hamiltonian picks as stationary eigenstates exactly such solutions which render
the nonlinear Hamiltonian itself PT symmetric, but observe coalescence and
bifurcation scenarios different from those known from linear PT symmetric
Hamiltonians.Comment: 16 pages, 9 figures, to be published in Journal of Physics
Random-Phase Solitons in Nonlinear Periodic Lattices
We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons exist when the nonlinear response time is much longer than the characteristic time of random phase fluctuations. The intensity profiles, power spectra, and statistical (coherence) properties of these stationary waves conform to the periodicity of the lattice. The general phenomenon of such solitons is analyzed in the context of nonlinear photonic lattices
Rotary dipole-mode solitons in Bessel photonic lattices
We address Bessel photonic lattices of radial symmetry imprinted in cubic
Kerr-type nonlinear media and show that they support families of stable
dipole-mode solitons featuring two out-of-phase light spots located in
different lattice rings. We show that the radial symmetry of the Bessel
lattices afford a variety of unique soliton dynamics including controlled
radiation-free rotation of the dipole-mode solitons.Comment: 12 pages, 4 figures, to appear in Journal of Optics B: Quantum and
Semiclassical Optic
PT-symmetric optical lattices
The basic properties of Floquet-Bloch (FB) modes in parity-time (PT)-symmetric optical lattices are examined in detail. Due to the parity-time symmetry of such complex periodic potentials, the corresponding FB modes are skewed (nonorthogonal) and nonreciprocal. The conjugate pairs of these FB modes are obtained by reflecting both the spatial coordinate and the Bloch momentum number itself. The orthogonality conditions are analytically derived for a single cell, for both a finite and an infinite lattice. Some of the peculiarities associated with the diffraction dynamics in PT lattices such as nonreciprocity, power oscillations, and phase dislocations, are also examined
Use of Equivalent Hermitian Hamiltonian for -Symmetric Sinusoidal Optical Lattices
We show how the band structure and beam dynamics of non-Hermitian
-symmetric sinusoidal optical lattices can be approached from the point of
view of the equivalent Hermitian problem, obtained by an analytic continuation
in the transverse spatial variable . In this latter problem the eigenvalue
equation reduces to the Mathieu equation, whose eigenfunctions and properties
have been well studied. That being the case, the beam propagation, which
parallels the time-development of the wave-function in quantum mechanics, can
be calculated using the equivalent of the method of stationary states. We also
discuss a model potential that interpolates between a sinusoidal and periodic
square well potential, showing that some of the striking properties of the
sinusoidal potential, in particular birefringence, become much less prominent
as one goes away from the sinusoidal case.Comment: 11 pages, 8 figure
PT-Symmetric Periodic Optical Potentials
In quantum theory, any Hamiltonian describing a physical system is mathematically represented by a self-adjoint linear operator to ensure the reality of the associated observables. In an attempt to extend quantum mechanics into the complex domain, it was realized few years ago that certain non-Hermitian parity-time (PT) symmetric Hamiltonians can exhibit an entirely real spectrum. Much of the reported progress has been remained theoretical, and therefore hasn't led to a viable experimental proposal for which non Hermitian quantum effects could be observed in laboratory experiments. Quite recently however, it was suggested that the concept of PT-symmetry could be physically realized within the framework of classical optics. This proposal has, in turn, stimulated extensive investigations and research studies related to PT-symmetric Optics and paved the way for the first experimental observation of PT-symmetry breaking in any physical system. In this paper, we present recent results regarding PT-symmetric Optics
Stability of vortex solitons in a photorefractive optical lattice
Stability of off-site vortex solitons in a photorefractive optical lattice is
analyzed. It is shown that such solitons are linearly unstable in both the high
and low intensity limits. In the high-intensity limit, the vortex looks like a
familiar ring vortex, and it suffers oscillatory instabilities. In the
low-intensity limit, the vortex suffers both oscillatory and Vakhitov-Kolokolov
instabilities. However, in the moderate-intensity regime, the vortex becomes
stable if the lattice intensity or the applied voltage is above a certain
threshold value. Stability regions of vortices are also determined at typical
experimental parameters.Comment: 3 pages, 5 figure
Soliton molecules in trapped vector Nonlinear Schrodinger systems
We study a new class of vector solitons in trapped Nonlinear Schrodinger
systems modelling the dynamics of coupled light beams in GRIN Kerr media and
atomic mixtures in Bose-Einstein condensates. These solitons exist for
different spatial dimensions, their existence is studied by means of a
systematic mathematical technique and the analysis is made for inhomogeneous
media
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