64 research outputs found
Quasiperiodic Envelope Solitons
We analyse nonlinear wave propagation and cascaded self-focusing due to
second-harmonic generation in Fibbonacci optical superlattices and introduce a
novel concept of nonlinear physics, the quasiperiodic soliton, which describes
spatially localized self-trapping of a quasiperiodic wave. We point out a link
between the quasiperiodic soliton and partially incoherent spatial solitary
waves recently generated experimentally.Comment: Submitted to PRL. 4 pages with 5 figure
Controlling soliton refraction in optical lattices
We show in the framework of the 1D nonlinear Schrödinger equation that the value of the refraction angle of a fundamental soliton beam passing through an optical lattice can be controlled by adjusting either the shape of an individual waveguide or the relative positions of the waveguides. In the case of the shallow refractive index modulation, we develop a general approach for the calculation of the refraction angle change. The shape of a single waveguide crucially affects the refraction direction due to the appearance of a structural form factor in the expression for the density of emitted waves. For a lattice of scatterers, wave-soliton interference inside the lattice leads to the appearance of an additional geometric form factor. As a result, the soliton refraction is more pronounced for the disordered lattices than for the periodic ones
Anderson localization in metamaterials and other complex media
We review some recent (mostly ours) results on the Anderson localization of
light and electron waves in complex disordered systems, including: (i)
left-handed metamaterials, (ii) magneto-active optical structures, (iii)
graphene superlattices, and (iv) nonlinear dielectric media. First, we
demonstrate that left-handed metamaterials can significantly suppress
localization of light and lead to an anomalously enhanced transmission. This
suppression is essential at the long-wavelength limit in the case of normal
incidence, at specific angles of oblique incidence (Brewster anomaly), and in
the vicinity of the zero-epsilon or zero-mu frequencies for dispersive
metamaterials. Remarkably, in disordered samples comprised of alternating
normal and left-handed metamaterials, the reciprocal Lyapunov exponent and
reciprocal transmittance increment can differ from each other. Second, we study
magneto-active multilayered structures, which exhibit nonreciprocal
localization of light depending on the direction of propagation and on the
polarization. At resonant frequencies or realizations, such nonreciprocity
results in effectively unidirectional transport of light. Third, we discuss the
analogy between the wave propagation through multilayered samples with
metamaterials and the charge transport in graphene, which enables a simple
physical explanation of unusual conductive properties of disordered graphene
superlatices. We predict disorder-induced resonances of the transmission
coefficient at oblique incidence of the Dirac quasiparticles. Finally, we
demonstrate that an interplay of nonlinearity and disorder in dielectric media
can lead to bistability of individual localized states excited inside the
medium at resonant frequencies. This results in nonreciprocity of the wave
transmission and unidirectional transport of light.Comment: 37 pages, 30 figures, Review pape
Nonreciprocal Anderson Localization in Magneto-Optical Random Structures
We study, both analytically and numerically, disorder-induced localization of
light in random layered structures with magnetooptical materials. The Anderson
localization in such structures demonstrates nonreciprocal features in the
averaged localization length and individual transmission resonances. We employ
short-wavelength approximation where the localization effects are strong, and
consider both the Faraday and Voigt magnetooptical geometries. In the Faraday
geometry, the transmission is strongly nonreciprocal for the circularly
polarized waves, whereas in the Voigt geometry, the nonreciprocity is much
weaker, and it may appear only for the individual transmission resonances of
the TM-polarized waves.Comment: 8 pages, 6 figure
Anderson Localization of Classical Waves in Weakly Scattering Metamaterials
We study the propagation and localization of classical waves in
one-dimensional disordered structures composed of alternating layers of left-
and right-handed materials (mixed stacks) and compare them to the structures
composed of different layers of the same material (homogeneous stacks). For
weakly scattering layers, we have developed an effective analytical approach
and have calculated the transmission length within a wide region of the input
parameters. When both refractive index and layer thickness of a mixed stack are
random, the transmission length in the long-wave range of the localized regime
exhibits a quadratic power wavelength dependence with the coefficients
different for mixed and homogeneous stacks. Moreover, the transmission length
of a mixed stack differs from reciprocal of the Lyapunov exponent of the
corresponding infinite stack. In both the ballistic regime of a mixed stack and
in the near long-wave region of a homogeneous stack, the transmission length of
a realization is a strongly fluctuating quantity. In the far long-wave part of
the ballistic region, the homogeneous stack becomes effectively uniform and the
transmission length fluctuations are weaker. The crossover region from the
localization to the ballistic regime is relatively narrow for both mixed and
homogeneous stacks. In mixed stacks with only refractive-index disorder,
Anderson localization at long wavelengths is substantially suppressed, with the
localization length growing with the wavelength much faster than for
homogeneous stacks. The crossover region becomes essentially wider and
transmission resonances appear only in much longer stacks. All theoretical
predictions are in an excellent agreement with the results of numerical
simulations.Comment: 19 pages, 16 figures, submitted to PR
Soliton pinning by long-range order in aperiodic systems
We investigate propagation of a kink soliton along inhomogeneous chains with
two different constituents, arranged either periodically, aperiodically, or
randomly. For the discrete sine-Gordon equation and the Fibonacci and
Thue-Morse chains taken as examples, we have found that the phenomenology of
aperiodic systems is very peculiar: On the one hand, they exhibit soliton
pinning as in the random chain, although the depinning forces are clearly
smaller. In addition, solitons are seen to propagate differently in the
aperiodic chains than on periodic chains with large unit cells, given by
approximations to the full aperiodic sequence. We show that most of these
phenomena can be understood by means of simple collective coordinate arguments,
with the exception of long range order effects. In the conclusion we comment on
the interesting implications that our work could bring about in the field of
solitons in molecular (e.g., DNA) chains.Comment: 4 pages, REVTeX 3.0 + epsf, 3 figures in accompanying PostScript file
(Submitted to Phys Rev E Rapid Comm
Kink propagation through disordered media
Using a collective-coordinate approach, we study kink propagation along nonlinear systems with
local, randomly distributed inhomogeneities. We develop a general method to compute dynamical
variable statistics which can be generalized to a number of soli ton-bearing systems, and we apply it
to the sine-Gordon equation as an example.Supported by the Comision Interministerial de Ciencia y Tecnologia (CICyT) of Spain through project MAT90- 0544, and S.A.G. is partially supported by a grant from the Israeli Ministry for Science and Development.Publicad
Umklapp-Assisted Electron Transport Oscillations in Metal Superlattices
We consider a superlattice of parallel metal tunnel junctions with a
spatially non-homogeneous probability for electrons to tunnel. In such
structures tunneling can be accompanied by electron scattering that conserves
energy but not momentum. In the special case of a tunneling probability that
varies periodically with period in the longitudinal direction, i.e.,
perpendicular to the junctions, electron tunneling is accompanied by "umklapp"
scattering, where the longitudinal momentum changes by a multiple of . We
predict that as a result a sequence of metal-insulator transitions can be
induced by an external electric- or magnetic field as the field strength is
increased.Comment: 5 pages, 3 figure
Interplay of disorder and nonlinearity in Klein-Gordon models: Immobile kinks
We consider Klein-Gordon models with a -correlated spatial disorder.
We show that the properties of immobile kinks exhibit strong dependence on the
assumptions as to their statistical distribution over the minima of the
effective random potential. Namely, there exists a crossover from monotonically
increasing (when a kink occupies the deepest potential well) to the
non-monotonic (at equiprobable distribution of kinks over the potential minima)
dependence of the average kink width as a function of the disorder intensity.
We show also that the same crossover may take place with changing size of the
system.Comment: 7 pages, 4 figure
Quantum dynamics in canonical and micro-canonical ensembles. Part I. Anderson localization of electrons
The new numerical approach for consideration of quantum dynamics and
calculations of the average values of quantum operators and time correlation
functions in the Wigner representation of quantum statistical mechanics has
been developed. The time correlation functions have been presented in the form
of the integral of the Weyl's symbol of considered operators and the Fourier
transform of the product of matrix elements of the dynamic propagators. For the
last function the integral Wigner- Liouville's type equation has been derived.
The numerical procedure for solving this equation combining both molecular
dynamics and Monte Carlo methods has been developed. For electrons in
disordered systems of scatterers the numerical results have been obtained for
series of the average values of the quantum operators including position and
momentum dispersions, average energy, energy distribution function as well as
for the frequency dependencies of tensor of electron conductivity and
permittivity according to quantum Kubo formula. Zero or very small value of
static conductivity have been considered as the manifestation of Anderson
localization of electrons in 1D case. Independent evidence of Anderson
localization comes from the behaviour of the calculated time dependence of
position dispersion.Comment: 8 pages, 10 figure
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