255 research outputs found
Surface modes and breathers in finite arrays of nonlinear waveguides
We present the complete set of symmetric and antisymmetric (edge and corner)
surface modes in finite one-- and two--dimensional arrays of waveguides. We
provide classification of the modes based on the anti-continuum limit, study
their stability and bifurcations, and discuss relation between surface and bulk
modes. We put forward existence of surface breathers, which represent
two-frequency modes localized about the array edges.Comment: Accepted for publication in Physical Review
Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays
We discuss the formation of self-trapped localized states near the edge of a
semi-infinite array of nonlinear waveguides. We study a crossover from
nonlinear surface states to discrete solitons by analyzing the families of odd
and even modes centered at different distances from the surface, and reveal the
physical mechanism of the nonlinearity-induced stabilization of surface modes.Comment: 4 double-column pages, 5 figures, submitted to Optics Letter
Nonlinear localized modes at phase-slip defects in waveguide arrays
We study light localization at a phase-slip defect created by two
semi-infinite mismatched identical arrays of coupled optical waveguides. We
demonstrate that the nonlinear defect modes possess the specific properties of
both nonlinear surface modes and discrete solitons. We analyze stability of the
localized modes and their generation in both linear and nonlinear regimes.Comment: 3 pages, 6 figures, submitted to Opt. Let
Multipole-mode surface solitons
We discover multipole-mode solitons supported by the surface between two
distinct periodic lattices imprinted in Kerr-type nonlinear media. Such
solitons are possible because the refractive index modulation at both sides of
the interface glues together their out-of-phase individual constituents.
Remarkably, we find that the new type of solitons may feature highly asymmetric
shapes and yet they are stable over wide domains of their existence, a rare
property to be attributed to their surface nature.Comment: 14 pages, 3 figures, to appear in Optics Letter
Antisymmetric solitons and their interactions in strongly dispersion-managed fiber-optic systems
By means of the variational approximation (VA), a system of ordinary
differential equations (ODEs) is derived to describe the propagation of
antisymmetric solitons in a multi-channel (WDM) optical fiber link subject to
strong dispersion management. Results are reported for a prototypical model
including two channels. Using the VA technique, conditions for stable
propagation of the antisymmetric dispersion-managed (ASDM) solitons in one
channel are found, and complete and incomplete collisions between the solitons
belonging to the different channels are investigated. In particular, it is
shown that formation of a bound inter-channel state of two ASDM solitons is
possible under certain conditions (but may be easily avoided). The VA
predictions for the single- and two-channel systems are compared with direct
simulations of the underlying partial differential equations. In most cases,
the agreement is very good, but in some cases (very closely spaced channels)
the collision may destroy the ASDM solitons. The timing-jitter suppression
factor (JSF) for the ASDM soliton in one channel, and the crosstalk timing
jitter induced by collision between the solitons belonging to the different
channels are also estimated analytically. In particular, the JSF for the ASDM
soliton may be much larger than for its fundamental-soliton counterpart in the
same system.Comment: 15 pages, 10 figures, accepted for publication in Optics
Communication
On classification of intrinsic localized modes for the Discrete Nonlinear Schr\"{o}dinger Equation
We consider localized modes (discrete breathers) of the discrete nonlinear
Schr\"{o}dinger equation
,
, . We study the diversity of the steady-state
solutions of the form and the intervals of the
frequency, , of their existence. The base for the analysis is provided
by the anticontinuous limit ( negative and large enough) where all the
solutions can be coded by the sequences of three symbols "-", "0" and "+".
Using dynamical systems approach we show that this coding is valid for
and the point is a point of
accumulation of saddle-node bifurcations. Also we study other bifurcations of
intrinsic localized modes which take place for and give the
complete table of them for the solutions with codes consisting of less than
four symbols.Comment: 33 pages, 14 figures. To appear in Physica
Robustness of Quadratic Solitons with Periodic Gain
We address the robustness of quadratic solitons with periodic
non-conservative perturbations. We find the evolution equations for
guiding-center solitons under conditions for second-harmonic generation in the
presence of periodic multi-band loss and gain. Under proper conditions, a
robust guiding-center soliton formation is revealed.Comment: 5 pages, 5 figures, submitted to Optics Communicatio
Walking vector soliton caging and releasing
We address the formation and propagation of vector solitons in optical
lattices in the presence of anisotropy-induced walk-off between ordinary and
extraordinary polarized field components. Stable vector solitons trapped by the
lattice form above a threshold power, while decreasing the lattice depth below
a critical value results in the abrupt release of the caged solitons, that then
move across the lattice and may get trapped in a desired lattice channel.Comment: 13 pages, 4 figures, to appear in Optics Letter
Applications of the wave packet method to resonant transmission and reflection gratings
Scattering of femtosecond laser pulses on resonant transmission and
reflection gratings made of dispersive (Drude metals) and dielectric materials
is studied by a time-domain numerical algorithm for Maxwell's theory of linear
passive (dispersive and absorbing) media. The algorithm is based on the
Hamiltonian formalism in the framework of which Maxwell's equations for passive
media are shown to be equivalent to the first-order equation, , where is a linear differential
operator (Hamiltonian) acting on a multi-dimensional vector built of the
electromagnetic inductions and auxiliary matter fields describing the medium
response. The initial value problem is then solved by means of a modified time
leapfrog method in combination with the Fourier pseudospectral method applied
on a non-uniform grid that is constructed by a change of variables and designed
to enhance the sampling efficiency near medium interfaces. The algorithm is
shown to be highly accurate at relatively low computational costs. An excellent
agreement with previous theoretical and experimental studies of the gratings is
demonstrated by numerical simulations using our algorithm. In addition, our
algorithm allows one to see real time dynamics of long leaving resonant
excitations of electromagnetic fields in the gratings in the entire frequency
range of the initial wide band wave packet as well as formation of the
reflected and transmitted wave fronts.Comment: 23 pages; 8 figures in the png forma
Nonlinear guided waves and spatial solitons in a periodic layered medium
We overview the properties of nonlinear guided waves and (bright and dark)
spatial optical solitons in a periodic medium created by a sequence of linear
and nonlinear layers. First, we consider a single layer with a cubic nonlinear
response (a nonlinear waveguide) embedded into a periodic layered linear
medium, and describe nonlinear localized modes (guided waves and Bragg-like
localized gap modes) and their stability. Then, we study modulational
instability as well as the existence and stability of discrete spatial solitons
in a periodic array of identical nonlinear layers, a one-dimensional nonlinear
photonic crystal. Both similarities and differences with the models described
by the discrete nonlinear Schrodinger equation (derived in the tight-binding
approximation) and coupled-mode theory (valid for the shallow periodic
modulations) are emphasized.Comment: 10 pages, 14 figure
- …