48 research outputs found
New features of modulational instability of partially coherent light; importance of the incoherence spectrum
It is shown that the properties of the modulational instability of partially
coherent waves propagating in a nonlinear Kerr medium depend crucially on the
profile of the incoherent field spectrum. Under certain conditions, the
incoherence may even enhance, rather than suppress, the instability. In
particular, it is found that the range of modulationally unstable wave numbers
does not necessarily decrease monotonously with increasing degree of
incoherence and that the modulational instability may still exist even when
long wavelength perturbations are stable.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
Interaction of pulses in nonlinear Schroedinger model
The interaction of two rectangular pulses in nonlinear Schroedinger model is
studied by solving the appropriate Zakharov-Shabat system. It is shown that two
real pulses may result in appearance of moving solitons. Different limiting
cases, such as a single pulse with a phase jump, a single chirped pulse,
in-phase and out-of-phase pulses, and pulses with frequency separation, are
analyzed. The thresholds of creation of new solitons and multi-soliton states
are found.Comment: 9 pages, 7 figures. Accepted to Phys. Rev. E, 200
Modulational instability in nonlocal nonlinear Kerr media
We study modulational instability (MI) of plane waves in nonlocal nonlinear
Kerr media. For a focusing nonlinearity we show that, although the nonlocality
tends to suppress MI, it can never remove it completely, irrespectively of the
particular profile of the nonlocal response function. For a defocusing
nonlinearity the stability properties depend sensitively on the response
function profile: for a smooth profile (e.g., a Gaussian) plane waves are
always stable, but MI may occur for a rectangular response. We also find that
the reduced model for a weak nonlocality predicts MI in defocusing media for
arbitrary response profiles, as long as the intensity exceeds a certain
critical value. However, it appears that this regime of MI is beyond the
validity of the reduced model, if it is to represent the weakly nonlocal limit
of a general nonlocal nonlinearity, as in optics and the theory of
Bose-Einstein condensates.Comment: 8 pages, submitted to Phys. Rev.
Stability of Attractive Bose-Einstein Condensates in a Periodic Potential
Using a standing light wave trap, a stable quasi-one-dimensional attractive
dilute-gas Bose-Einstein condensate can be realized. In a mean-field
approximation, this phenomenon is modeled by the cubic nonlinear Schr\"odinger
equation with attractive nonlinearity and an elliptic function potential of
which a standing light wave is a special case. New families of stationary
solutions are presented. Some of these solutions have neither an analog in the
linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger
equation. Their stability is examined using analytic and numerical methods.
Trivial-phase solutions are experimentally stable provided they have nodes and
their density is localized in the troughs of the potential. Stable
time-periodic solutions are also examined.Comment: 12 pages, 18 figure
Statistical Theory for Incoherent Light Propagation in Nonlinear Media
A novel statistical approach based on the Wigner transform is proposed for
the description of partially incoherent optical wave dynamics in nonlinear
media. An evolution equation for the Wigner transform is derived from a
nonlinear Schrodinger equation with arbitrary nonlinearity. It is shown that
random phase fluctuations of an incoherent plane wave lead to a Landau-like
damping effect, which can stabilize the modulational instability. In the limit
of the geometrical optics approximation, incoherent, localized, and stationary
wave-fields are shown to exist for a wide class of nonlinear media.Comment: 4 pages, REVTeX4. Submitted to Physical Review E. Revised manuscrip
Standard and Embedded Solitons in Nematic Optical Fibers
A model for a non-Kerr cylindrical nematic fiber is presented. We use the
multiple scales method to show the possibility of constructing different kinds
of wavepackets of transverse magnetic (TM) modes propagating through the fiber.
This procedure allows us to generate different hierarchies of nonlinear partial
differential equations (PDEs) which describe the propagation of optical pulses
along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium
and derive an extended Nonlinear Schrodinger equation (eNLS) with a third order
derivative nonlinearity, governing the dynamics for the amplitude of the
wavepacket. In this derivation the dispersion, self-focussing and diffraction
in the nematic are taken into account. Although the resulting nonlinear
may be reduced to the modified Korteweg de Vries equation (mKdV), it also has
additional complex solutions which include two-parameter families of bright and
dark complex solitons. We show analytically that under certain conditions, the
bright solitons are actually double embedded solitons. We explain why these
solitons do not radiate at all, even though their wavenumbers are contained in
the linear spectrum of the system. Finally, we close the paper by making
comments on the advantages as well as the limitations of our approach, and on
further generalizations of the model and method presented.Comment: "Physical Review E, in press
Interaction of N solitons in the massive Thirring model and optical gap system: the Complex Toda Chain Model
Using the Karpman-Solov''ev quasiparticle approach for soliton-soliton
interaction I show that the train propagation of N well separated solitons of
the massive Thirring model is described by the complex Toda chain with N nodes.
For the optical gap system a generalised (non-integrable) complex Toda chain is
derived for description of the train propagation of well separated gap
solitons. These results are in favor of the recently proposed conjecture of
universality of the complex Toda chain.Comment: RevTex, 23 pages, no figures. Submitted to Physical Review