278 research outputs found
A combined regular-logarithmic perturbation method for signal-noise interaction in amplified optical systems
We present a novel perturbation method for the nonlinear Schrödinger equation (NLSE) that governs the propagation of light in optical fibers. We apply this method to study signal-noise interactions in amplified multispan fiber-optic systems. Being based on a combination of the regular perturbation (RP) and logarithmic perturbation, the method is especially suitable for modeling the simultaneous presence of nonlinear and dispersive effects. Even after linearization, it retains the contribution of the quadratic perturbation terms of the NLSE, thereby achieving higher accuracy than an RP with comparable complexity. We revise parametric gain and nonlinear phase-noise effects under the new theory.We finally consider several examples and evaluate the probability density function of the optical or postdetection signal and the bit-error rate of an NRZ–OOK system. All of the results are compared with other models and with multicanonical Monte Carlo simulations
Solutions to the Optical Cascading Equations
Group theoretical methods are used to study the equations describing
\chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable
by inverse scattering techniques. On the other hand, these equations do share
some of the nice properties of soliton equations. Large families of explicit
analytical solutions are obtained in terms of elliptic functions. In special
cases, these periodic solutions reduce to localized ones, i.e., solitary waves.
All previously known explicit solutions are recovered, and many additional ones
are obtainedComment: 21 page
Coupled Nonlinear Schr\"{o}dinger equation and Toda equation (the Root of Integrability)
We consider the relation between the discrete coupled nonlinear
Schr\"{o}dinger equation and Toda equation. Introducing complex times we can
show the intergability of the discrete coupled nonlinear Schr\"{o}dinger
equation. In the same way we can show the integrability in coupled case of dark
and bright equations. Using this method we obtain several integrable equations.Comment: 11 pages, LateX, to apper in J. Phys. Soc. Jpn. Vol. 66, No
Theory of Pump Depletion and Spike Formation in Stimulated Raman Scattering
By using the inverse spectral transform, the SRS equations are solved and the
explicit output data is given for arbitrary laser pump and Stokes seed profiles
injected on a vacuum of optical phonons. For long duration laser pulses, this
solution is modified such as to take into account the damping rate of the
optical phonon wave. This model is used to interprete the experiments of Druhl,
Wenzel and Carlsten (Phys. Rev. Lett., (1983) vol. 51, p. 1171), in particular
the creation of a spike of (anomalous) pump radiation. The related nonlinear
Fourier spectrum does not contain discrete eigenvalue, hence this Raman spike
is not a soliton.Comment: LaTex file, includes two figures in LaTex format, 9 page
Complexes of stationary domain walls in the resonantly forced Ginsburg-Landau equation
The parametrically driven Ginsburg-Landau equation has well-known stationary
solutions -- the so-called Bloch and Neel, or Ising, walls. In this paper, we
construct an explicit stationary solution describing a bound state of two
walls. We also demonstrate that stationary complexes of more than two walls do
not exist.Comment: 10 pages, 2 figures, to appear in Physical Review
Mixed perturbative expansion: the validity of a model for the cascading
A new type of perturbative expansion is built in order to give a rigorous
derivation and to clarify the range of validity of some commonly used model
equations.
This model describes the evolution of the modulation of two short and
localized pulses, fundamental and second harmonic, propagating together in a
bulk uniaxial crystal with non-vanishing second order susceptibility
and interacting through the nonlinear effect known as ``cascading'' in
nonlinear optics.
The perturbative method mixes a multi-scale expansion with a power series
expansion of the susceptibility, and must be carefully adapted to the physical
situation. It allows the determination of the physical conditions under which
the model is valid: the order of magnitude of the walk-off, phase-mismatch,and
anisotropy must have determined values.Comment: arxiv version is already officia
Instability of two interacting, quasi-monochromatic waves in shallow water
We study the nonlinear interactions of waves with a doubled-peaked power
spectrum in shallow water. The starting point is the prototypical equation for
nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries
equation. Using a multiple-scale technique two defocusing coupled Nonlinear
Schr\"odinger equations are derived. We show analytically that plane wave
solutions of such a system can be unstable to small perturbations. This
surprising result suggests the existence of a new energy exchange mechanism
which could influence the behaviour of ocean waves in shallow water.Comment: 4 pages, 2 figure
INVERSE SCATTERING TRANSFORM ANALYSIS OF STOKES-ANTI-STOKES STIMULATED RAMAN SCATTERING
Zakharov-Shabat--Ablowitz-Kaup-Newel-Segur representation for
Stokes-anti-Stokes stimulated Raman scattering is proposed. Periodical waves,
solitons and self-similarity solutions are derived. Transient and bright
threshold solitons are discussed.Comment: 16 pages, LaTeX, no figure
- …