In array of nonlinear waveguides, a giant compression of the input beam can be achieved by exciting a rogue
wave. Input field almost homogeneously distributed over hundreds of waveguides concentrates practically all the
energy into a single waveguide at the output plane of the structure. We determine the required input profile of
the electric field to achieve maximal energy concentration at output. We illustrate the phenomenon modeling
the array by direct numerical simulations of the discrete nonlinear Schrodinger equation.
This paper summarizes analytic results describing the spectral broadening associated with fiber modulation
instability as described by analytic breather solutions of the nonlinear Schrodinger equation. These solutions
allow the prediction of spectral properties of both noise-driven and induced modulation instability processes. In
the latter case, the ability to describe MI with an analytic formalism allows the design of optimized experiments
to generate ultrashort pulse trains from weakly-modulated initial fields. These results are examples of only a
very small number of analytic descriptions of optical field propagation in highly nonlinear fiber.
Recent investigations in nonlinear fiber optics have shown a renewed interest in certain classes of analytical solutions of
the Nonlinear Schrödinger equation which, although present in the mathematical literature for 25 years, have been
largely overlooked in studies of nonlinear fiber propagation. In this paper we review recent experiments that have shown
the power of this analytic approach.
We consider various aspects of supercontinuum generation in the quasi-CW regime through analysis, numerical
simulations and experiments. A new interpretation of certain features of the developing spectrum in terms of localized
periodic structures known as "Akhmediev Breathers" is proposed. We also briefly consider the role of breather
collisions and turbulence in the presence of higher order dispersion and show that they lead to the formation of very large
amplitude localized structures that may be analogous to the infamous oceanic rogue waves.
The development of the supercontinuum spectrum in the quasi-CW regime is studied analytically, numerically and
experimentally. An interpretation in terms of localized periodic structures known as "Akhmediev Breathers" is
proposed. Theory, numerical simulation and experiment are in excellent agreement. We also briefly consider the role of
breather collisions in the presence of higher order dispersion and show that they lead to the formation of very large
amplitude localized structures that may be analogous to the infamous oceanic rogue waves.
By using a reduced model for dissipative optical soliton beams, we show that there are two disjoint
sets of fixed points. These correspond to stationary solitons of the radial complex cubic-quintic Ginzburg -
Landau equation with concave and convex phase profiles, respectively. We confirm these results by numerical
simulations which reveal soliton solutions of two different types: continuously self-focussing and continuously
self-defocusing.
The region of transition between solitons and fronts in dissipative systems governed by the complex Ginzburg-
Landau equation is rich with bifurcations. We found that the number of transitions between various types of
localized structures is enormous. For the first time, we have found a sequence of period-doubling bifurcations of
creeping solitons and also a symmetry-breaking instability of creeping solitons. Creeping solitons may involve
many frequencies in their dynamics resulting, in particular, in a variety of zig-zag motions.
We present several recent observations of temporal behavior of dissipative solitons and multi-soliton complexes in a laser ring cavity. Attractors, collisions and pulsations are discussed both in experiment and numerical simulations.
We present a review of known and new theoretical results on short-pulse propagation in optical systems with either slow or fast saturable absorbers. The analysis is based on using a modified complex Ginzburg-Landau equation. We show that in addition to the normal 'plain pulse' solutions, various other types of composite pulse solutions can exist. These composite solutions are formed from simpler solutions and may be considered as bound states of plain solitons or plain solitons and fronts. In the former case the bound states can be analyzed using the 'interaction plane' and balance equations.
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