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
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.
The formation of fibre Bragg grating dispersion?managed multisolitons depends on the presence of asymmetric terms in the transfer function of the chirped fibre gratings employed. Given this dependence on higher order terms, it seems clear that the influence of third order dispersion in the fibre link must be important. We study the tolerance of fiber Bragg grating dispersion managed multisolitons to the presence of third order dispersion in the fibre link. On the other hand, the transfer function of a fibre Bragg grating is sensible to its operating conditions, such as pressure and temperature, as well as being subject to experimental indetermination in their manufacture. We study the robustness of multisoliton solutions to the effect of pseudo?random variations in the gratings’ parameters.
Dispersion management with fiber Bragg gratings is studied in a system with zero net dispersion at distances of megameters. The formation of multisoliton states of two and more solitons is observed at long enough distances. These multisoliton solutions present fixed values for the peak powers, phase difference and distance between adjacent pulses, and can propagate for long distances without deformation, being the noise amplification the ultimate limitation to propagation. The formation of these bound states is related to the combined action of nonlinear effects on the fiber link and higher order dispersion terms both on the fiber and the transfer function of the gratings. Higher order effects on the gratings, which are usually neglected, can acquire great relevance in schemes in which a very high number of gratings is used. The distance between peaks in the multisoliton state is lower than the typical interaction distance between adjacent solitons, so they could be used to increase the capacity of the channel.
Chromatic dispersion is one of the most important transmission limitations in systems operating at 1550 nm, and much effort has been invested in obtaining dispersion compensation schemes for standard fibers already installed. Various different fiber Bragg grating dispersion compensation schemes are studied or a system composed of a directly modulated 1550 nm single-mode semiconductor laser signal propagating through a standard nonlinear fiber link. The laser diode is simulated by its stochastic rate equations, while the apodized chirped fiber Bragg gratings are obtained by numerical resolution of their coupled-mode equations. The optimal grating length for dispersion compensation after transmission through 100 km standard single-mode fiber is obtained by means of minimizing the eye opening penalty of the signal. Pre and post-compensation cases are analyzed separately, and differences between both cases are discussed in detail. Different optimal grating lengths arise for each case, and better results are obtained in general with post-compensation. Pulses with a FWHM of the order of 65 ps with various laser chirp parameters are reconstructed using a 5.75 cm chirped grating with a 16th- order Gaussian apodization function.
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.