Jose M Soto-Crespo

Multipulse operation of a Ti:sapphire laser mode locked by an ion-implanted semiconductor saturable-absorber mirror

We show results obtained from a semiconductor saturable-absorber mirror mode-locked Ti:sapphire soliton laser that was operated in the multiple-pulse regime. Double, triple, and quadruple pulses were observed when the dispersion was decreased below a critical value. The pulse pairs and triplets were either widely separated or closely coupled, and spectra that resembled those of constant as well as rotating phase differences between pulses were observed. We explain our observations in the framework of the generalized complex Ginzburg‐ Landau equation as the master equation of the laser.

Does the nonlinear Schrodinger equation correctly describe beam propagation

The parabolic equation (nonlinear Schrödinger equation) that appears in problems of stationary nonlinear beam propagation (self-focusing) is reconsidered. It is shown that an additional term, which involves changes of the propagation constant along the propagation direction, should be taken into account. The physical consequences of this departure from the standard approximation, which uses the parabolic equation, are discussed. A numerical simulation showing the difference between the new approach and the standard nonlinear Schrödinger equation is given as an example.

Phase-locked stationary soliton states in birefringent nonlinear optical fibers

We consider stationary soliton states in a birefringent optical fiber with two components locked in phase. Two values of the phase difference between the two components of the soliton states are studied: 0 and π/2. These cases allow us to find composite soliton states in a simple way. The bifurcation diagrams for the coupled soliton states in these two cases are constructed. The stability of these soliton states is examined also.

Quantized separations of phase-locked soliton pairs in fiber lasers

We report the discovery of a quantization of the separation between phase-locked soliton pairs that is related to the radiation waves known as Kelly sidebands, in a passively mode-locked fiber ring laser. Our numerical simulations that predict this phenomenon have been confirmed by our experimental results.

Relative phase locking of pulses in a passively mode-locked fiber laser

In a passively mode-locked fiber ring laser, we report the experimental observation of relative phase locking of pulses in a wide variety of cases. Relative phase locking is observed in bunches of N pulses separated by more than 20 pulse widths as well as in close pulse pairs. In the latter case, the phase relationship between the two pulses is measured to be ±π/2, which is related to theoretical predictions formerly obtained from a Ginzburg–Landau distributed model. We have developed a simplified numerical model adapted to our laser, which keeps its essential features while significantly reducing the number of free parameters. The agreement with the experiment is excellent.

Dissipative soliton resonances in laser models with parameter management

Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. We have found that the DSR phenomenon is robust and does not disappear when perturbations are introduced into the model. In particular, parameter management is benign to DSR: the resonance property remains intact even when a pulse experiences periodic changes of system parameters in a laser cavity. We also show that high energy pulses emerging from a laser cavity can be compressed to shorter durations with the help of linear dispersive devices.

Rogue waves in optical fibers in presence of third-order dispersion, self-steepening, and self-frequency shift

Rogue waves in optical fibers can be mathematically described by the nonlinear Schrodinger equation and its extensions that take into account third-order dispersion, self-steepening, and self-frequency shift. These equations are integrable in special cases such as the Sasa–Satsuma or the Hirota equations. However, approximate polynomial solutions can also be obtained in cases beyond these integrable ones. We present these solutions and confirm their validity using numerical simulations.

Interrelation between various branches of stable solitons in dissipative systems––conjecture for stability criterion

Abstract We show that the complex cubic-quintic Ginzburg–Landau equation has a multiplicity of soliton solutions for the same set of equation parameters. They can either be stable or unstable. We show that the branches of stable solitons can be interrelated, i.e. stable solitons of one branch can be transformed into stable solitons of another branch when the parameters of the system are changed. This connection occurs via some branches of unstable solutions. The transformation occurs at the points of bifurcation. Based on these results, we propose a conjecture for a stability criterion for solitons in dissipative systems.

Dissipative ring solitons with vorticity

We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation. In dissipative media, radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters. Beyond the region of stability, the solitons lose the radial symmetry but may remain stable, keeping the same value of the topological charge. We have found bifurcations into solitons with n-fold bending symmetry, with n independent on m. Solitons without circular symmetry can also display (m + 1)-fold modulation behaviour. A sequence of bifurcations can transform the ring soliton into a pulsating or chaotic state which keeps the same value of the topological charge as the original ring.

Light bullets and dynamic pattern formation in nonlinear dissipative systems

In the search for suitable new media for the propagation of (3+1) D optical light bullets, we show that nonlinear dissipation provides interesting possibilities. Using the complex cubic-quintic Ginzburg-Landau equation model with localized initial conditions, we are able to observe stable light bullet propagation or higher-order transverse pattern formation. The type of evolution depends on the model parameters.