mode-locking

We will present our recent results regarding the observation of soliton explosions in an all-normal dispersion fibre laser. Using a real time dispersive Fourier transform we were able to make single shot measurements of the spectrum showing how the explosion happens in frequency space and how this translates to the temporal behaviour of the pulse. Simulations of the generalised nonlinear Schrodinger equation agree well with the experimental results and highlight the regions between stability and chaos in such systems. Further investigations highlight the presence of optical rogue waves and chimera states in such a laser which will be discussed in the presentation.

Multimode lasers are widely used in medical, industrial, and technological applications. In particular, mode-locked semiconductor lasers are low cost, compact, and efficient sources of short optical pulses with high repetition rates suitable for application in telecommunication networks. A conventional technique to the theoretical studies of these lasers is based on numerical integration of a system of partial differential equations for the electric field envelope and carrier density. Here we use an alternative approach to describe multimode lasers, based on the use of delay differential equations (DDEs). We investigate DDE models of different multimode laser devices, - nonlinear mirror mode-locked lasers generating short optical pulses, frequency swept lasers with a long dispersive fiber delay line, and broad area external cavity semiconductor lasers. In addition to numerical simulations of these models we perform an analytical linear stability analysis that reveals modulational, Turing-type, and flip instabilities of CW regimes. We demonstrate the existence of bistability, chaotic regimes, square waves, as well as temporal and spatio-temporal (light bullets) localised structures of light and discuss their properties and interaction.

Time-Delayed dynamical systems (DDSs) materialize in situations where distant, point-wise, nonlinear nodes exchange information that propagates at a finite speed. They describe a large number of phenomena in nature and they exhibit a wealth of dynamical regimes such as localized structures, fronts and chimera states. A fertile perspective lies in their interpretation as spatially extended diffusive systems which holds in the limit of long delays. However, DDSs are considered devoid of dispersive effects, which are known to play a leading role in pattern formation and wave dynamics. In particular, second order dispersion in nonlinear extended media governs the Benjamin-Feir (modulational) instability and also controls the appearance of cavity solitons in injected Kerr fibers. Third order dispersion is the lowest order non-trivial parity symmetry breaking effect, which leads to convective instabilities and drifts.

In this contribution, we review our recent results regarding how second and third order dispersion may appear naturally in DDSs by using a more general class of Delayed Systems, the so-called Delay Algebraic Delay Differential Equations. This class of DDS appears for instance in the modeling of Vertical External-Cavity Surface-Emitting Lasers (VECSELs) and we illustrate our general result studying the effect of third order dispersion onto the optical pulses found in the output of a passively mode-locked VECSEL and link our results with the Gires-Tournois interferometer. We show that third order dispersion leads to the creation of satellites on one edge of the pulse which induces a new form of pulse instability. Our results are in good agreement with the experiment. Finally, we connect these results with the possibility of obtaining Light bullets, that is to say, pulses of light that are simultaneously confined in the transverse and the propagation directions, in mode-locked VECSELs.