Temporal cavity soliton interaction in passively mode-locked semiconductor lasers

Weak interaction due to gain saturation and recovery of temporal cavity solitons in a delay differential model of a long cavity semiconductor laser is studied numerically and analytically using an asymptotic approach. It is shown that apart from usual soliton repulsion leading to a harmonic mode-locking regime a soliton attraction is also possible in a laser with nonzero linewidth enhancement factor. It is shown numerically that the attraction can lead either to a soliton merging or to a pulse bound state formation

Temporal cavity soliton interaction in passively mode-locked semiconductor lasers

Weak interaction of temporal cavity solitons due to gain saturation and recovery in a delay differential model of a long cavity semiconductor laser is studied numerically and analytically using an asymptotic approach. It is shown that in addition to the usual soliton repulsion leading to a harmonic mode-locking regimes a soliton attraction is also possible in a laser with nonzero linewidth enhancement factor. It is shown numerically that this attraction can lead either to a pulse merging or to a pulse bound state formation.Comment: 8 pages, 6 figure

Non-local and local temporal cavity soliton interaction in delay models of mode-locked lasers

Interaction equations governing slow time evolution of the coordinates and phases of two interacting temporal cavity solitons in a delay differential equation model of a nonlinear mirror mode-locked laser are derived and analyzed. It is shown that non-local pulse interaction due to gain depletion and recovery can lead either to a development of harmonic mode-locking regime, or to a formation of closely packed incoherent soliton bound state with weakly oscillating intersoliton time separation. Local interaction via electric field tails can result in an anti-phase or in-phase stationary or breathing harmonic mode-locking regime

Dynamics of an inhomogeneously broadened passively mode-locked laser

We study theoretically the effect of inhomogeneous broadening of the gain and absorption lines on the dynamics of a passively mode-locked laser. We demonstrate numerically using travelling wave equations the formation of a Lamb-dip instability and suppression of Q-switching in a laser with large inhomogeneous broadening. We derive simplified delay-differential equation model for a mode-locked laser with inhomogeneously broadened gain and absorption lines and perform numerical bifurcation analysis of this model

Neutral delay differential equation Kerr cavity model

A neutral delay differential equation (NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second and higher order dispersions being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the limit, where the model can be reduced to the Lugiato--Lefever equation (LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes

Passive mode-locking with slow saturable absorber: A delay differential model

We propose and study a new model describing passive mode-locking in a semiconductor laser - a set of differential equations with time delay. Analytical analysis of this model is performed under the slow saturable absorber approximation. Bifurcations responsible for the appearance and break-up of mode-locking regime are studied numerically

Q-switching instability in a mode-locked semiconductor laser

We suggest analytic estimates for the Q-switching instability boundary of the continuous-wave mode-locking regime domain for a ring cavity semiconductor laser. We use a differential delay laser model that allows to assume large gain and loss in the cavity, which is a typical situation for this laser class. The slow saturable absorber approximation is applied to derive a map that describes the transformation of the pulse parameters after a round trip in the cavity. The Q-switching instability boundary is then obtained as a Neimark-Sacker bifurcation curve of this map. We study the dependence of this boundary on laser parameters and compare it with the boundaries obtained by the New stability criterion and by direct numerical analysis of the original differential model. Further modification of our approach, based on the hyperbolic secant ansatz for the pulse shape, is used to estimate the width and repetition rate of the mode locking pulses

Dynamics of an inhomogeneously broadened passively mode-locked laser

We study theoretically the effect of inhomogeneous broadening of the gain and absorption lines on the dynamics of a passively mode-locked laser. We demonstrate numerically using travelling wave equations the formation of a Lamb-dip instability and suppression of Q-switching in a laser with large inhomogeneous broadening. We derive simplified delay-differential equation model for a mode-locked laser with inhomogeneously broadened gain and absorption lines and perform numerical bifurcation analysis of this model

Temporal solitons in an optically injected Kerr cavity with two spectral filters

We investigate theoretically the dynamical behavior of an optically injected Kerr cavity where the chromatic dispersion is induced by propagation of light through two Lorentzian spectral filters with different widths and central frequencies. We show that this setup can be modeled by a second order delay differential equation that can be considered as a generalization of the Ikeda map with included spectral filtering, dispersion, and coherent injection terms. We demonstrate that this equation can exhibit modulational instability and bright localized structures formation in the anomalous dispersion regime

Neutral delay differential equation Kerr cavity model

A neutral delay differential equation (NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second and higher order dispersion being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the limit, where the model can be reduced to the Lugiato-Lefever equation (LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes.Comment: 9 pages, 9 figure