Dynamics of temporally localized states in passively mode-locked semiconductor lasers

Abstract

We study the emergence and the stability of temporal localized structures in the output of a semiconductor laser passively mode-locked by a saturable absorber in the long cavity regime. For large yet realistic values of the linewidth enhancement factor, we disclose the existence of secondary dynamical instabilities where the pulses develop regular and subsequent irregular temporal oscillations. By a detailed bifurcation analysis we show that additional solution branches that consist in multi-pulse (molecules) solutions exist. We demonstrate that the various solution curves for the single and multi-peak pulses can splice and intersect each other via transcritical bifurcations, leading to a complex web of solution. Our analysis is based upon a generic model of mode-locking that consists in a time-delayed dynamical system, but also upon a much more numerically efficient, yet approximate, partial differential equation. We compare the results of the bifurcation analysis of both models in order to assess up to which point the two approaches are equivalent. We conclude our analysis by the study of the influence of group velocity dispersion, that is only possible in the framework of the partial differential equation model, and we show that it may have a profound impact on the dynamics of the localized states.

Discrete light bullets in passively mode-locked semiconductor lasers

“…This way the pulses interact not only within one system but also with those in the neighboring nodes, leading to a different balance between attraction and repulsion. Since the coupled Haus equations limit, [25][26][27] the observed dLBs can be interpreted as the fully localized analogues of the periodic train of pulse clusters consisting of two or more closely packed pulses in the array as found in Ref. 22.…”

“…However, if operated in the so-called long-cavity regime, the mode locked pulses become individually addressable temporal localized states coexisting with the off solution. [24][25][26] In this regime, the round-trip time is much longer than the semiconductor gain recovery time, which is the slowest variable. This temporal confinement regime was found to be compatible with an additional spatial localization mechanism, leading to the formation of stable three-dimensional light bullets, i.e., localized pulses of light that are simultaneously confined in the transverse and propagation directions.…”

Temporal cavity solitons in a delayed model of a dispersive cavity ring laser

“…DDE laser models can be derived from the travelling wave equations under certain non-restrictive simplifying physical assumptions and proved to be a viable alternative to the standard models based on partial differential equations. In addition to asymptotic stability analysis [25,33] the DDE approach allows for numerical study of continuous wave (CW) and periodic intensity regimes using well-developed Floquet theory and software packages such as DDE-BIFTOOL [10,17,23,25,32,33,36].…”

Logic gates on stationary dissipative solitons

“…Moreover, the basic CGLE can easily be extended to more general models accounting for the impact of such high-order effects as third-order dispersion, fourth-order spectral filtering, self-stepping, and stimulated Raman scattering [28][29][30][31][32] as well as an external control [33,34]. In fact, more specific models have been used to study the turbulent-like intensity * tvr@jlu.edu.cn; tvr@rian.kharkov.ua and polarization rogue waves in a Raman fiber laser [35], stationary solitary pulses in a dual-core fiber laser [36], the interaction of stationary, oscillatory and exploding counter-propagating dissipative solitons [37,38], the existence of stable three-dimensional dissipative localized structures in the output of a laser coupled to a distant saturable absorber [39], the emergence and the stability of temporally localized structures in the output of a semiconductor laser passively mode locked by a saturable absorber in the long-cavity regime [40], and dissipative solitons in Bose-Einstein condensates [41][42][43][44][45][46].…”