Abstract

Passive mode-locking (PML) leads to the emission of temporal pulses much shorter than the cavity round-trip. It is achieved by combining two elements, a laser amplifier providing gain and a nonlinear loss element, usually a saturable absorber. It was recently shown [1] that individually addressable temporal Localized Structures (LSs) coexisting with the off solution can evolve from the PML regime when the round-trip τ is much longer than the gain recovery time τ_g. Furthermore, it was also demonstrated that, in this regime, the transverse profile of these LSs can self-organize yielding a new robust Light Bullet formation scenario [2]. The equation governing the transverse profile A(r_⊥, t) of these LBs is the so-called Rosanov equation that reads ∂_tA = [f(|A|²) + iΔ_⊥]A albeit with a particular form of the nonlinear function f(|A|²), different from the one found in the literature on static auto-solitons [3]. This makes the bifurcation analysis of such an equation a particularly relevant topic in order to make predictions regarding the stability and the domain of existence of these light bullets.

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