Cavity Light Bullets in Passively Mode-Locked Semiconductor Lasers

We demonstrate the existence of stable three-dimensional dissipative localized structures in the output of a laser coupled to a distant saturable absorber. These phase invariant cavity light bullets are individually addressable and can be envisioned for three-dimensional optical information storage. An effective theory provides for an intuitive picture and allows us to relate their formation to the morphogenesis of static spatial autosolitons and temporal cellular patterns.

Figure 1

Real and imaginary parts (a),(b) and intensity (c) spatiotemporal distributions in the case of a single LB. The arbitrary phase of the LB was chosen to be zero at the peak intensity. The gain and absorption spatiotemporal profiles are represented in (d) and (e), respectively. The gain value is $G_0=0.687G_{\mathrm{th}}$.

Figure 2

Spatiotemporal traces for the gain $G(x,z)$ (a) and for the absorption $Q(x,z)$ (b) in a regime where $N=4$ LBs are present. The vertical time window corresponds to a single round-trip in the cavity, such that each LB appears once. The inset in (b) highlights the difference between the relaxation time scales of the material variables. The variable with the slowest recovery time $G$ defines the effective temporal extent of the LB. The gain value is $G_0=0.674G_{\mathrm{th}}$.

Figure 3

Isosurface representation of a three-dimensional LB at which the intensity (a) and the real (b) and imaginary (c) parts are 1% of the maximal value. The multiple curves in (c) indicate that the LB is spatially oscillating. The gain value is $G_0=0.694G_{\mathrm{th}}$.

Figure 4

Bifurcation diagram as a function of $G_0$. We represent the drift velocity of the LB in (a) and its energy in (b). The single LB regime occurs as a SNL bifurcation around $G_{\mathrm{SN}}=0.671G_{\mathrm{th}}$. The red dot at $G_0=0.674G_{\mathrm{th}}$ corresponds to the situation depicted in Fig. 2, while the green circle corresponds to the onset of an AH bifurcation at $G_H\sim 0.698G_{\mathrm{th}}$, where the transverse profile of the LB starts to oscillate in time.

Figure 5

Bifurcation diagram of Eq. (4) as a function of the gain parameter $G_0$. (a),(b) represent the evolution of the spectral parameter $\omega$ while the spatially integrated intensity $\mathrm{E}$ is depicted in (c),(d). Stable regions are depicted in blue. The multiple solutions are depicted in (e). The main solution is stable in the vicinity of the Saddle-Node bifurcation occurring at $G_{\mathrm{sn}}=0.606G_{\mathrm{th}}$ and loses its stability via an AH bifurcation at $G_h=0.63G_{\mathrm{th}}$. We represent the transverse profile oscillations slightly above $G_h$ in (f).