Three-Dimensional Light Bullets in Arrays of Waveguides

We report the first experimental observation of three-dimensional light bullets, excited by femtosecond pulses in a system featuring quasi-instantaneous cubic nonlinearity and a periodic, transversally modulated refractive index. Stringent evidence of the excitation of light bullets is based on time-gated images and spectra which perfectly match our numerical simulations. Furthermore, we reveal a novel evolution mechanism forcing the light bullets to follow varying dispersion or diffraction conditions, until they leave their existence range and decay.

Figure 1

(a) Layout of the experiment. A focused 170-fs infrared pulse centered at ${\lambda }_0=1550\mathrm{nm}$ excites the central waveguide of a sample of the waveguide array (b). The output radiation of the sample is characterized by an infrared camera (IR-Camera) and by a spatially resolved optical gating via frequency mixing in a $25\mathrm{\text{−}}\mu \mathrm{m}$-thin β-barium borate crystal with a delayed 60-fs probe pulse at ${\lambda }_p=800\mathrm{nm}$. (c) Experimental discrete linear diffraction pattern at the end of a 50-mm-long sample. Parameters of the sample: array made of 91 silica cores embedded in a fluoride-doped silica glass; lattice period of $d=33.2\pm 0.4\mu \mathrm{m}$, a core radius of $r=9.8\pm 0.2\mu \mathrm{m}$, and an index contrast of $\Delta n=1.2\times {10}^{-3}$.

Figure 2

Experimental observation and simulation of LBs for a 40-mm-long waveguide array. Spatial infrared camera image (first column). Temporal cross-correlation trace of the central waveguide (second column) with the original experimental data (blue line) and after deconvolution of the probe pulse profile (red line). Experimental spatiotemporal images (third column) and corresponding simulated spatiotemporal images derived (fourth column). Surfaces in the spatiotemporal images are normalized isointensity levels as indicated in the legend in (d). The three rows correspond to the three different input peak powers.

Figure 3

Numerical propagation of LBs in the central waveguide for $P_0=0.9\mathrm{MW}$. (a) Wave packet evolution in the time-propagation plane. The diffraction and dispersion length corresponding to a ${\tau }_{\mathrm{FWHM}}=25\mathrm{fs}$ pulse for the minimal and maximal central wavelength of the LB are overlaid to the graph for comparison. (b) Plot of pulse duration and central wavelength for the brightest LB seen in (a).

Figure 4

Experimental (left) and simulated (right) FROG traces of the pulse propagating in the central waveguide measured at the output of samples. Top: $L=25\mathrm{mm}$. Center: $L=40\mathrm{mm}$. Bottom: $L=60\mathrm{mm}$. The wavelength scale is shown between the columns. Input power $P_0=0.9\mathrm{MW}$.

Figure 5

Green line: Trajectory in parameter space of the brightest LB appearing in the simulation of Fig. 3a. The blue-red surface shows the locus of the ideal stationary LB solution of the discrete NLSE. Energy or wavelength plane: regions of stability and existence of ideal LB; A–C indicate different phases of the trajectory (see text for details). Gray lines: Projection of the trajectory onto the orthogonal planes.