Red Solitons: Evidence of Spatiotemporal Instability in ${\chi }^{(2)}$ Spatial Soliton Dynamics

In ${\chi }^{(2)}$ three-wave mixing, the noise-seeded spatiotemporal modulational instability has a dramatic impact on the spatial soliton formation and on their stability, leading to the occurrence of a temporal breakup on the 20 fs scale and to the counterintuitive observation of spatial solitons with no apparent participation of the high-frequency field in the self-trapping.

Figure 1

Transverse fluence distribution for the output signal (full line) and output pump (dashed line) beams for OPA excitation and two different frequency-tuning conditions (a) and (b), with the same pump-pulse energy, $E_p=2\mu \mathrm{J}$.

Figure 2

(a)–(f) Spatiotemporal intensity maps of the output pump WP for OPA excitation and two different frequency-tuning conditions (top and bottom); (a),(b) experimental data; (c),(d) smoothed numerical data; (e),(f) high resolution numerical data. (g),(h) Experimental (full line) and calculated (circles) autocorrelation of the pump WP, spatially averaged over a $30\mu \mathrm{m}$ diameter circular spot at the beam center. In (g) a zoom of the peak of (h) is reported. Input-pulse energy as in Fig. 1.

Figure 3

Frequency-tuning dependence of the pump-to-signal (peak) fluence ratio, $F_p/F_s$, for OPA excitation. Squares: experimental; triangles: $3\mathrm{D}+1$ spatiotemporal model; circles: $2\mathrm{D}+1$ spatial model; stars: $1\mathrm{D}+1$ temporal model. Fluences from the $3\mathrm{D}+1$ model are calculated by temporal integration. All data refer to the same input (peak) intensity.

Figure 4

SHG excitation. Phase-mismatch dependence of the ratio between the output FH and SH energies (experimental: balls), or intensities (cw model: stars), integrated within the FWHM diameter. All data are at taken at threshold.