Figure 1

Experimental setup. The pulse shaper consists of a liquid-crystal-based spatial light modulator (SLM) with amplitude and phase masks in a 4$f$ setup with two diffraction gratings (G). The desired initial shape is carved from the OPO pulses; the result is monitored by an optical spectrum analyzer (OSA). $\lambda /2$, half-wave retarder; PBS, polarizing beam splitter. The DM fiber link is described in the text. Flip mirrors (FM) steer either the fiber input or the fiber output signal towards data acquisition. BS, beam splitter; BBO, frequency-doubling $\beta -{\mathrm{BaB}}_2{\mathrm{O}}_4$ crystal; CCD, camera. Both second-harmonic generation (SHG) frequency-resolved optical gating (FROG) and blind FROG measurement is provided; the latter requires a sample of the OPO pulse as a reference. Both pulse shaping and data acquisition are computer controlled for automated parameter scans.Reuse & Permissions

Figure 2

Evolution of separation between pulses in a pair when the initial separation is varied. Data are shown for three different launch energies (left, center, and right columns); the indicated numbers refer to single-pulse energies. Upper row: Cross-correlation traces measured at fiber end, color coded. The left pulse was centered on $t=0$ to remove timing fluctuations. Lower row: Measured separation and velocity (data points) compared to initial separation (dashed lines). Stable equilibrium ${\sigma }_{\mathrm{eq}}\approx 0.72\mathrm{ps}$ is characterized by the separation crossing the input separation in the appropriate direction (see text), and simultaneously the velocity being equal to zero.Reuse & Permissions

Figure 3

Global interaction pattern of a pair of dispersion-managed solitons. (a) Separation of DM solitons after ten dispersion periods when the pulse energy $E_{\mathrm{sol}}$ and initial separation ${\sigma }_{\mathrm{in}}$ are varied. Data are obtained from 1600 individual autocorrelation measurements. Also shown are numerically predicted equilibrium separations for the realistic (dashed line) and ideal (dotted line) cases. (b) Left side: Same data as in (a) but normalized to the respective equilibrium separation ${\sigma }_{\mathrm{eq}}$ of the realistic case. The branches of first collision (diagonal) and equilibrium separation (horizontal) are marked by dash-dotted and dashed lines, respectively. Right side: example of measured autocorrelation traces at $E_{\mathrm{sol}}=25.5\mathrm{pJ}$ in gray scale. A periodic breakup of the soliton pair is observed at $2.1{\sigma }_{\mathrm{eq}}<{\sigma }_{\mathrm{in}}<3.1{\sigma }_{\mathrm{eq}}$. (c)As (b) but from full numerical simulation for comparison.Reuse & Permissions

Figure 4

Cross-correlation measurement of fiber output signals when the parameters of the pulse pair are varied. Left column: Opposite-phase pulse pairs with 11.7 pJ pulse energy (top) and in-phase pulse pairs (bottom). Center column: Similar but at 14.4 pJ. Opposite-phase pulse pairs maintain their double-pulse structure, whereas in-phase pairs tend to merge. Right column: Continuous variation of phase difference at 14.4 pJ. Markers indicate corresponding parameters in the center column.Reuse & Permissions

Figure 5

Timing of fiber output signals when the relative phase is continuously varied. Shown are ICC traces of fiber output signals at ${\sigma }_{\mathrm{in}}=750\mathrm{fs}$. From left to right the (single-)pulse energy is increased. At low energy the double-pulse structure remains intact at all phases; at higher values there is clear phase dependence. The pair is preserved best at the medium energy and at $\phi =\pi$ or just above.Reuse & Permissions

Figure 6

Evolution of separations between pulses in a triplet when the initial separation is varied. Data are shown for three different launch energies (left, center, and right columns); the indicated numbers refer to single-pulse energies. Upper row: Cross-correlation traces measured at the fiber end, color coded. Lower row: Measured separations and velocities. Initial separation and velocity (the latter always zero) are shown as dashed lines for comparison. See text.Reuse & Permissions

Figure 7

Cross-correlation measurements of fiber output signals when the parameters of the pulse triplets are varied. Left column: Soliton triplets at $9.9\mathrm{pJ}$ pulse energy with opposite (top) and same (bottom) phase. Center column: Similar but at $11.7\mathrm{pJ}$. Opposite-phase triplets maintain their structure, whereas in-phase groups tend to collapse except for sufficiently large initial separations. Right column: Continuous variation of the phase difference at $11.7\mathrm{pJ}$. Markers indicate corresponding parameters in the center column. The triplet structure is maintained for relative phases $0.9\pi \le \phi \le 1.2\pi$; else it decays. Launch conditions: ${\sigma }_{\mathrm{in}}=750\mathrm{fs}$, $E_{\mathrm{sol}}=11.7\mathrm{pJ}$.Reuse & Permissions

Figure 8

Comparison of single DM soliton (a), two-soliton molecule (b), and three-soliton molecule (c). Field amplitudes of the simulated input signals (gray area), and the same of the simulated (hatched area) and measured (black solid curve) output signals. The phase is shown in red (simulation) and blue (experimental); error bars for the latter represent scatter from repeated FROG reconstructions.Reuse & Permissions