Fig. 1. Experiment setup and results in our previous studies [25]. The NIR femtosecond laser is coupled into the x-y surface of (a) a pure LN thin plate sample with dimensions of 5  mm(x)×20  mm(y)×1  mm (z), and (b) a z cut PPLN crystal of the same size with poling period of 6.96 μm. (c) and (d) The input pump and output broadened spectra experimentally recorded in systems (a) and (b), respectively.

Fig. 2. Spectral illustration for synergic 2nd-NL and 3rd-NL effects.

Fig. 3. (a) Experiment and simulation results of the pump (black) and broadened spectrum (red) from pure LN. (b) Simulated spectrum evolution during the pump femtosecond pulse transmitting 1 mm thick pure LN crystal with the action of the 3rd-NL effect along with linear dispersion. The overall calculated (c) broadening spectra and (d) temporal-frequency distributions, and (e) energy hotspot distribution maps plotted in the temporal-frequency configuration are provided in variation with the transmission distance under the synergic actions of the linear dispersion and 3rd-NL. The blue lines shown in (c) and (d) are the calculation results considering single 3rd-NL effect in comparison.

Fig. 4. (a) Illustration for phase difference calculation in the interference model and the calculated temporal frequency shift considering the dispersion, the SPM, and the dispersion + SPM, respectively, after a 1 mm transmission distance in the pure LN crystal. The hatched area represents the value of Δϕmax and the orange regions represent the value for Δϕ(ωi). (b) Calculated Δϕmax in variation with the transmission distance. (c) Calculated phase difference in variation with δω, where the pink dotted lines represent destructive interference and the green dotted lines represent constructive interference. The intersection points match the peaks and valleys in (d) the spectrum diagram plotted with normalized frequency shifts, respectively.

Fig. 5. (a) Experimental and simulated spectrum profile for the input pump pulse and the broadened FW pulse transmitting after a 1 mm PPLN thin plate. (b) Generated SHW spectrum profile considering the dispersion and the 2nd-NL SHG process (the black line), the synergic dispersion, the 2nd-NL SHG, and the 3rd-NL SPM process (the red line), respectively. (c) SHW spectrum evolution in variation with the transmission distance corresponding to the cases of the black line and red line in (b). (d) Calculated maximum phase shift for FW and SHW in variation with the transmission distance. (e) Calculated δω(t) for SHW at different transmission distances.

Fig. 6. Simulated spectra of FW and SHW under different pump energies: (a) 10 μJ, (b) 30 μJ, (c) 50 μJ, (d) 70 μJ, (e) 90 μJ, and (f) 110 μJ.

Fig. 7. (a) Simulated SHW energy as a function of the transmission distance with increasing pump energies. The dotted inflection points indicate the generation of a new spectral peak. (b)–(d) Temporal-frequency illustration for phase-mismatch calculation after the pulse propagating 0.4 mm within the 1 mm length PPLN crystal. The red lines in (b) and (c) indicate the SPM-induced intrapulse wavelength distribution. The SHW pulse is plotted in the reference frame moving with the group velocity of the FW; thus, the 650 nm component in (c) temporally lags behind the 1300 nm component in (b). The horizontal black dotted line in (d) represents the phase-matching condition Δk=0, with the corresponding wavelengths of FW and SHW shown in the blue and green dotted lines in (b) and (c).