Fig. 1. (a) SEM image of a PhC waveguide made of a GaP slab and close-up before the removal of the etching mask (red rectangle). The waveguide design (blue rectangle) indicates the relevant parameters, the radius of the holes, $r$; the period of the triangular lattice, $a$; the width of the defect line, $W$; and the transverse shift of the first row of holes, $s$. (b) Calculated (dashed) and measured (solid thick) average group index. The thin blue solid line is the calculated group index in the slow section. The cyan circle corresponds to the FWM experiment ($n_g=19$). (c) Corresponding second-order dispersion (same codes). (d) Transmission spectrum, including fiber-to-waveguide coupling (dashed line represents insertion losses). The red lines are a guide for the eyes.

Fig. 2. Picosecond pulse propagation and soliton dynamics. (a) Autocorrelation traces, experimental (grey circles) and calculated (red line). (b) Corresponding experimental output (grey circles) and input (cyan line) spectra. The calculated output spectrum (solid red line) is also represented with the calculated input one (dashed black line). (c) Calculated evolution of the pulse at some specified positions inside the waveguide. (d) Evolution of peak power P, pulse energy W, and duration $\mathrm{\Delta }t$.

Fig. 3. (a) Measurement of the nonlinear absorption for $n_g=11$ through the plot of the inverse transmission versus the peak power $\frac{T_0}{T}=1+2\mathfrak{I}(\gamma )P{L}_{\text{eff}}$ in the waveguide. (b) Nonlinear phase shift ${\mathit{\varphi }}_{\mathrm{NL}}$. (c) Calculated inverse linear and nonlinear cross sections $A_{\text{eff}}$ and $1/A_{{\chi }^{(3)}}$ as a function of the group index (see Appendix A). (d) Nonlinear parameter $\gamma$ versus group index. Estimate from the spectral broadening (magenta squares), values used in the model (green circles), and calculated (solid line) using $n_2=3.5\times {10}^{-18}{\mathrm{W}}^{-1}·{\mathrm{m}}^{-2}$. The dashed red line represents the $n_g^2$ dependence as a guide for the eyes.

Fig. 4. Four-wave mixing experiment with ps pulses at 2 GHz rate. (a) Output spectra corresponding to two different coupled peak power levels and spectrum of the pump at input. (b) Measured conversion efficiency as a function of the pump-probe detuning as the pump power is increased. The colored solid lines stand for the theory. The peak conversion efficiency $\eta$ is plotted versus the pump power in the inset and compared with the model (solid lines), which also provides the parametric gain $G$. Filled circles correspond to the plots according to the color code.

Fig. 5. Cascaded four-wave mixing experiment with ns pulses. (a) Output spectra and (b) raw conversion efficiency (${\eta }_L$) as a function of the peak power. The dashed line corresponds to $\eta \propto P^2$. Detail of (c) the output and (d) the input at maximum peak power: experimental (red) and calculated (black) spectra.