Blue Self-Frequency Shift of Slow Solitons and Radiation Locking in a Line-Defect Waveguide

We investigate experimentally resonant radiation processes driven by slow solitons in a dispersion-engineered photonic crystal waveguide in a regime virtually free of dissipative nonlinear processes (two-photon absorption and Raman scattering). Strong (30% energy conversion) Cherenkov-like radiation accompanied by the blue self-frequency shift of the soliton is observed close to the zero dispersion point, and is explained in terms of the soliton-radiation locking of the velocity.

Figure 1

PhC-WG dispersion: (a) GVD vs wavelength; (b) group index $n_g(\lambda )$. Inset (c): transmission spectrum. ${\lambda }_0$ indicates the first zero of the GVD.

Figure 2

(a) Output spectra (log scale) for different input peak powers, when the input pulse is detuned by $\delta \lambda =-4.8\mathrm{nm}$ (a SSFS of $-1\mathrm{nm}$ is indicated). (b) Output spectra observed for different input detunings $\delta \lambda$ (the spectra are recorded after tuning the laser and hence correspond to slightly different powers, as indicated). The arrows locate the input wavelengths.

Figure 3

Output spectrum (linear scale) for an input detuning $\delta \lambda =-1.8\mathrm{nm}$, showing strong soliton recoil with increasing power.

Figure 4

(a) Color map of spectrum evolution from Eq. (1) with $P_c=2.8\mathrm{W}$, $\delta \lambda =-3.4$, over 3 mm (twice the PhC-WG length). Here detuning is referred to the input wavelength. The gray curve gives the peak power vs $z$. (b) Simulated spectrogram (time-wavelength map) at PhC-WG output ($z=1.5\mathrm{mm}$). A Blackman sliding window is used to avoid spurious oscillations in the spectrum. (c) Comparison between experimental and simulated (at $z=1.5\mathrm{mm}$) spectra. The blue curve is the numerical input.

Figure 5

Radiation-soliton detuning vs soliton wavelength. The linear resonance curve ($k_{\mathrm{nl}}=0$, thick red curve and dots calculated using the interpolated dispersion, and the measured values, respectively) is compared with the limit arising from $\mathrm{GVD}+\mathrm{TOD}$ (dot-dashed line), and with the nonlinear resonance curve ($k_{\mathrm{nl}}\ne 0$) corresponding to $P_c=6\mathrm{W}$. For completeness linear mismatch curves corresponding to $2\pi$ over $L$ are also reported (dashed). The squares (cyan) are the detunings measured at the waveguide output vs output soliton wavelength. The blue dashed line indicates group velocity matching.