Two-photon correlation of broadband-amplified spontaneous four-wave mixing

We measure the time-energy correlation of broadband, spontaneously seeded four-wave mixing (FWM), and demonstrate time-frequency coupling effects; specifically, we observe a power-dependent splitting of the correlation in both energy and time. By pumping a photonic crystal fiber with narrowband picosecond pulses we generate FWM in a unique regime, where broadband ($>100$ nm) sidebands are generated that are incoherent, yet time-energy correlated. Although the observed time-energy correlation in FWM is conceptually similar to parametric down-conversion, its unique dependence on pump intensity due to self- and cross-phase-modulation effects yields spectral and temporal structure in the correlations. While these effects are minute compared to the time duration and bandwidth of the FWM sidebands, they are well observed using sum-frequency generation as a precise, ultrafast, wide-bandwidth correlation detector.

Figure 1

Measured four-wave-mixing spectra, for three different pump peak power levels $0.65$, $0.87$, and $1.1$ kW (pulse duration 6 ps).

Figure 2

(a) Experimental setup. FWM correlated signal-idler beams are generated by 6 ps pulses at 789 nm in a 12-cm-long PCF with zero dispersion at 784 nm, and the correlation is measured by SFG in a $200-\mu$m-thick BBO crystal, noncollinearly phase matched over the entire spectrum. A prism pair spatially separates the signal, idler, and pump, allowing pump blocking, and serves to control dispersion. The signal beam is directed through a computer-controlled delay line with a 30 nm step ($0.1$ fs), and the idler beam passes through a magnifying and inverting telescope required to ensure phase matching over the entire signal-idler bandwidth for the noncollinear SFG. The top right inset is a magnification of the noncollinear SFG configuration. Negative dispersion (in order to compensate for dispersion of lenses, crystals, etc.) is inserted by the prisms and by a set of chirped mirrors in the idler path ($-70{\text{fs}}^2$ per bounce). SFG spectra are measured with a spectrometer coupled to a cooled, intensified CCD camera. (b) Calculated residual phase mismatch for SFG into $\Omega =2\omega$ at the BBO crystal.

Figure 3

Two-dimensional maps of SFG spectrum per relative signal-idler delay, and sections from each at zero delay. (a) Low pump pulse intensity ($0.62$ kW peak power). A strong peak at $\Omega =2{\omega }_p$, with a width of 25 fs, is the signature of two-photon coherence of the signal and idler pairs. (b) Similar map for a higher pump peak power of $0.84$ kW, showing broadening of the coherent peak. (c) Map at high pump peak power (1 kW) demonstrating splitting of the coherent peak in both frequency and time. For this intensity the bottom graph shows cross sections at optimum delay for the left peak (blue, dashed line) and right peak (red, dash-dotted line), and zero delay (green, full line). The small feature at $-50$ fs delay observed at all intensities may be due to residual high-order dispersion.

Figure 4

(a) SFG broadening and splitting as a function of the pump broadening. The dashed line marks the identity between the width of the SPM-broadened pump and the SFG. Clearly identity is followed at high pump splittings (high power) and violated at low pump broadening (low power). For pump wavelengths closer to the zero dispersion of the PCF, the “transition” from a single-peaked to a split SFG spectrum occurs at increasingly higher pump intensities. The graphs at the bottom show the spectra of the pump after the PCF with the corresponding SFG spectra, measured at the points labeled (a), (b), and (c) in the top panel.