Figure 3. Optical locking of independent lasers.

Optical cross-correlators measure the relative timing between two pulses. The principle of the device is illustrated in a. In the first stage, two input pulses with arbitrary timing are mixed in a nonlinear crystal resulting in an SFG signal with intensity that depends on their overlap. To determine which pulse arrived first, one of them is delayed by a fixed amount Δ, before they are overlapped again in the second SFG stage. The difference between the SFG intensities allows the exact input timing to be determined without sign ambiguity. A characteristic cross-correlator curve is traced, as illustrated, if the input timing is scanned continuously. A measured scan of the relative timing between the Ti:sapphire pump–probe laser and optical reference laser at FLASH results in the cross-correlator response plotted in b. Outside of the regions where the detector is limited (±1 V), the measured curve matches the curve calculated based on the input laser pulse durations. Once calibrated, the relative timing between the two pulses can be determined with sub-femtosecond accuracy within the ~400 fs dynamic range of the cross-correlator. Using this for feedback, the cavity length of the pump–probe oscillator is varied to lock the relative timing. The residual jitter between the external laser and reference is shown in c, as measured with an independent optical cross-correlator and is found to be (5±1) fs r.m.s., with accuracy given by the numerical fit to the corresponding distribution shown in d.