High-resolution Interferometric Diagnostics for Ultrashort Pulses

6.4 Temporal metrology of high-harmonic generationresponse at all points in the interaction region. The individual single-atom responses are summedtogether to calculate the final result.6.4 Temporal metrology of high-harmonic generationThe principles of femtosecond metrology in the optical and IR also apply to HHG, but there aresubstantially greater challenges due to the weakness of the radiation and the lack of suitable opticalcomponents such as mirrors, beamsplitters and nonlinear crystals.Since a well-characterized reference is usually unavailable, HHG temporal characterizationmethods must be self-referencing, and therefore require a time-nonstationary or nonlinear operation.Although the usual second and third order frequency mixing processes used for optical andIR characterization are not currently available for HHG, there are several alternatives. The mostwidely used is two-colour ionization using both the XUV pulse and the laser. In this method, thetwo fields are focused into an atomic gas where the XUV produces photoelectrons due to singlephotonabsorption. The amplitude and phase of the XUV field are mapped directly onto the wavefunctionof photoelectrons. The photoelectrons are then streaked — shifted in momentum by theelectric field of a laser pulse — and the photoelectron spectrum is monitored as a function of theXUV-laser delay using, for example, a time of flight (TOF) electron spectrometer. A typical setupfor photoelectron streaking is shown in Fig. 6.11.Using the framework of the SFA, one can show that the streaking acts as a temporal phasemodulation. The derivation mirrors that leading to the continuum amplitude (6.7), except thatoptical field ionization by the laser is replaced by photoionization by the XUV. Recombinationis ignored, and one is interested in the momentum distribution after the fields have passed i.e.t →∞. The result is ∞b(p,∞)=−i d(p + A(t b )) · E X (t b )exp i φ s (t b )+i (W + I p )t b dtb (6.24)−∞149