High-resolution Interferometric Diagnostics for Ultrashort Pulses

2.3 Introduction to ultrashort pulse metrologyχ (2)τE (t − τ)χ (2) Ĩ (ω)E (t )E (t − τ)τFigure 2.8: Typical apparatus for measuringthe sonogram; the angularly dispersive elementis drawn as a prism but could equallybe a grating.E (t )Figure 2.9: Typical apparatus for measuringan SHG-FROG.be resolved by incorporating additional information, such as a measurement of the pulse spectrum,or performing some additional measurements. General proofs of the nonexistence of additionalexact ambiguities are rare. The action of noise and other experimental distortions, whichmay introduce approximate ambiguities, is also rather difficult to analyse. In general, the probabilityof encountering an ambiguity increases with pulse complexity, particularly when multiplesubpulses are present [131, 132]. Also, the presence of ambiguities appears to depend on numericalparameters, particularly the discretisation of data [133–136].2.3.5.1 SonographySonograms consist of a frequency gate followed by a time gate; the frequency gate is a tunablebandpass filter, whilst the time gating may be accomplished using a streak camera [137–139],electronic sampling of the intensity [138], or a nonlinear optical interaction [140–142] with a gatepulse. In the well-known methods considered here, all the temporal gates may be representedby (2.20), where the gate function G (t ) determines the temporal resolution of the measurement,which for streak cameras and electronic sampling is 10ps and 50ps respectively. The recordedsignal isB(τ,ω p )= ∞−∞ ∞ G (t − τ) E (ω)R(ω;ω p )e −i ωt dω−∞2dt (2.35)where R(ω;ω p ) is the response of a tunable bandpass filter with centre frequency ω p . One implementationof a sonogram is shown in Fig. 2.8.Sonograms are intuitive time-frequency representations. In particular, by taking moments37