High-resolution Interferometric Diagnostics for Ultrashort Pulses

2. BACKGROUNDover τ, the frequency-dependent group-delay can be directly extracted [141, 142]. Whilst this isoften a useful quantity, for example in measurements of fibre dispersion, it must be integrated toobtain the complete spectral phase, an approach which struggles when the spectrum of the pulsecontains nulls or if the phase contains discontinuities. General phase retrieval from the sonogramrequires an iterative algorithm [140, 143]. In contrast with many spectrographic distributions, thesonogram does not possess the time-reversal ambiguity and the sign of any group-delay dispersionis directly reflected in the data.Single-shot sonograms may also be acquired. Using the angularly-varying phase matchingresponse of upconversion in a nonlinear crystal, it is possible to achieve a frequency-to-spacemapping which serves as the spectral gate [144], whilst a noncollinear second order interactionprovides the time gate. Alternatively, the pulse may be dispersed using a prism or grating, andthen crosscorrelated in noncollinear single-shot fashion using two-photon absorption on a CCDcamera [145, 146].2.3.5.2 SpectrographyIn spectrograms, the gating order is reversed with respect to sonograms; the temporal gate is appliedbefore the frequency gate. The latter is usually a spectrometer with enough resolution toresolve all the spectral features of the signal; the spectrogram is therefore the spectral intensity ofthe gated unknown pulse. Early usage of spectrograms [147–149] was restricted to interpretationsof the chirp and did not attempt full retrieval of the amplitude and phase. The development of analgorithm for inverting the spectrogram to retrieve the unknown pulse [45] heralded the introductionof FROG. This approach has become popular, and many variations have been developed.Second-harmonic generation (SHG)-FROG. InSHG-FROG the unknown pulse undergoes sumfrequencygeneration with a delayed replica in a second-order nonlinear medium [150–152]. Themeasured trace is thenB(τ,ω)= ∞−∞2E (t )E ∗ (t − τ)e i ωt dt. (2.36)An apparatus for obtaining an SHG-FROG trace is shown in Fig. 2.9.Since it uses a second order nonlinearity, it is the most sensitive of the FROG family, and has38