High-resolution Interferometric Diagnostics for Ultrashort Pulses

2. BACKGROUND2.3.4.1 Second-order correlationsSecond-order autocorrelations are obtained by mixing the unknown pulse and the time-delayedreplica in a material with a second order response. The detected signal may be light producedthrough second-harmonic generation, two-photon absorption on a photodetector, or two-photonfluorescence, and in the most general case is of the formB AC2 (τ)== ∞−∞ ∞−∞|E (t )+E (t − τ)| 4 (2.29) E 2 (t )+2E (t )E (t − τ)+E 2 (t − τ) 2 (2.30)From (2.30), the second-order autocorrelation is seen to be the coherent sum of individual secondharmonics of the pulse and its delayed replica (first and third summands) and a pulse resultingfrom sum-frequency mixing (second summand).Noncollinear arrangement. Figure 2.6 shows two possible noncollinear arrangements for acquiringthe second-order autocorrelation. In Fig. 2.6(a), the signal is produced by second-harmonicgeneration. The individual second-harmonic beams propagate in different directions and do notarrive at the detector, and hence only the mixing term in (2.30) appears in the signal. The remainingsignal is the intensity autocorrelation [20, 98–101]: ∞B AC2 (τ)= I (t )I (t − τ) dt . (2.31)−∞In Fig. 2.6(b), the signal is produced by a two-photon absorbing detector. Although all terms in(2.30) appear in the signal, the two beams have a spatially varying time delay. Averaged across thearea of the detector, interference between the terms is washed out. The detected signal is thenequal to (2.31) except for the presence of constant background terms.The intensity autocorrelation is the autoconvolution of the temporal intensity. As such it doescontain some information on the spectral phase via that quantity’s influence on the pulse duration.However, there are many significant ambiguities [102, 103]. One common approach to esti-32