High-resolution Interferometric Diagnostics for Ultrashort Pulses

4.1 Sequential acquisition of shears{Γ k (ω)} are shown in Fig. 4.4(b). The resulting retrieved phase, for the double-shear reconstruction,is shown in Fig. 4.4(c). Similarly to the numerical demonstration in section 3.9, I evaluatedthe RMS phase variation, shown in Fig. 4.4(d). For a fair comparison of the precision of singleanddouble-shear reconstructions, I averaged together pairs of single-shear reconstructions, thusincreasing their SNR by a factor of 2 to create an ensemble of 25 before computing the statistics.The double-shear reconstruction is much more precise, particularly in the spectral wings. Thismanifests as a palpable improvement in the time domain, shown in Fig. 4.5. A global indication ofthe precision is given by the RMS field variation, eq. (A.13), which was 0.12 and 0.02 in the singleanddouble-shear cases respectively.|E (ω)|Γ(ω)φ (rad)RMS err.15105010−1210−110.50(a)(b)(c)(d)780 790 800 810 820λ (nm)|E (t )|0.20.10−2 −1.5−2 −1 0t (ps)Figure 4.4: (Color online) (a) Spectral intensity ofthe unknown pulse. (b) Phase differences fromsmall (blue) and large (red) shears, averaged overthe ensemble. (c) Retrieved phase, averaged overthe ensemble. (d) RMS variation of the retrievedphase over the ensemble for the single- (blue, thickline) and double- (red, thin line) shear reconstructions.Figure 4.5: (Color online) Temporal amplitudeof the single-shear (blue, lightshade) and double-shear reconstructions(red, dark shade), averaged over thewhole ensemble. The region representsthe mean plus/minus one standard deviation.The inset is a zoomed-in view ofthe shorter subpulse.I also checked the accuracy of the reconstruction by numerically isolating the two subpulseswith a temporal filter and verified that their relative energies were in agreement with our mea-97