High-resolution Interferometric Diagnostics for Ultrashort Pulses

3.9 Numerical comparison of single- and multi-shear retrieval1E (t )0.50−1000 −500 0 500 1000t (fs)Figure 3.9: (Color online) Temporal amplitude of the notched pulse (black), and the single-shear(blue, light shade) and double-shear reconstructions (red, dark shade). The shaded areas representthe mean plus/minus one standard deviation over the whole ensemble.reconstruction is very poor, with an RMS field variation of 0.33. This is reduced to 0.02 in thedouble-shear reconstruction. The typical RMS error between the reconstructed and unknownpulses is 0.26 and 0.006 for the two cases respectively. The precision of the phase of the singleshearreconstruction, shown in Fig. 3.8(b), is also very poor — it varies across the pulse but isgreater than 0.5 for a significant fraction of the spectral energy. The double-shear reconstructionachieves a significant improvement, with a typical RMS phase variation of 0.03 rad in regions ofsignificant spectral intensity. Because the relative phase of the two spectral lobes strongly affectsthe temporal profile, the double-shear measurement produces a dramatic improvement in thetime domain as shown in Fig. 3.9. The amplitude fluctuations in the single-shear case are nearly100%, whereas the double-shear gives a very precise reconstruction.The preceding example demonstrated that multi-shear is successful bridging a large spectralgap where the signal falls well below the noise level. I now consider a situation where multi-shearis not strictly necessary but, as predicted in the previous section, will improve the precision. Theunknown pulse was originally a Gaussian with transform-limited duration (intensity FWHM) 30 fs.Quadratic dispersion of 1000fs 2 was applied, along with sinusoidal ripples in the spectral phase ofperiod 12.6 mrad/fs and amplitude 0.5 rad. In the time domain, this produces a series of satellitepulses separated by 500 fs, the inverse of the period of the ripples. The pulse therefore has only a89