High-resolution Interferometric Diagnostics for Ultrashort Pulses

7. LATERAL SHEARING INTERFEROMETRY FOR HIGH-HARMONIC GENERATIONand experiment evident from an examination of the entire data set. First, the higher harmonicstend to agree better. Second, the agreement tends to deteriorate towards negative z values i.e.as the gas jet moves upstream of the focus. Third, in cases where the simulated phase is flat inthe centre but changes sharply in the wings, the experiments capture the flat middle but not, ingeneral, the sharp changes.7.6 Physical interpretationBecause the simulation and experiment are largely in agreement, the former can be used to disectthe physics leading to the observed spatial profiles. Section 7.6.1 describes the spatial distributionof the single-atom response leading to the transverse macroscopic behaviour — that is, the profilesthat would be observed if the target were infinitely thin. Then, section 7.6.2 summarises howphase-matching and other longitudinal macroscopic effects modify the profiles.7.6.1 Single-atom response and transverse macroscopic effectsFigure 7.14 shows the laser intensity profile at the focus that is used in the simulations. Harmonics13–23 are below the classical cutoff at the peak intensity. The first step in calculating the spatialprofiles is computing the single-atom response at each point in the focus. Since the calculationignores all spatial variation in the laser field except for peak intensity I L (r,z ) and phase φ L (r,z ),the single-atom response may be completely described by its intensity dependence. This is shownin Fig. 7.15 for harmonics 13, 19 and 25.Figure 7.15 shows the amplitude and phase of the harmonics over the range of laser intensitiesin the focus. The usual linear dependence on intensity is observed for the long and short trajectoriesbelow cutoff and the dominant (long in this case) trajectory above cutoff. The sum, given bythe uniform approximation, exhibits constructive and destructive interference, with rapid phasejumps accompanying the latter when the field goes through a node. The spatial distribution ofthe single-atom response is shown in Fig. 7.16. In harmonics 13 and 19, quantum-path interferenceproduces an annular amplitude distribution. Phase discontinuities accompany the points ofdestructive interference. The phase has been set to zero on axis so that only radial variations are174