High-resolution Interferometric Diagnostics for Ultrashort Pulses

7.6 Physical interpretation0.525kT (rad/µm)00.500.5191320-2φ (rad)0−5 0 5Gas jet z (mm)−5 0 5z (mm)Figure 7.21: Simulated far-field profiles of the full macroscopic response for harmonics 13, 19 and25. The amplitude (left column) is normalized and on a linear scale. The phase (right column) hasbeen set to zero on axis and is wrapped to [−π,π], with colour scale shown.7.6.3 Trends in the gas jet z scanHaving deconstructed the physical processes leading to the macroscopically observed spatial profiles,I shall now discuss some trends observed in both the measurements and the simulations.Harmonic 25 is perhaps the simplest to understand because the intensity is always below thecutoff so there is no significant splitting into the long and short trajectories. There is no quantumpath interference and the phase of the single-atom response is always linear with the intensity.The spatial profiles are Gaussian-like, and may be characterized by their on-axis amplitude andphase curvatureσ −2k T= − 1E (0)∂ 2 E (k T )∂ kT2 kT =0, φ 2,kT = ∂ 2 φ(k T )∂ k 2 TkT =0. (7.14)Applied to a chirped Gaussian profile, σ kT is the width and φ 2,kT is the chirp. Corresponding definitionsσr−2 and φ 2,r may be written in the near field. The far-field curvatures extracted from simulationand experiment are plotted in Fig. 7.22. The far-field width is smaller for negative z , becauseof the cancellation of the intensity-dependent dipole phase by the converging laser wave-front inthe near field. For positive z , the near field acquires a strongly divergent wavefront, producing a181