High-resolution Interferometric Diagnostics for Ultrashort Pulses

8.4 Example (t ) (a.u.)0.20−0.2(a)8060(b)1-1103011Order40201-22-12031211232220−1 −0.5 0 0.5 1 1.5t (opt. cycles)Figure 8.2: (a) Pulsed drive field, zoomed in on central region. (b) Harmonic order versus recombinationtime of the quantum orbits of a 5.0 fs, 800 nm, 5 × 10 14 Wcm −2 drive field in Argon. Theorbits are labelled by excursion length and recombination event βm, and short (long) orbits aresolid (dashed).5 × 10 14 Wcm −2 , in Argon. Mathematically, the drive field is 2cos D (t )=E 0 cos 2 −1 (2 1/4 )t cos(ω D t ) (8.14)T FWHMwhere I use a cosine-squared pulse for analytical tractability. The quantum path analysis is shownin Fig. 8.2.For these orbits, I evaluated the action-sensitivities to the in-phase and quadrature controlfields using (8.5). A sample of the results are shown in Fig. 8.3. For subfigures (a) and (b), thecontrol-to-drive phase advance per half-cycle ∆φ CD is small enough so that over the five halfcyclesthe net rotation is less than 2π. The first-order trajectories therefore do not overlap. Also,for these values of ω C /ω D the higher-order trajectories have larger action-sensitivity and do notoverlap the first-order trajectories. In particular, for ω C /ω D = 0.6 one has ∆φ CD = 2π/5, so the 5trajectories are equally spread around the circle. However, for ω C /ω D = 0.5 (not shown) ∆φ CD =−π/2 so that orbits separated by 4 half-cycles coincide azimuthally. For Fig. 8.3(c), the control-195