High-resolution Interferometric Diagnostics for Ultrashort Pulses

8. QUANTUM-PATH INTERFEROMETRY IN HIGH-HARMONIC GENERATION200(a) 30(b) 50αI αI0−200−4002000−200−400L1-1(c) 60L1-1S1-1S1-1L10S11S10S10L10S11L11L11L1-1(d) 70C1-1S1-1S11S10L10S10L10C11L11−400 0 400α Q−400 0 400α QFigure 8.14: Intensity of dipole response in control-field sensitivity space | ˜ (j ) (ω;ᾱ)| 2 showingorbit selection filters (white polygons) and perturbative control-field sensivities ¯S (j )ω,C(black dots)labelled in αβm notation. The colour scale is logarithmic with dynamic range 10 4 .is 1 inside the curve and 0 outside. A smooth decay is not needed since the curve traces a lineof zero energy. For simplicity, I used polygons, drawn with the mouse using a simple interactivecomputer program. For overlapping orbits, the polygon is drawn approximately through the saddlewhich separates them. The filters themselves never overlap — if the polygons overlap thenthe computer program arbitrarily sets one of the filters to zero in the overlap area. In this wayI maintain condition (8.28). Because the orbits evolve gradually with frequency and it is laboriousto draw a filter polygon for each frequency, I only drew polygons at every 10 th harmonic, andused a simple linear interpolation routine for in-between frequencies. Figure 8.14 shows the filterpolygons at four different frequencies, overlaid upon the dipole response.The filtered orbit amplitudes, obtained using (8.26) and (8.27), are shown in Fig. 8.15. Approachingcutoff, there is a discontinuity as one switches from describing the dipole response asthe sum of long and short trajectories to a single dominant trajectory. However below cutoff, the210