High-resolution Interferometric Diagnostics for Ultrashort Pulses

6. HIGH-HARMONIC GENERATION30(S31)2(L31)22r (µm)201033331.544030(S51)24(L51)241L coh (mm)r (µm)201033330.54440−4 −2 0 2 4−4 −2 0 2 4z (mm)z (mm)40Figure 6.10: Phase-matching diagram for short trajectories (left column) and long trajectories(right column) and harmonics 31 (top row) and 51 (bottom row) for a 5 × 10 14 W/cm 2 800 nm fieldof waist 50 µm in 0.01 atm Argon. The purple arrows show the single-atom response wave-vector(the arrows are scaled by the same factors as the axes of the plots, so that the off-axis componentis greatly exaggerated.) The contour lines show the laser intensity in units of 10 14 W/cm 2 .tive index changes dynamically, providing an ultrafast temporal phase modulation. This causes ablue-shift, which is most pronounced at the most intense regions of the pulse where ionization occursrapidly [386–388]. For few-cycle pulses this temporal phase modulation actually assists withphase matching for high photon energies [384, 389]. Ionization also causes defocusing since thecenter of the beam is more intense, leading to greater ionization and a lower refractive index. Dispersionand absorption from neutral atoms play a significant role as the gaseous region becomeslonger than a few millimeters [390–392]. Self-phase modulation may also play a role, particularlywith molecular targets [393].To include all of this behaviour, a numerical code is needed. Any such code consists of twoparts. A propagation code for the drive field, which incorporates diffraction, dispersion and nonlineareffects such as ionization, outputs the temporal profile of the drive field at all points in theinteraction region. This is fed into a single-atom response code, which computes the single-atom148