High-resolution Interferometric Diagnostics for Ultrashort Pulses

6.2 Theory of the single-atom response (t ) (a.u.)0.20−0.2(a)Order806040200(b)L10S10L11S11L32S21L21S32S33L22L33S220 0.5 1 1.5 2t r (opt. cycles)ρ4 0 52KE (U p )005t r − t b (rad)Figure 6.6: (a) Drive laser field. (b) Harmonicorder versus recombination time ofthe quantum orbits of a CW drive fieldof 5 × 10 14 W/cm 2 in Argon. The orbitsare labelled by type (short/long), excursionlength and recombination event αβm.Short trajectories are solid, long trajectoriesare dashed. The classical solutions are alsoshown (grey).Figure 6.7: Intensity-derivative of the actionfor a monochromatic field, for the short(blue) and long (green) trajectories.the trip time, with β = 1 being the shortest. Finally, m = ...,−1,0,1,... labels the recombinationtimes, with m = 0 being the first recombination after t = 0. Another useful label is the birth eventγ = m − β.Figure 6.6 shows the emission frequency versus the real part of the return time for a CW field,and also illustrates the trajectory labelling system. Additionally, the classical trajectories are shown,and agree closely with the stationary-point solutions.In the stationary-phase approximation, the contribution from an individual stationary point isproportional to the value of the integrand at that point, but modified by a prefactor which dependsinversely on the local second derivative of the integration variables. Details of the derivation are141