High-resolution Interferometric Diagnostics for Ultrashort Pulses

6. HIGH-HARMONIC GENERATIONderivative can be completely summarized by a normalized coefficient ρ (j ) , defined by∂ S (j )ω∂ I= − ρ (j ) ω−IpU p. (6.22)4ω 3 LI have used this definition for consistency with a recent review [377]. The intensity coefficientfor a monochromatic field is plotted against excursion time and return kinetic energy in Fig. 6.7.One can see that ρ rises monotonically with the excursion time, and is therefore greater for thelong trajectories. For an 800 nm field at cutoff, the intensity-derivative takes the value of 12.8 ×10 −14 W −1 cm 2 in SI units 1 . The intensity-dependent dipole phase plays an important role in themacroscopic effects which shape the single-atom response into what is actually observed. Theseare the subject of the next section.6.3 Theory of the macroscopic responseThe field produced HHG is the coherent superposition of the single-atom response from everyparticle in the target, and is strongly influenced by the nature of this superposition. In understandingthis one must consider the variation of the laser field throughout the interaction region,how this in turn leads to a variation in the amplitude and phase of the single-atom response, andhow these varying single-atom responses combine to give the observed field.In this discussion it is useful to distinguish between purely transverse macroscopic effects,arising from variations in the single-atom response in a single transverse plane, and longitudinalmacroscopic effects, arising from the superposition of the response from different transverseplanes. One can think of the transverse macroscopic response as that which would be observedif the gas target were very thin. An important transverse macroscopic effect arises from the combinationof the radial decay of the laser intensity with the differing intensity-dependent phasesof the long and short trajectories [378]. This is illustrated in Fig. 6.8. Both trajectories have a divergentwavefront (Fig. 6.8(a)), but for the long trajectory the effect is greater. At the focus, this1In SI units, (6.22) is∂ S (j )ω∂ I2E 2 t (6.23)3au auwhere Z 0 is the vacuum impedance and E au and t au are the atomic units of electric field strength and time respectively.= − ρ(j )ω 3 LZ 0144