High-resolution Interferometric Diagnostics for Ultrashort Pulses

6. HIGH-HARMONIC GENERATION10080log 10I0−1Harmonic6040−2−320−40−5 (t ) (au)0.20−0.2−2 −1 0 1 2t (opt. cycles)Figure 6.5: Spectrogram of high-harmonic generation using a 7 fs pulse at 800 nm with peakintensity 5 × 10 14 Wcm −2 in Argon. The photon energy from a classical calculation (solid whitelines) and a quantum trajectories calculation (dashed white lines) is shown.can be ignored. One introduces the ansatz |ψ〉 = e iI ptg (t )|g 〉 +d 3 vf (v,t )|v〉(6.5)which comprises a ground state |g 〉 with amplitude g (t ) and a continuum of plane waves |v〉 withamplitude f (v,t ). The oscillations of the ground state are factored out. The key idea behind theSFA is that the laser field transfers population from the ground state into the continuum states; theground state is otherwise unperturbed. The continuum states are driven only by the laser field; onthem the effect of the ionic potential is ignored.Substituting (6.5) into (6.3) and applying the bra 〈v| yieldsi ∂ f (v,t )∂ t v2= g (t ) (t ) · d(v)+2 + I p f (v,t )+i (t ) · ∇ v f (v,t ). (6.6)136