High-resolution Interferometric Diagnostics for Ultrashort Pulses

6.2 Theory of the single-atom responseKE (Up) (t ) (E0)10−142(a)(b)0−3 −2 −1 0 1 2 3t (opt. cycles)Figure 6.3: Classical trajectory analysis for 2.62 optical cycle pulse (equivalent to 7.0 fs pulse at800 nm). (a) Electric field; (b) Recollision kinetic energies for first (blue), second (green) and third(red) returns.and for an accurate picture one must treat each half-cycle individually.Figure 6.3 shows a classical trajectory analysis for a 7.0 fs pulse at 800 nm, with a carrierenvelopephase offset of zero. The greatest recollision energy is attained by electrons born onehalf-cycle before the peak of the envelope. For photon energies below the maximum, several trajectoriescontribute.The classical description is physically intuitive and gives a quantitative prediction of the structureof the emitted radiation in the time-frequency domain (t ,ω). That is, it predicts significantenergy at time-frequency co-ordinates (t r (t b ),ω r (t b )) for all birth times that result in a recollision.However it does not attach an amplitude or a phase to the emitted radiation — this requires theincorporation of wave-like properties of the electron [366]. The quantum-mechanical evolutionof the electron is most accurately described by the time-dependent Schrödinger equation, which Ishall introduce in the next section. However it should be noted that many features of the classicalmodel are recovered by applying a realistic set of assumptions to the time-dependent Schrödingerequation (TDSE). These assumptions constitute the strong field approximation (SFA) and the133