High-resolution Interferometric Diagnostics for Ultrashort Pulses

6. HIGH-HARMONIC GENERATION00−I p−I pp 220 13 2ω = p 22 + I p00−I p−I pFigure 6.1: The three-step model of high-harmonic generation.When discussing the single-atom response I use atomic units, in which the mass and chargeof an electron, the reduced Planck constant ħh and Coulomb’s constant are all set to unity.6.2.1 Classical trajectory analysisMany important features of the single-atom response may be predicted by treating the electron asa classical charged particle and following its motion in the time-varying electric field. One treatesthe ionized electron as if it were “born” with zero velocity at the nucleus, taken as the origin. Afterionization, the effect of the Coloumb potential on the electron’s motion is ignored. For electricfield strengths below 10 18 Wcm −2 , the electron velocity remains nonrelativistic and hence the opticalmagnetic field may also be ignored. The electron thus experiences a force − (t ). Integrationof the equations of motion for an electron born with zero velocity at time t b gives velocityv(t ,t b )=A(t ) − A(t b ) and position tx(t ,t b )=t bA(t ) dt − A(t b )(t − t b ) (6.1)where A(t )=− (t ) dt is the field vector potential. The recombination times are found by solvingx(t ,t b )=0 for t > t b . Depending on the birth time and the electric field profile, particularly its130