Modeling harmonic generation by a zero-range potential

Abstract

High-order harmonic emission by one electron in a laser field bound to a zero-range potential is extensively discussed. The model yields an expression for the emission rates in the form of a one-dimensional integral that has to be calculated numerically. The solution is based on the quasienergy wave function of the ground state. The approach is very significantly facilitated by suppressing the harmonic components of the wave function at the position of the zero-range potential. This approximation is found to be very accurate except for the third harmonic. In spite of the simplicity of the model, the harmonic spectrum exhibits a very involved structure, occasional harmonics being strongly suppressed, with cusps and spikes for certain evenly spaced intensities. The latter are due to channel closings for the same intensities in above-threshold ionization. The harmonics near and beyond the cutoff of the plateau are amenable to a completely analytical approximation. This approximation shows how the classical model of Krause, Schafer, and Kulander [Phys. Rev. Lett. 68, 3535 (1992)] is embedded in a fully-quantum-mechanical description. Results are also given for the harmonic production rates in an elliptically polarized laser field; they display fair agreement with recent measurements. The model should adequately describe harmonic emission by negative ions with just one bound s state. Moreover, it also gives a fair description of harmonic emission by an atom, particularly if the ground-state energy of the zero-range potential is adjusted not to the binding energy of the atom, but rather to the energy difference between the ground state and the first excited state. The reason why this is appropriate is found in lowest-order perturbation theory, which sheds some light on the physical origin of the plateau.