A unified theory of high-harmonic generation: Application to polarization properties of the harmonics

A general framework is given of how to derive expressions for high-harmonic generation in close analogy to the derivation of the Keldysh amplitude for ionization. As in the former, the approximation made consists of neglecting the effect of the binding potential in intermediate states. The approach can be used for arbitrary binding potentials, but is best suited to short-range potentials at high intensities. It is almost exact for a zero-range potential for arbitrary intensity. Various models that have been used before by some of the authors, such as the effective dipole model and the zero-range potential model, emerge as special cases. The relation between the $S$-matrix element for high-harmonic generation and the dipole-moment expectation value is discussed, as well as the relation of both to the dipole-dipole correlation function. An exact functional relationship between high-harmonic generation and the total ionization rate is presented. For the case of an elliptically polarized monochromatic driving field, the polarization properties of the emitted harmonics, viz. their ellipticity and the offset angle of their polarization ellipse, are evaluated for both the zero-range potential model and the effective-dipole model, and compared. The predictions of both models generally agree, there are, however, some qualitative differences for the harmonics around the end of the plateau.