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-har monic generation in close analogy to the derivation of the Keldysh amp litude for ionization. As in the former, the approximation made consis ts of neglecting the effect of the binding potential in intermediate s tates. The approach can be used for arbitrary binding potentials, but is best suited to short-range potentials at high intensities. It is al most 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-harm onic generation and the dipole-moment expectation value is discussed, as well as the relation of both to the dipole-dipole correlation funct ion. An exact functional relationship between high-harmonic generation and the total ionization rate is presented. For the case of an ellipt ically polarized monochromatic driving field, the polarization propert ies of the emitted harmonics, viz. their ellipticity and the offset an gle of their polarization ellipse, are evaluated for both the zero-ran ge potential model and the effective-dipole model, and compared. The p redictions of both models generally agree, there are, however, some qu alitative differences for the harmonics around the end of the plateau.