High Harmonic Generation Beyond the Electric Dipole Approximation

A generalization of the analytical theory of high harmonic generation in the long wavelength limit and in the single active electron approximation is developed taking into account the magnetic dipole and electric quadrupole interaction. Quantum mechanical and classical theories are found to be in excellent agreement, which allows one to explain the influence of multipole effects in terms of an intuitive picture. For Ti:S lasers ( $0.8\mu \mathrm{m}$) multipole contributions are found to be small below an intensity of about ${10}^{17}\mathrm{W}/{\mathrm{cm}}^2$, at which harmonic radiation with photon energies of several keV is generated. This promises the extension of high harmonic generation well into the sub-nm wavelength regime.