This paper presents an analytical study of high-order harmonic generation (
HHG) by quantum systems possessing permanent dipole moments (PDMs), such as
atoms/molecules placed in a static electric field or polar molecules. HHG
by conventional, non-PDM systems typically demonstrated a plateau in the en
velope of harmonics followed by a steep fall in harmonic intensities when t
he harmonic number exceeds a certain threshold. This paper shows that the H
HG by PDM systems results in a significant extension of the plateau to high
er frequencies and a slower decline of intensities at frequencies higher th
aw the end of the plateau. Moreover. there occurs a substantial growth of t
he total, summed intensity of all components of the scattering spectrum. Ot
her physically interesting distinctive features of the HHG by PDM systems a
re: the presence of both odd and even harmonics of the laser frequency in t
he scattering spectrum; a tripler structure of both odd and even harmonics;
and the appearance of a component at the doubled Rabi frequency (i.e. at a
frequency much lower than the laser frequency). The results are obtained b
y using the adiabatic basis for the analysis of a multi-quantum resonance i
n a two-level system possessing PDMs.