  A generalization of non-perturbative QED model for high harmonic generation
is developed for the multi-mode optical field case. By introducing
classical-field-dressed quantized Volkov states analytically, a formula to
calculate HHG for hydrogen-like atom in ultrashort intense laser pulse is
obtained, which has a simple intuitive interpretation. The dressed state QED
model indicates a new perspective to understand HHG, for example, the presence
of the weak even-order harmonic photons, which has been verified by both
theoretical analysis and numerical computation. Long wavelength approximation
and strong field approximation are involved in the development of the
formalism.
