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.
