The effect of dressing on high-order harmonic generation in vibrating H$_2$ molecules

We develop the strong-field approximation for high-order harmonic generation in hydrogen molecules, including the vibrational motion and the laser-induced coupling of the lowest two Born-Oppenheimer states in the molecular ion that is created by the initial ionization of the molecule. We show that the field dressing becomes important at long laser wavelengths ($\approx 2 \mu$m), leading to an overall reduction of harmonic generation and modifying the ratio of harmonic signals from different isotopes.