Two-photon resonant excitation of vibrational levels of diatomic molecules by laser radiation

A theoretical investigation is made of the two-photon resonant excitation of vibrational levels of diatomic molecules by single-frequency laser radiation. Equations are derived for the calculation of the probability of an allowed two-photon resonant transition in the fundamental vibrational band of a molecule. It is shown that the probability of a two-photon transition in the $P$ and $R$ branches of molecules with a nonzero projection of the electron momentum ($\Lambda\neq0$) onto the axis joining nuclei is several orders of magnitude higher than the corresponding probability of a transition in $S$, $Q$, and $O$ branches of molecules with $\Lambda=0$ and $\Lambda\neq0$. Carbon dioxide laser frequencies coinciding to within $\sim0.04$ cm$^{-1}$ with the frequencies of allowed two-photon transitions in molecular CO and NO gases are identified. A numerical calculation is given of the two-photon absorption coefficients $\kappa^2$ of these gases: at a pressure of 100 mm Hg and for a pumping power density of $\sim10^9$ W/cm$^2$ these coefficients are $8\times10^{-9}$ and $10^{-6}$ cm$^{-1}$ for CO and NO, respectively. The probability of an allowed two-photon resonant transition is evaluated for the case when a quasiresonant intermediate level is present. This is illustrated by a numerical calculation of the two-photon absorption coefficient of the first vibrational harmonic of the HCl molecule. For an HCl pressure of $\sim1$ mm Hg, a pumping power density of $10^7$ W/cm$^2$, and a detuning of 10 cm$^{-1}$ between the frequencies of the laser and the quasiresonant intermediate transition, the two-photon absorption coefficient of HCl is $\sim10^{-4}$ cm$^{-1}$.