Effects Of Stark Shifts On Two-Photon Sidemode Instabilities

In a recent paper,1 we considered the stability of single-mode operation in two-photon lasers and two-photon optical bistability.2 The models assumed that two photons of equal or nearly equal frequencies span the atomic two-photon transition, with no resonant intermediate levels. The paper neglects possible Stark shifts of the two levels due to virtual transitions to nonresonant levels and back. For one-photon processes, these virtual transitions can be neglected because they have one nonresonant denominator. They cannot in general be neglected for the two-photon case, however, since all transition probabilities have at least one nonresonant denominator. In this paper we give formulas and illustrations for the two-photon two-level absorption and coupling coefficients including Stark shifts. For vanishing shifts, the coefficients have symmetric spectra that look very similar to their one-photon counterparts, but for nonzero shifts, they have asymmetric spectra with exaggerated resonances. These resonances appear to increase the likelihood of instabilities for certain combinations of pump detuning and Stark shifts.