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International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems

Effects Of Stark Shifts On Two-Photon Sidemode Instabilities

Snlomo Ovadia, Murray Sargent

Published Jan 1, 1985• 0 citations

Abstract

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.

DOI: 10.1364/idlnos.1985.wd4

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Steady-state interactions of one, two, and three waves with two-photon two-level media are treated semiclassically. Dynamic Stark shifts as well as dynamic Stark splittings are included in the theory. The intermediate levels are assumed to be nonresonant, and one wave is allowed to have arbitrarily large intensity. The theory parallels the one-photon theory of multiwave mixing couched in terms of population pulsations. We find the one-, two-, and three-wave two-photon absorption coefficients and the three-wave coupling coefficients. We find similarities and significant differences between the one- and two-photon polarizations of the medium. The work treats two-photon saturation spectroscopy, laser- and optical-bistability instabilities, and phase conjugation with a unified formalism.

The physics of the two-photon absorption process is investigated for a three-state system. The density-matrix equations for the two-photon interaction are solved in the steady-state limit assuming that the pump laser radiation is monochromatic. Collisional broadening, saturation, and Stark shifting of the two-photon resonance are investigated in detail by numerical solution of the steady-state density-matrix equations. Analytical expressions for the saturation intensity and the Stark shift are derived for the case where the single-photon transitions between the intermediate state and the initial and final states are far from resonance with the pump laser. For this case, it is found that the direction of the Stark shift is dependent on the relative magnitudes of the dipole-moment matrix elements for the single-photon transitions that couple the intermediate state with the initial and final states. Saturation and Stark shifting are also investigated for the case where the single-photon transitions between the intermediate state and the initial and final states are close to resonance with the pump laser.

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