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Journal de physique

Doppler-free two-photon dispersion

G. Grynberg, Martin Devaud, Christos Flytzanis, Bernard Cagnac

Published Jan 1, 1980• 19 citations
Publisher

Abstract

We present in this paper a calculation of the non-linear susceptibility near a Doppler-free two-photon transition. In the case of a two-level system, we find a non-perturbative solution. We deduce new effects on the non-linear refractive index which are related to the change of the linear susceptibility because of the transfer of atoms between the ground and excited levels. In the case of a more complex system, we study at the lowest order of perturbation the anisotropy induced by one beam on the other. At last, we show that it is easy to observe a bistable behaviour when atoms, inside a Pérot-Fabry cavity, interact with a beam whose wavelength is close to a two-photon resonance.

DOI
10.1051/jphys:01980004109093100

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We present in this paper a calculation of the non-linear susceptibility near a Doppler-free two-photon transition. In the case of a two-level system, we find a non-perturbative solution. We deduce new effects on the non-linear refractive index which are related to the change of the linear susceptibility because of the transfer of atoms between the ground and excited levels. In the case of a more complex system, we study at the lowest order of perturbation the anisotropy induced by one beam on the other. At last, we show that it is easy to observe a bistable behaviour when atoms, inside a Pérot-Fabry cavity, interact with a beam whose wavelength is close to a two-photon resonance.
Transmission characteristics of a nonlinear Fabry-Perot interferometer with two independent optical beams are considered under steady-state conditions. The sum frequency of two beams is taken to be near a two-photon resonance of the nonlinear medium. Two beams are coupled through the intensity-dependent susceptibility and influence propagation of each other in a mutual way. A set of two coupled-state equations is derived and it incorporates saturated absorption and dispersion as well as the effect of optical Stark shift. The system is found to have as many as seven stationary states, and at most, three are stable among them. The degenerate case of a single beam in two-photon resonance with the medium is also considered with particular emphasis on the effect of the optical Stark shift on optical bistability.
The authors consider the effect of the quadratic Doppler term on the inhomogeneous complex optical susceptibility of a two-level system for a weak beam in the presence of a saturating, counter-propagating wave, with both waves at the same frequency. There is a red shift of the resonance frequency in the absorption as well as in the dispersion. That red shift is a function of the temperature of the medium and the degree of saturation. An asymmetry of the absorption and dispersion curves is also observed which becomes stronger when the authors approach relativistic velocities of the particles. They also study for comparison purposes the effect of the quadratic Doppler term in the particular case of only one strong beam, without the weak one. They show the different behaviour of the red shift between the two cases.
A novel mechanism is proposed for optical bistability by utilizing the effect of interference which occurs when two levels are coupled by a one-photon resonance and by a two-photon resonance. The resulting bistability does not require atomic saturation, so the bistability can be observed at relatively low incident intensities, and the mechanism is essentially Doppler free, since it occurs by a two-photon process involving absorption of counterpropagating beams of the same frequency. A significant feature is that two-photon bistability can be controlled not only by the magnitude of the field of the one-photon resonance but also by its phase, and an oscillation or amplification of the field of the two-photon resonance can be observed under certain conditions by the mechanism of the parametric interaction of the field of the one-photon resonance and the field of the two-photon resonance through a nonlinear medium.
The authors consider the Doppler-broadened index of refraction of a two-level molecule of a gas for a weak travelling electromagnetic plane wave in the presence of a strong plane wave travelling in the opposite direction at the same frequency. The authors use the FVH vector model for a two-level system to calculate the real part of the non-linear susceptibility of the gas. The optical dispersion curve exhibits a wiggle at the centre line, that broadens and deepens as the gas is increasingly saturated by the strong incident wave.