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Journal de physique

Optical nutation in a gaussian beam resonator

François Rohart, B. Macke

Published Jan 1, 1980• 10 citations
Publisher

Abstract

We examine the transient behaviour of a plane-spherical resonator driven by a continuous wave and filled by an optically thin gas which is suddenly switched on exact resonance with the driving field. Contrary to previous treatments, the axial and transversal field distributions and the molecular motions through the standing wave are taken into account. This is achieved by projecting the induced gas polarization on the fundamental gaussian mode of the resonator and the results are given in a quasi analytic form. An oscillatory response is only obtained when the Rabi frequency is large with respect to the Doppler line width and for a bad quality resonator. Some of the theoretical predictions have been supported by an experiment at a 6 mm-wavelength.

DOI
10.1051/jphys:01980004108083700

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We examine the transient behaviour of a plane-spherical resonator driven by a continuous wave and filled by an optically thin gas which is suddenly switched on exact resonance with the driving field. Contrary to previous treatments, the axial and transversal field distributions and the molecular motions through the standing wave are taken into account. This is achieved by projecting the induced gas polarization on the fundamental gaussian mode of the resonator and the results are given in a quasi analytic form. An oscillatory response is only obtained when the Rabi frequency is large with respect to the Doppler line width and for a bad quality resonator. Some of the theoretical predictions have been supported by an experiment at a 6 mm-wavelength.
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We analyze the transient response induced by a resonant, weak probe laser in a three-level V-type system driven by a strong, resonant coupling laser. The Rabi oscillation of the probe transition contains two frequencies determined by the coupling laser, and the ratio of the two-frequency components can be controlled by a time delay between the probe and the coupling laser. In particular, when both lasers are turned on simultaneously, the optical nutation with the frequency approximately equal to the Rabi frequency of the coupling laser is dominant; when the probe laser is turned on well after the steady state is reached for the coupling transition, the Rabi oscillation of the probe transition still occurs, and the oscillatory frequency is approximately equal to half of the Rabi frequency of the coupling laser. When both the probe and the coupling lasers are strong, the mutual interaction of the two fields and the atomic system may revive the optical nutation with each other.
An exact expression of the gain constant of two-level molecules (or atoms) in a standing-wave optical field is obtained for a special case where the optical frequency is in exact resonance with the molecular transition and the longitudinal and transverse relaxations have equal decay constants. Secondly, an exact form of gain constant as a function of frequency detuning which decribes the shape of Lamb dip or saturated absorption is shown for another case where the transverse relaxation is much faster than the longitudinal relaxation. A flat velocity distribution of molecules at Doppler limit is assumed in either case.
The optically non-linear response of arbitrary planar semiconductor resonators (microresonators) is studied theoretically. We use a versatile approach that takes into account the finite beam width as well as pulse length of the incident light, and incorporates the non-linearity consistently. The intensity-dependent non-linearity of semiconductors is described by appropriate phenomenological models. We show that the propagation characteristic of the leaky waves excited controls the response behaviour of the resonators. Conditions for switching and optical bistability are identified. The effect of various parameters on the response is studied numerically.
A cold gas of polarizable particles moving in the optical potential of a standing wave high finesse optical resonator acts as a dynamic refractive index. For a sufficiently strong cavity pump the optical forces generated by the intra cavity field perturb the particles phase space distribution, which shifts the optical resonance frequency and induces a nonlinear optical response. By help of the corresponding Vlasov equation we predict that beyond the known phenomenon of optical bi-stability one finds regions in parameter space, where no stable stationary solution exists. The atom field dynamics then exhibits oscillatory solutions converging to stable limit cycles of the system. The linearized analytical predictions agree well with corresponding numerical solutions of the full time dependent equations and first experimental observation in both cases.
In this article, we review three areas of study in which the resonant interaction between atoms and laser radiation plays a central role. Firstly, coherent optical transients are discussed in which the direct observation of this interaction can be studied via the detection of the Rabi frequency in optical nutations. Secondly, the response of atoms to resonant radiation in an optical cavity leading to optical bistability and other effects is described. Finally, the new field of atom manipulation by resonant laser fields is introduced, in particular, the deflection of atomic beams. The underlying theoretical framework for the experiments performed is discussed, ranging from full quantum electrodynamic to semiclassical models.