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Journal of the Optical Society of America B

Light-pressure-induced nonlinear dispersion in a Doppler-broadened medium: theory and experimental proposal

Rudolf Grimm, J. Mlynek

Published Aug 1, 1988• 10 citations
Publisher

Abstract

We study the effect of resonant light pressure on the optical response of a Doppler-broadened atomic medium to a single monochromatic laser field. As a main consequence of the spontaneous scattering force, a novel contribution to the optical dispersion of the atomic gas is predicted, which shows a pronounced nonlinear intensity dependence; moreover, for a given laser intensity, its strength is closely related to the laser-beam diameter. Most importantly, this light-pressure-induced dispersion displays an even symmetry with respect to the optical Doppler detuning; as a result, the total dispersion curve of the medium can be changed substantially. In addition to a detailed theoretical description of the phenomenon, we propose a simple experiment based on frequency-modulation spectroscopy for the measurement of the predicted nonlinear dispersion feature.

DOI
10.1364/josab.5.001655

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We study the effect of resonant light pressure on the optical response of a Doppler-broadened atomic medium to a single monochromatic laser field. As a main consequence of the spontaneous scattering force, a novel contribution to the optical dispersion of the atomic gas is predicted, which shows a pronounced nonlinear intensity dependence; moreover, for a given laser intensity, its strength is closely related to the laser-beam diameter. Most importantly, this light-pressure-induced dispersion displays an even symmetry with respect to the optical Doppler detuning; as a result, the total dispersion curve of the medium can be changed substantially. In addition to a detailed theoretical description of the phenomenon, we propose a simple experiment based on frequency-modulation spectroscopy for the measurement of the predicted nonlinear dispersion feature.
We report on detailed studies of the effect of resonant light pressure on the optical response of an atomic gas to a single monochromatic laser field. In this very elementary situation of laser spectroscopy, the redistribution of atomic velocities that is induced by spontaneous light pressure leads to a novel contribution to the optical dispersion curve of the medium. This light-pressure-induced dispersion phenomenon displays a pronounced nonlinear dependence on the laser intensity. Moreover, for a given intensity, its strength is closely related to the laser beam diameter. As most important feature, this light-pressure-induced dispersion displays an even symmetry with respect to the optical detuning from line center. As a result, the total Doppler-broadened dispersion curve of the gas can become asymmetric, and a significant shift of the dispersion line center can occur. In addition to a detailed theoretical description of the phenomenon, we report on its experimental investigation on the \ensuremath{\lambda}=555.6 nm 1^{1}1S0{\mathit{S}}_{0}S0​${\mathrm{\ensuremath{-}}}^{3}$P1{\mathit{P}}_{1}P1​ transition in atomic ytterbium vapor with the use of frequency-modulation spectroscopy. The experimental findings are in good quantitative agreement with theoretical predictions.
We report on the observation of a light-pressure-induced dispersion of laser light interacting with a Doppler-broadened atomic medium. This novel dispersion feature displays an even symmetry with respect to the optical Doppler detuning; it is due to the small modification of the atomic velocity distribution caused by the spontaneous scattering force. Our phase-sensitive measurements were performed on the $\ensuremath{\lambda}=555.65$ nm $^{1}S_{0}\ensuremath{-}^{3}P_{1}$ transition in ytterbium vapor by the use of frequency-modulation spectroscopy. The experimental results are in good agreement with theoretical predictions.
We report on the observation of a light-pressure-induced asymmetry of the well-known absorption dip occurring in optical saturation spectroscopy. This asymmetry is due to the small modification of the atomic velocity distribution that is caused by the spontaneous scattering force of the saturating light field. Our measurements were performed on the \ensuremath{\lambda}=555.65 nm 1S0^{1}\mathrm{S}_{0}1S0​${\mathrm{\ensuremath{-}}}^{3}$P1{\mathrm{P}}_{1}P1​ transition in atomic ytterbium vapor by the use of a frequency-modulated test field propagating collinearly with the scattering field. The experimental results clearly confirm theoretical predictions and demonstrate the significance of the phenomenon for high-resolution laser spectroscopy.
We report the results of studying the effect of the resonant light pressure force on the amplitude and frequency properties of the nonlinear susceptibility and well known absorption resonance dip occurring in optical saturation spectroscopy of two level atomic gas. On the basis of numerical solutions of the Liouville and Fokker-Plank equations the behaviour pattern of the velocity distribution function of a two-level atomic gas in relation to the saturation intensity and time of interaction with a strong resonant optical field was obtained. Time course of the velocity distribution function due to the action of spontaneous light pressure force leads to modification of the nonlinear susceptibility, absorption saturation resonant line form and to change of frequency dip relative to the atomic resonant frequency transition. The represented numerical modeling results explained qualitatively a number ofexperimental facts, that could not be explained before.
Nonlinear effects in pulse propagation through a medium consisting of four-level double-$\ensuremath{\Lambda}$-type systems are studied theoretically. We apply three continuous-wave driving fields and a pulsed probe field such that they form a closed interaction loop. Due to the closed loop and the finite frequency width of the probe pulses, the multiphoton resonance condition cannot be fulfilled, such that a time-dependent analysis is required. By identifying the different underlying physical processes we determine the parts of the solution relevant to calculate the linear and nonlinear response of the system. We find that the system can exhibit a strong intensity-dependent refractive index with small absorption over a range of several natural linewidths. For a realistic example we include Doppler and pressure broadening and calculate the nonlinear self-phase modulation in a gas cell with sodium vapor and argon buffer gas. We find that a self-phase modulation of $\ensuremath{\pi}$ is achieved after the propagation of a few centimeters through the medium while the absorption and pulse shape distortion in the corresponding spectral range is small.
We develop a field-nonlinear theory of sub-Doppler spectroscopy in a gas of two-level atoms, based on a self-consistent solution of the Maxwell-Bloch equations in the mean field and single-atom density matrix approximations. This makes it possible to correctly take into account the effects caused by the free motion of atoms in a gas, which lead to a nonlinear dependence of the spectroscopic signal on the atomic density even in the absent of a direct interatomic interaction (e.g., dipole-dipole interaction). Within the framework of this approach, analytical expressions for the light field were obtained for an arbitrary number of resonant waves and arbitrary optical thickness of a gas medium. Sub-Doppler spectroscopy in the transmission signal for two counterpropagating and co-propagating waves has been studied in detail. A previously unknown red shift of a narrow sub-Doppler resonance is predicted in a counterpropagating waves scheme, when the frequency of one wave is fixed and the frequency of the other wave is varied. The magnitude of this shift depends on the atomic density and can be more than an order of magnitude greater than the known shift from the interatomic dipole-dipole interaction (Lorentz-Lorenz shift). The found effects, caused by the free motion of atoms, require a significant revision of the existing picture of spectroscopic effects depending on the density of atoms in a gas. Apart of fundamental aspect, obtained results are important for precision laser spectroscopy and optical atomic clocks.