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Optics and Spectroscopy

Nonlinear interaction of two monochromatic fields at close frequencies inside an inhomogeneously broadened absorption line

E. Y. Opleukhin, T. V. Radina, Evald E. Fradkin

Published Sep 1, 1988• 0 citations
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Abstract

An experimental arrangement for determining the widths of levels is proposed, based on a theoretically developed model. A two-level medium is irradiated with a strong biharmonic electromagnetic field. The behavior of nonlinear absorption coefficients at frequencies of the incident field is studied. Equations are derived which give relative relaxation constants in terms of experimental data.

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An experimental arrangement for determining the widths of levels is proposed, based on a theoretically developed model. A two-level medium is irradiated with a strong biharmonic electromagnetic field. The behavior of nonlinear absorption coefficients at frequencies of the incident field is studied. Equations are derived which give relative relaxation constants in terms of experimental data.
Using the exact solution for a sine-driven two-level system we have calculated the nonlinear absorption coefficient of a gas of two-level molecules with homogeneous (hard collisions, spontaneous decay) and inhomogeneous (Doppler effect) broadening mechanisms. We have studied the dependence of the form of the absorption lines on relaxation parameters, on the strength of the electric field, and for various ratios between the homogeneous and inhomogeneous linewidths. We include considerations about saturation of the medium caused by the external field that gives rise to the so-called power broadening of the spectral lines. The dependence of the linewidth on the saturation parameters and on the relaxation parameters is determined. These parameters appear in the ratio of the purely homogeneous and purely inhomogeneous linewidths. Asymptotic behaviors of this linewidth for the homogeneous limit and for the inhomogeneous limit are also determined.
The nonlinear absorption or gain characteristics of an optical-frequency, Doppler-broadened atomic resonance involving levels with closely spaced structure are analyzed. The level structures are assumed to be resolved with respect to their natural widths, but not necessarily with respect to the Doppler width at the optical transition. The radiation field consists of two closely spaced monochromatic frequencies lying within the Doppler width of the resonance. This type of radiation field may be obtained, for example, from a laser operating in two of its Fabry-Perot resonator modes. It is shown that, because of saturation of level populations and double-quantum Raman transitions between levels, appreciable nonlinear coupling takes place between the two fields. This coupling shows a resonance behavior when the frequency separation of the two applied fields becomes equal to the frequency splitting between two of the components which form either level structure. The width of this resonance is determined entirely by the natural widths of these two level components and not by the Doppler width of the optical transition or the natural width of other level components. When such a resonance occurs, the over-all gain or attenuation characteristics of the atomic resonance change drastically. In practice the frequency spacing of the fields may be kept constant while the level structures are tuned, e.g., magnetically. The effects are analyzed for cases of running-wave and standing-wave radiation fields. The use of this effect in precise determination of level structures as well as mode or transition coupling of a gas laser is discussed. Portions of the analysis are applicable to resonances with more general forms of inhomogeneous broadening.
It is shown that induced transitions of an ensemble of two-level articles with an inhomogeneously broadened line in the field of a phase-modulated pulse are analogous to Landau-Zener inelastic transitions in molecules when their terms cross. Even for T% T:, where T and T: are, respectively, the pulse width and the inhomogeneous relaxation time of the medium, a transition of particles of the entire spectrum ( T:) - ' from an upper to a lower level is possible, signifying the complete removal by the pulse of the energy stored in the active medium. Analysis of the dynamics of a phase-modulated pulse by means of the Maxwell-Bloch equations shows, in addition, the possibility of amplifying it without the development of field-amplitude oscillations.
Using the exact solution for a sine-driven two-level atom we have calculated the nonexponential attenuation experienced by a monochromatic electromagnetic beam nearly resonant with a gas of two-level atoms. The atoms are assumed to undergo collision, spontaneous decay plus inhomogeneous (Doppler, etc.) broadening. Resulting intensity-vs-distance plots for a plane wave are given for various degrees of relative homogeneous and inhomogeneous linewidths, for several saturation conditions and for several detuning frequencies. A comparison is also made with collision-broadened and linear attenuation regimes.
We explain the utility of third-order nonlinear susceptibility, χ (3) (ω 2 ; ±ω 1 , ∓ω1{\mp}\omega_{1}∓ω1​, ω 2 ), for the observation of resonances with homogeneous widths from inhomogeneously broadened distributions in three-level systems related to Raman or two-photon allowed electronic transitions. The line narrowing and high resolution capabilities are demonstrated theoretically using a model for inhomogeneous distributions of transitions in which we regard an absorption spectrum as the composition of some inhomogeneously broadened substructures. The experimental methods to separate a signal having frequency ω 2 from ingoing beam at the same frequency are outlined.
A theoretical analysis is made of the nonlinear (in respect of the radiation intensity) rotation of the plane of polarization occuring in an atomic medium subjected to a static magnetic field near one-photon (two-level atoms) and two-photon (three-level atoms) resonances. A study is also made of the influence of a strong monochromatic pump wave on the propagation of a weak nonmonochromatic wave. The wave functions and quasienergies are calculated for a three-level system in static magnetic and monochromatic electromagnetic fields near a two-photon resonance. It is shown that the Verdet constant and the refractive index of such a system depend on the magnitude and relative sign of the frequency detuning from resonance. Proximity to a two-photon resonance destroys the polarizability of a medium for either sign of the detuning.