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Journal of Applied Physics

Near-resonance nonlinear propagation of monochromatic radiation in a gas medium

J. I. Cotrim Vasconcellos

Published Apr 1, 1979• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.326190

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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.
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.
We have calculated t he nonlinear real index of refraction variations of a gas medium due to a strong monochromatic radiation causing saturation effects. The gas is supposed to be composed of two-leve1 molecules with which the externa1 field is nearly resonant. We assume homogeneous (hard collisions, sponfaneous decay) and inhomogeneous (Doppler effect) broadening mechanisms acting on the real index of refraction of the medium. The nonlinear dispersion of the medium is studied as a function of the detuning f requencies, saturation c onditions and for various ratios between the homogeneous and inhomogeneous linewidths. In particular, the modification of the index of refraction due to saturation effects are emphasized. Calculamos as v ariacoes do ind ice de refracao real nao-l inear de um meio gasoso devidas a uma radiacao monocromatica intensa que causa efeitos de saturacao. Supoe-se que o gas seja composto de moleculas de dois n iveis com as quais o campo externo e quase ressonante. Supomos mecan i smos de alargamento homogeneos (c01 isoes duras, deca imento espontâneo) e inomogeneas (efeito Doppler) a gindo sobre o ind ice de refracao real do meio. A dispersao nao - linear do meio e estudada como uma funcao das frequencias de detuningl', das condicoes de saturacao e para varias razoes entre as larguras de l inha homogeneas e inomogeneas. Em part icular, sao enfat izadas as mod if icacoes do ind ice de refracao dev idas a ef e i tos de saturacao.
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.
A three-dimensional theory for the resonant interaction of electromagnetic waves with a gas of two-level atoms is formulated in terms of macroscopic variables. The theory is utilized to find the steady-state attenuation of a plane wave in the presence of another plane wave running in the opposite direction with different amplitude. Contributions are included from the reflection of the oppositely running wave by an induced standing-wave inhomogeneity in the population inversion of the medium. The resulting attenuation and reflection coefficients are expressed as velocity integrals of continued fractions. Correspondence is made with existing gas-laser theories, yielding the formulation of a high-intensity ring-laser theory. Analytic approximations for the coefficients are presented for the Doppler-limit cases of both waves weak, one wave weak, and negligible reflection (rate-equation approximation). More-general cases have been calculated numerically. The attenuation coefficients exhibit a Lamb-dip feature. The relative depth of the dip increases rapidly with power at low saturation levels, slowly at high saturation, and is greater in the attenuation of the weaker wave. The width of the dip is nonlinearly power broadened. The shape of the dip is very nearly Lorentzian, except for one special case at high power in which the line splits. The propagation equations for the two waves are integrated over long absorption paths. A large resulting attenuation increases the relative size of the dip while decreasing the power broadening.
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.
A previously developed theory of spontaneous emission from driven systems has been applied to the case of a Doppler broadened gas of two level atoms radiating into free space. The power spectrum of those photons radiated nearly parallel to the propagation vector of the driving field is predicted to differ from that of the undriven system. The case of zero attenuation coefficient (population equality in the two resonance levels) and the driving field tuned to the center of the Doppler line, is investigated in particular. When the saturation parameter is large there is strong suppression, in an interval about the central frequency comparable to the saturated width, of the spontaneous emission whose spectral components are phased for amplitude modulation relative to the driving field. An amount of power equal to that suppressed, but with spectral components phased for phase modulation relative to the driving field, is radiated in an interval about the central frequency comparable to the homogeneous width.