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International Scientific-Technical Conference on Actual Problems of Electronic Instrument Engineering (APEIE)

Shift and Broadening of Absorption and Dispersion Resonance by Saturation Parameter

А. К. Дмитриев, Nickolai. N. Golovin, Савинов Константин Николаевич, Vyacheslav S. Boldyrev, Александр Петрович Карпик

Published Nov 10, 2023• 0 citations

Abstract

Within the framework of the classical model, which describes electrons as damped harmonic oscillators in an external electromagnetic field, expressions for the absorption and dispersion coefficients in the second order of smallness in the saturation parameter are found for a uniformly broadened line at a low concentration of oscillators, when the amplitude of the field produced by neighboring electrons is significantly less amplitude of the external field. It is shown that with increasing saturation parameter, the shape of the dispersion resonance becomes asymmetric, that at small saturation parameter leads to its linear shift to the "red" region. At the same time, as the saturation parameter increases, the dispersion resonance broadens (increases the interval between the maximum and minimum of the dispersion curve) and, in addition, there is a relative increase in the low-frequency amplitude compared to the high-frequency one. As for the shape of the absorption line, just as for the dispersion resonance, as saturation parameter increases, an asymmetry of the line shape appears which is accompanied by a shift to the "red" region. Because the low-frequency wing of the absorption line shifts toward the resonance center faster than the high-frequency wing moves away from the center, a narrowing of the resonance from the saturation parameter is observed. The dependence of this narrowing is nonlinear. In this case, the maximum of the absorption resonance linearly shifts to the "blue" region at the same speed as the dispersion line shifts to the "red" one.

DOI: 10.1109/apeie59731.2023.10347748

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Within the framework of the classical model, which describes electrons as damped harmonic oscillators in an external electromagnetic field, expressions for the absorption and dispersion coefficients in the second order of smallness in the saturation parameter are found for a uniformly broadened line at a low concentration of oscillators, when the amplitude of the field produced by neighboring electrons is significantly less amplitude of the external field. It is shown that with increasing saturation parameter, the shape of the dispersion resonance becomes asymmetric, that at small saturation parameter leads to its linear shift to the "red" region. At the same time, as the saturation parameter increases, the dispersion resonance broadens (increases the interval between the maximum and minimum of the dispersion curve) and, in addition, there is a relative increase in the low-frequency amplitude compared to the high-frequency one. As for the shape of the absorption line, just as for the dispersion resonance, as saturation parameter increases, an asymmetry of the line shape appears which is accompanied by a shift to the "red" region. Because the low-frequency wing of the absorption line shifts toward the resonance center faster than the high-frequency wing moves away from the center, a narrowing of the resonance from the saturation parameter is observed. The dependence of this narrowing is nonlinear. In this case, the maximum of the absorption resonance linearly shifts to the "blue" region at the same speed as the dispersion line shifts to the "red" one.

Optical harmonic generation and mixing in the gas phase has been proposed as a technique for the generation of coherent radiation in the vacuum ultraviolet and soft x-ray spectral region. At the high field strengths required by these processes the interaction between atoms and the electromagnetic field shows intensity-dependent resonances. In this paper we modify harmonic generation theory to include the effect of these frequency shifts. Closed-form expressions for generated dipole moment, absorption probability, and coherence length are presented. The most important consequences of frequency shifts on resonantly enhanced processes are that the pump laser must be tuned away from the small-field resonance frequency, that the conversion efficiency may saturate, and that the dispersion of the medium may change sign. As an example, the generation of 198-\AA{} radiation by a five-photon mixing process in

{\mathrm{Li}}^{+}

is considered.

A formalism introduced previously by the author is used to calculate the shape of an absorption line in a gas, taking account of the "resonance" interaction between like atoms. The most serious approximation is the neglect of the effect of translational motion. An asymmetric line is obtained, with the maximum shifted slightly toward the red. Some simple classical considerations also agree qualitatively with the results. Various properties of the line shape obtained are briefly discussed. The neglect of translational motion makes it impossible to compare the results with experiments performed up to the present time.

The lowest order nonlinear effects due to saturation in the simultaneous resonant absorption of several oscillating fields by a low-pressure gas are considered. The analysis is based on a perturbation solution of the Boltzmann equation for the density matrix of the gas in a quantum statistical description. Within certain ranges of the parameters involved, it is shown that: (1) When the gas is irradiated by two oscillating linearly polarized fields of different frequencies well within the Doppler-broadened width of the same absorption line, maximum absorption of both fields occurs when the two linear polarizations are perpendicular to each other. (2) When the gas is in a static magnetic field and irradiated by two right-circularly polarized fields at ${\ensuremath{\omega}}_{0}$ and ${\ensuremath{\omega}}_{0}+\ensuremath{\Delta}\ensuremath{\omega}$, and two left-circularly polarized fields at ${\ensuremath{\omega}}_{0}$ and ${\ensuremath{\omega}}_{0}\ensuremath{-}\ensuremath{\Delta}\ensuremath{\omega}$, all well within the Doppler width of the respective Zeeman components ($\ensuremath{\Delta}m=+1 \mathrm{and} \ensuremath{-}1$) of the same absorption line, there exists a definite phase relationship among the fields whereby absorption of all four fields is simultaneously at a maximum. Although these effects are quite small in normal spectroscopic work, manifestation of both effects is readily observable in gaseous He-Ne optical masers.

The problem of saturation of intersubband absorption and optical rectification in asymmetric quantum wells is discussed theoretically using the density matrix formalism. The effects of the electron-electron interaction are taken into account. It is shown that near the resonance the spectral shapes of the nonlinear optical absorption coefficient and the nonlinear optical rectification coefficient are very similar. In the absence of the electron-electron interaction the spectral responses are nearly Lorentzian. The electron-electron interaction plays an important role in heavy doped systems. In structures with large spatial separation of the ground and the excited states wave functions, the depolarization effect is small and the absorption spectrum is affected mainly by the electrostatic Coulomb interaction. This interaction shifts the absorption peak to higher energy by an amount depending on the intensity of the incident light and leads to the significant distortion (asymmetry) of the line.

One characteristic normally used to distinguish inhomogeneous broadening from homogeneous broadening is the saturation behavior occurring when irradiation takes place at line center. The usual behavior found is that the absorption coefficient decreases as a negative power of 1 + I/Isat; a power of −1 indicates homogeneous broadening and a power of −½ denotes inhomogeneous broadening. It is shown here that, in the rate equation limit, this behavior is followed in most cases even though the homogeneous and inhomogeneous absorption profiles can have any line shape. The homogeneous line shape, in particular, need not be Lorentzian; its line center saturation behavior will be the same as that of a Lorentzian, however. If the inhomogeneous broadening is due to a distribution of atomic center frequencies, in the inhomogeneous limit the usual line center saturation behavior will be found no matter what the combination of homogeneous and inhomogeneous line shapes. However, if the broadening is inhomogeneous because of a distribution, among the individual atoms, in any property of the absorption profile other than center frequency (for example, the homogeneous linewidth), the saturation properties are not as simple, and in fact the inhomogeneous limit may not even exist.