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Resonance lineshape of saturated absorption and saturated dispersion of molecules accelerated in the earth’s gravity field

Natalia M. Kachalova, V. I. Romanenko, Леонід Петрович Яценко

Published May 8, 1994• 0 citations
OpenAlex

Abstract

The Spectral resolution of saturated absorption spectroscopy has been increased from Doppler broadening limited value 106– 106 to 1012. In ref. 1, the evidence of most narrow saturated absorption resonances with absolute halfwidth 50 Hz was given and the possibility to proceed registering resonances with the width Γ ≤ 10 Hz. The new level of resolution requires the developing of the theory of saturated absorption and saturated dispersion spectroscopy that account for broadening factors whose contribution in the shape of broad resonances is negligible.

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The advent of lasers has revolutionized the methods and possibilities of spectroscopy. Their monochromaticity permits the study of extremely narrow spectral features which would not have been resolved using classical techniques. Moreover, their extreme spectral power density, in giving rise to the field of nonlinear optics, which will be studied in Chapter 7, has resulted in the development of new and powerful spectroscopic techniques. These techniques, of which we describe briefly some examples in this complement, have as their basis the fact that an atom does not respond linearly when subjected to a very intense light field. First of all we shall describe the broadening mechanisms that explain the fact that the experimentally measured widths of atomic or molecular resonances are larger than those that would be observed if the atoms were isolated and at rest. We shall introduce in Section 3G.1 the concept of homogeneous width, which can be considered as the intrinsic width of a transition, and inhomogeneous width which concerns the variation of the frequency of a given transition that occurs because of the state of motion of the atom, or because of factors in its environment. We shall explain why it is possible, using nonlinear optical techniques to eliminate the effects of inhomogeneous broadening on recorded spectra, resulting in an improvement over the resolution of conventional techniques. We shall then concentrate more specifically on Doppler broadening , which is the most commonly encountered source of inhomogeneous broadening, describing two nonlinear optical techniques, saturated absorption spectroscopy (in Section 3G.2) and two-photon spectroscopy (in Section 3G.3), which enable it to be overcome.

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Abstract Some important types of spectroscopic experiments which allow to detect substructures masked by the Doppler width of the lines are discussed within a unified theoretical framework. It is pointed out that, in case of a three‐ or more‐level system, besides saturation effects also processes of Raman type play an essential role. The effect of high intensity of one (monochromatic) partial wave on the shape and width of the resonances (inverted Lamb dip) is studied in detail taking fully into account the dynamic Stark effect in addition to the power‐broadening of the holes burnt into the absorption profile.

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1. Introduetion For a long time aresolution of the optical met h ods was worse compared to that of the methods u s ed in the other wave length ranges. The last years saw a c ons i d er able progre s s in optical spectros copy in improving aresolution. This i s du e to tho development of new physical co nc epts und erlying the a t tai n­ ment of nonlinear s uper na r r ow optical r e sonanc es wi t h no Doppler broad ening. At present thre e methods are u sed to obtain narrow optical resonances: the mothod of s a t ur a t ed ab sorption, two-photon resonances in a standing-wavo field, and r esonances in s epar­ ated optical fields. The three methods involve the elimination of the influence of Doppl er broadening , so the narrowness of resonances is mostly determined by the time of coherent part­ icles-field interaction. The first t wo methods are weI l knovm and developed (see /1/). Just these methods h ave permitted receiving the principal results on obtaining and using super­ narrow resonances. The saturation resonances with a relative width of < 10- 11 have been obtained by using telescopic beam expanders to increase the time of particles-field interaction. The development of the third method has been started in 1976 (see / 2/). This method has showed interesting potentialities. The use of forbidden transitions and tunable lasers will permit to obtain resonanceswith a relative width of < 10- 13• Narrow resonances enabled one to observe in optics some phenomena that could not be earlier studied. Some results in this field received in the Institut e of Thermophysics of the Siberian Branch of the USSR Academy of Sciences are discussed in this r epor t .

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Line shapes of saturated absorption spectroscopy in optically thick media

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The line shapes of saturation spectroscopy in optically thick two-level media are calculated for atomic and molecular transitions. Line narrowing and distortion effects due to propagation are presented. For Doppler-broadened media it is shown that, due to multiphoton processes, the natural linewidth limits the ultimate narrowing that can be reached. Thus, up to ${\ensuremath{\alpha}}_{0}L=20,$ only when the rate-equation approximation is valid subhomogeneous linewidths are expected.

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Linewidth in saturated absorption spectroscopy for two-level atoms: an empirical formula

Geol Moon, Heung‐Ryoul Noh

We present an empirical formula for linewidth in saturated absorption spectroscopy for two-level atoms with cycling transition lines, taking the coherence term in the Doppler-broadened limit into account. The full width at half-maximum is obtained as (1+(1+as0)b)γt, where s0 is the on-resonance saturation parameter, γt is the transverse decay rate, and a and b are the parameters that depend on γt. We find that as γt increases, a and b approach 1 and 1/2, respectively. These are the typical values in the case without the coherence term.

Applied Optics•May 7, 2018•1 citation
The Spectral resolution of saturated absorption spectroscopy has been increased from Doppler broadening limited value 106– 106 to 1012. In ref. 1, the evidence of most narrow saturated absorption resonances with absolute halfwidth 50 Hz was given and the possibility to proceed registering resonances with the width Γ ≤ 10 Hz. The new level of resolution requires the developing of the theory of saturated absorption and saturated dispersion spectroscopy that account for broadening factors whose contribution in the shape of broad resonances is negligible.
The advent of lasers has revolutionized the methods and possibilities of spectroscopy. Their monochromaticity permits the study of extremely narrow spectral features which would not have been resolved using classical techniques. Moreover, their extreme spectral power density, in giving rise to the field of nonlinear optics, which will be studied in Chapter 7, has resulted in the development of new and powerful spectroscopic techniques. These techniques, of which we describe briefly some examples in this complement, have as their basis the fact that an atom does not respond linearly when subjected to a very intense light field. First of all we shall describe the broadening mechanisms that explain the fact that the experimentally measured widths of atomic or molecular resonances are larger than those that would be observed if the atoms were isolated and at rest. We shall introduce in Section 3G.1 the concept of homogeneous width, which can be considered as the intrinsic width of a transition, and inhomogeneous width which concerns the variation of the frequency of a given transition that occurs because of the state of motion of the atom, or because of factors in its environment. We shall explain why it is possible, using nonlinear optical techniques to eliminate the effects of inhomogeneous broadening on recorded spectra, resulting in an improvement over the resolution of conventional techniques. We shall then concentrate more specifically on Doppler broadening , which is the most commonly encountered source of inhomogeneous broadening, describing two nonlinear optical techniques, saturated absorption spectroscopy (in Section 3G.2) and two-photon spectroscopy (in Section 3G.3), which enable it to be overcome.
Abstract Some important types of spectroscopic experiments which allow to detect substructures masked by the Doppler width of the lines are discussed within a unified theoretical framework. It is pointed out that, in case of a three‐ or more‐level system, besides saturation effects also processes of Raman type play an essential role. The effect of high intensity of one (monochromatic) partial wave on the shape and width of the resonances (inverted Lamb dip) is studied in detail taking fully into account the dynamic Stark effect in addition to the power‐broadening of the holes burnt into the absorption profile.
1. Introduetion For a long time aresolution of the optical met h ods was worse compared to that of the methods u s ed in the other wave length ranges. The last years saw a c ons i d er able progre s s in optical spectros copy in improving aresolution. This i s du e to tho development of new physical co nc epts und erlying the a t tai n­ ment of nonlinear s uper na r r ow optical r e sonanc es wi t h no Doppler broad ening. At present thre e methods are u sed to obtain narrow optical resonances: the mothod of s a t ur a t ed ab sorption, two-photon resonances in a standing-wavo field, and r esonances in s epar­ ated optical fields. The three methods involve the elimination of the influence of Doppl er broadening , so the narrowness of resonances is mostly determined by the time of coherent part­ icles-field interaction. The first t wo methods are weI l knovm and developed (see /1/). Just these methods h ave permitted receiving the principal results on obtaining and using super­ narrow resonances. The saturation resonances with a relative width of < 10- 11 have been obtained by using telescopic beam expanders to increase the time of particles-field interaction. The development of the third method has been started in 1976 (see / 2/). This method has showed interesting potentialities. The use of forbidden transitions and tunable lasers will permit to obtain resonanceswith a relative width of < 10- 13• Narrow resonances enabled one to observe in optics some phenomena that could not be earlier studied. Some results in this field received in the Institut e of Thermophysics of the Siberian Branch of the USSR Academy of Sciences are discussed in this r epor t .
The line shapes of saturation spectroscopy in optically thick two-level media are calculated for atomic and molecular transitions. Line narrowing and distortion effects due to propagation are presented. For Doppler-broadened media it is shown that, due to multiphoton processes, the natural linewidth limits the ultimate narrowing that can be reached. Thus, up to ${\ensuremath{\alpha}}_{0}L=20,$ only when the rate-equation approximation is valid subhomogeneous linewidths are expected.
The authors consider the Doppler-broadened index of refraction of a two-level molecule of a gas for a weak travelling electromagnetic plane wave in the presence of a strong plane wave travelling in the opposite direction at the same frequency. The authors use the FVH vector model for a two-level system to calculate the real part of the non-linear susceptibility of the gas. The optical dispersion curve exhibits a wiggle at the centre line, that broadens and deepens as the gas is increasingly saturated by the strong incident wave.
We present an empirical formula for linewidth in saturated absorption spectroscopy for two-level atoms with cycling transition lines, taking the coherence term in the Doppler-broadened limit into account. The full width at half-maximum is obtained as (1+(1+as0)b)γt, where s0 is the on-resonance saturation parameter, γt is the transverse decay rate, and a and b are the parameters that depend on γt. We find that as γt increases, a and b approach 1 and 1/2, respectively. These are the typical values in the case without the coherence term.