Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Experimental and Theoretical Physics

Power broadening of a diffusion resonance

David A. Shapiro, М. Г. Степанов

Published May 1, 1998• 0 citations
Publisher

Abstract

We derive an expression in terms of cylinder functions for the shape of a nonlinear resonance in a two-level system with a rapidly decaying level. We show that when the natural linewidth is negligible, the square of the total width is the sum of squares of the power and diffusion widths. The traditional variational approximation yields a correct value for the full width at half maximum, but distorts the line profile. We derive a formula for the absorbed power as a function of the incident wave intensity for comparable power and diffusion broadening. The formula is found to be valid for a power width that is small or large compared to the diffusion width, and in a new intermediate domain where homogeneous saturation becomes inhomogeneous.

DOI
10.1134/1.558559

Related papers

Nonlinear absorption of monochromatic radiation near a gas-medium resonance

J. I. Cotrim Vasconcellos

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.

Physical Review A•Jan 1, 1979•1 citation

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

Transit-time effects in power-broadened Doppler-free saturation resonances

John E. Thomas, M. J. Kelly, J.‐P. Monchalin +2 more

A density-matrix calculation of the line shape for a Doppler-broadened two-level system subjected to a plane-standing-wave laser field with a Gaussian intensity profile is presented to fifth order in perturbation theory. The primary new result is that, for fixed pressure and intensity, the power-broadening contribution to the linewidth is at a minimum when the beam radius is approximately equal to the mean free path. In addition, an analytic solution for the linewidth in the collision-dominated regime is presented for general collision parameters.

Physical Review A•Jun 1, 1977•17 citations

Saturation broadening by inhomogeneous fields

James C. Camparo

According to the standard Karplus-Schwinger theory of saturation broadening, saturated line shapes are Lorentzians with linewidths that increase linearly with the perturbing field strength. This, however, is not what is observed experimentally when the saturating field is inhomogeneous. If the saturating field strength varies significantly over the experimental signal volume, we find that the saturated line shapes are strikingly non-Lorentzian. The ``sharpness'' of the experimental line shapes is quantified by an ``effective linewidth,'' which is the half width at half maximum of a Lorentzian that approximates the experimental line shape near line center. For certain classes of inhomogeneous fields, we find that this effective linewidth increases approximately as the square root of the saturating field strength, rather than linearly. We show that this class of inhomogeneous fields is distinguished by the presence of a node in the field geometry, and that the effect arises because the line shape near line center is dominated by the atomic population in the vicinity of the node. These results indicate the importance of understanding and accounting for inhomogeneous field effects when extracting physical information from experimental line shapes.

Physical Review A•Jan 1, 1989•13 citations

Calculation of Resonance Broadening

Haider R. Zaidi

The line-shape function is expressed in terms of three boundary functions related to the two-particle Green's function. The transverse as well as the longitudinal interaction among atoms is considered, using the photon propagator approach. The broadening of one of the radiative states through the resonance interaction with the ground state is considered in detail. The contributions of multiple transfer of excitation and of two-body scattering are calculated separately. Several validity conditions are also obtained which clarify the approximations in the existing results. The velocity dependence of the width parameter is investigated in some detail; our results differ considerably from the existing results because we have included higher-order contributions. The extreme low-density region [where (collision width) \ensuremath{\sim} (natural width)] is also considered; the linewidth is found to be nonlinear in the number density. The additional contribution of the coupling between the radiative states is also calculated in a special case.

Physical Review•Sep 5, 1968•33 citations

Generalized line broadening and saturation behavior

Albert T. Rosenberger

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.

Annual Meeting Optical Society of America•Jan 1, 1989•0 citations
We derive an expression in terms of cylinder functions for the shape of a nonlinear resonance in a two-level system with a rapidly decaying level. We show that when the natural linewidth is negligible, the square of the total width is the sum of squares of the power and diffusion widths. The traditional variational approximation yields a correct value for the full width at half maximum, but distorts the line profile. We derive a formula for the absorbed power as a function of the incident wave intensity for comparable power and diffusion broadening. The formula is found to be valid for a power width that is small or large compared to the diffusion width, and in a new intermediate domain where homogeneous saturation becomes inhomogeneous.
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 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.
A density-matrix calculation of the line shape for a Doppler-broadened two-level system subjected to a plane-standing-wave laser field with a Gaussian intensity profile is presented to fifth order in perturbation theory. The primary new result is that, for fixed pressure and intensity, the power-broadening contribution to the linewidth is at a minimum when the beam radius is approximately equal to the mean free path. In addition, an analytic solution for the linewidth in the collision-dominated regime is presented for general collision parameters.
According to the standard Karplus-Schwinger theory of saturation broadening, saturated line shapes are Lorentzians with linewidths that increase linearly with the perturbing field strength. This, however, is not what is observed experimentally when the saturating field is inhomogeneous. If the saturating field strength varies significantly over the experimental signal volume, we find that the saturated line shapes are strikingly non-Lorentzian. The ``sharpness'' of the experimental line shapes is quantified by an ``effective linewidth,'' which is the half width at half maximum of a Lorentzian that approximates the experimental line shape near line center. For certain classes of inhomogeneous fields, we find that this effective linewidth increases approximately as the square root of the saturating field strength, rather than linearly. We show that this class of inhomogeneous fields is distinguished by the presence of a node in the field geometry, and that the effect arises because the line shape near line center is dominated by the atomic population in the vicinity of the node. These results indicate the importance of understanding and accounting for inhomogeneous field effects when extracting physical information from experimental line shapes.
The line-shape function is expressed in terms of three boundary functions related to the two-particle Green's function. The transverse as well as the longitudinal interaction among atoms is considered, using the photon propagator approach. The broadening of one of the radiative states through the resonance interaction with the ground state is considered in detail. The contributions of multiple transfer of excitation and of two-body scattering are calculated separately. Several validity conditions are also obtained which clarify the approximations in the existing results. The velocity dependence of the width parameter is investigated in some detail; our results differ considerably from the existing results because we have included higher-order contributions. The extreme low-density region [where (collision width) \ensuremath{\sim} (natural width)] is also considered; the linewidth is found to be nonlinear in the number density. The additional contribution of the coupling between the radiative states is also calculated in a special case.
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.