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

Physical Review A

Saturation broadening by inhomogeneous fields

James C. Camparo

Published Jan 1, 1989• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.39.69

Related papers

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

Saturation effects and the dip in single-mode laser radiation curve

T. V. Radina

We show that the dip in the intensity line shape of a single-mode laser can appear at definite experimental conditions in cases both of nonhomogeneously broadened line as well as homogeneously broadened line of the atomic transition. In both cases the dip is explained by the nonlinear character of the phenomenon. The saturation of the population difference of the involved atomic energy levels has its maximum in the vicinity of the line center. Therefore the saturation of the amplification is at maximum near the atomic line center, and, as a consequence, the lasing power is reduced.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 15, 2007•0 citations

Understanding the characteristics of gain saturation for homogeneously broadened laser medium from the point of view of the bandwidth

Geguo Du

It is very important to understand the characteristics of gain saturation for homogeneously broadened laser medium. Assuming a Lorentzian lineshape function with a linewidth of ΔνH, we have derived the analytical functions of the gain coefficient under three different conditions: 1) a small and 2) a large signal incident on the medium respectively, and 3) a small signal accompanied by a large signal simultaneously incident on the medium. We have found that the bandwidth Δν of the gain coefficient is equal to the linewidth ΔνH for condition 1) and 3) while it is Δ ν = 1 + I ν 1 / I s Δ ν H for condition 2). Here, I v 1 and Is are the intensity of the large signal and the saturation intensity at the center frequency Vo, respectively. The reasons are also presented for such results. For condition 2), gain saturation effect is strongly dependent on the frequency of the large signal: the more the frequency deviates from the center frequency, the weaker the gain saturation effect. This results an increase of the bandwidth. For condition 3), the intensity of the large signal only changes the distribution of populations on the upper and lower energy levels. Hence, the shape of the gain coefficient does not change with the gain reduction of the small signal, thus, its bandwidth remains the same.

Education and Training in Optics and Photonics•Jan 1, 2007•0 citations

Understanding the characteristics of gain saturation for homogeneously broadened laser medium from the point of view of the bandwidth

Geguo Du

It is very important to understand the characteristics of gain saturation for homogeneously broadened laser medium. Assuming a Lorentzian lineshape function with a linewidth of ΔνH, we have derived the analytical functions of the gain coefficient under three different conditions: 1) a small and 2) a large signal incident on the medium respectively, and 3) a small signal accompanied by a large signal simultaneously incident on the medium. We have found that the bandwidth Δν of the gain coefficient is equal to the linewidth ΔνH for condition 1) and 3) while it is Δν = √1+Iν1 / IsΔνH for condition 2). Here, Iν1 and Is are the intensity of the large signal and the saturation intensity at the center frequency ν0, respectively. The reasons are also presented for such results. For condition 2), gain saturation effect is strongly dependent on the frequency of the large signal: the more the frequency deviates from the center frequency, the weaker the gain saturation effect. This results an increase of the bandwidth. For condition 3), the intensity of the large signal only changes the distribution of populations on the upper and lower energy levels. Hence, the shape of the gain coefficient does not change with the gain reduction of the small signal, thus, its bandwidth remains the same.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 3, 2015•0 citations

Power broadening of a diffusion resonance

David A. Shapiro, М. Г. Степанов

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.

Journal of Experimental and Theoretical Physics•May 1, 1998•0 citations

Power-dependent line-shape corrections for quantitative spectroscopy

Thomas M. Stace, Gar-Wing Truong, James D. Anstie +2 more

The Voigt profile---a convolution of a Gaussian and a Lorentzian---accurately describes the absorption lines of atomic and molecular gases at low probe powers. Fitting experimental absorption data to such a Voigt profile yields both the Lorentzian natural linewidth and the Gaussian Doppler broadening. However, as the probe power increases, saturation effects change the absorption line shape, such that it is no longer accurately described by a Voigt profile. Naively fitting a simple Voigt profile to the absorption line therefore introduces spurious power dependence into the extracted Doppler component. Using a simple atomic model, we calculate power-dependent corrections to the Voigt profile, which are parametrized by the Gaussian Doppler width, the Lorentzian natural linewidth, and the optical depth. We show numerically and experimentally that including the correction term substantially reduces the spurious power dependence in the fitted Gaussian width.

arXiv:1203.2828•Physical Review A•Jul 17, 2012•16 citations
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.
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.
We show that the dip in the intensity line shape of a single-mode laser can appear at definite experimental conditions in cases both of nonhomogeneously broadened line as well as homogeneously broadened line of the atomic transition. In both cases the dip is explained by the nonlinear character of the phenomenon. The saturation of the population difference of the involved atomic energy levels has its maximum in the vicinity of the line center. Therefore the saturation of the amplification is at maximum near the atomic line center, and, as a consequence, the lasing power is reduced.
It is very important to understand the characteristics of gain saturation for homogeneously broadened laser medium. Assuming a Lorentzian lineshape function with a linewidth of ΔνH, we have derived the analytical functions of the gain coefficient under three different conditions: 1) a small and 2) a large signal incident on the medium respectively, and 3) a small signal accompanied by a large signal simultaneously incident on the medium. We have found that the bandwidth Δν of the gain coefficient is equal to the linewidth ΔνH for condition 1) and 3) while it is Δ ν = 1 + I ν 1 / I s Δ ν H for condition 2). Here, I v 1 and Is are the intensity of the large signal and the saturation intensity at the center frequency Vo, respectively. The reasons are also presented for such results. For condition 2), gain saturation effect is strongly dependent on the frequency of the large signal: the more the frequency deviates from the center frequency, the weaker the gain saturation effect. This results an increase of the bandwidth. For condition 3), the intensity of the large signal only changes the distribution of populations on the upper and lower energy levels. Hence, the shape of the gain coefficient does not change with the gain reduction of the small signal, thus, its bandwidth remains the same.
It is very important to understand the characteristics of gain saturation for homogeneously broadened laser medium. Assuming a Lorentzian lineshape function with a linewidth of ΔνH, we have derived the analytical functions of the gain coefficient under three different conditions: 1) a small and 2) a large signal incident on the medium respectively, and 3) a small signal accompanied by a large signal simultaneously incident on the medium. We have found that the bandwidth Δν of the gain coefficient is equal to the linewidth ΔνH for condition 1) and 3) while it is Δν = √1+Iν1 / IsΔνH for condition 2). Here, Iν1 and Is are the intensity of the large signal and the saturation intensity at the center frequency ν0, respectively. The reasons are also presented for such results. For condition 2), gain saturation effect is strongly dependent on the frequency of the large signal: the more the frequency deviates from the center frequency, the weaker the gain saturation effect. This results an increase of the bandwidth. For condition 3), the intensity of the large signal only changes the distribution of populations on the upper and lower energy levels. Hence, the shape of the gain coefficient does not change with the gain reduction of the small signal, thus, its bandwidth remains the same.
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.
The Voigt profile---a convolution of a Gaussian and a Lorentzian---accurately describes the absorption lines of atomic and molecular gases at low probe powers. Fitting experimental absorption data to such a Voigt profile yields both the Lorentzian natural linewidth and the Gaussian Doppler broadening. However, as the probe power increases, saturation effects change the absorption line shape, such that it is no longer accurately described by a Voigt profile. Naively fitting a simple Voigt profile to the absorption line therefore introduces spurious power dependence into the extracted Doppler component. Using a simple atomic model, we calculate power-dependent corrections to the Voigt profile, which are parametrized by the Gaussian Doppler width, the Lorentzian natural linewidth, and the optical depth. We show numerically and experimentally that including the correction term substantially reduces the spurious power dependence in the fitted Gaussian width.