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Acta Optica Sinica

Atomic velocity-changing collisions in polarization excitation spectroscopyII

Ang Z

Published Jan 1, 1982• 0 citations
OpenAlex

Abstract

Polarization intermodulated excitation (POLINEX) spectroscopy is a new nonlinear high resolution speotroscopy. It combines polarization spectroscopy with intermodulated fluorescence speotroscopy. So the POLINEX spectrosoopy has some advantages of them. In author's former paper, we had used the rate equation approach to analyze how the Doppler background caused by atomic collisions was eliminated and how the Loren-tzian line shape was kept. In this paper, we use the semiolassioal theory of Lamb to analyze the POLINEX speotroscopy further more. This method is more reasonable. Considering laser beam's polarization, energy level's degeneracy and collision cross relaxation, by means of the equation of motion of density matrix, we have calculated the polarizability of the atomic system submitted to laser beams I1 and I2 to the third order x(3). Then, from x(3) we have evaluated nonlinear components of the absorption coefficient a. So we can obtain the strength and shape of the intermodulated signal in POLINEX spectroscopy. The conclusion is in conformity with the experimental results. Moreover, it predicts the pressure shift and pressure broadening which can't be predicted by the rate equation approach.

Related papers

Atomic velocity-changing collisions in polarization intermodulated excitation spectroscopy

Ang Z

Polarization intermodulated excitation (POLINEX) spectroscopy is a new developing Doppler-free spectroscopic technique which combines the advantages of the polarization spectroscopy and the intermodulated fluorescence speotroscopy. In this technique, a tunable laser beam is circular polarized first and then divided into two parts of nearly same intensities. Two rotating polarizers of different modulated frequencies are used to change the directions of these linear polarized beams periodically with time. When they interact with the atoms, the fluorescence signal are detected via a lock-in amplifier. The POLINEX spectroscopy can effectively eliminate the Doppler-broadened pedestal due to the velocity-changing collisions among atoms as the polarization-modulation is used instead of the amplitude modulation. And that pedestal is a problem in the original saturated spectroscopy and the intermodulated fluorescence spectroscopy. Meanwhile, there is no asymmetry of the line-shape in the polarization spectroscopy, because only the fluorescent or opto-galvanic signal are detected in this new method. In this paper a study of velocity-changing collisions in POLINEX spectroscopy using the rate equation approach is presented. A kernel function is introduced to describe the probability of atom moving out or in the state V (velocity) and m (magnetic quantum number) and the related terms additional to the rate equations. We calculate the total absorption rate and pick out the term concerning the mutual absorption (intermodulated signal). The amplitude of signal is proportional to the difference of the absorption rate when the senses of polarization of two counter-propagating laser beams are same or perpendicular to each other. We obtain the results which show the term related with the Doppler-broadened pedestal being cancelled after the operation of Glebsch-Gordon coefficients. These results coincide with the experiments performed before. Using the density matrix approach we can obtain the same results.

Acta Optica Sinica•Jan 1, 1982•0 citations

Phase orthogonality in polarization intermodulated excitation (POLINEX) spectroscopy

Guozheng Yan, Z Wang

This paper reports the phase orthogonality both theoreitically and experimentally in POLINEX spectroscopy with a modulated polarization and a fixed polarization of two linearly polarized optical beams. It is possible to make the phase of the Doppler-free signal orthogonal to that of the Doppler-broadened background, if the fixed polarizer is properly adjusted.

Acta Optica Sinica•Jan 1, 1983•0 citations

Polarization spectroscopy using short-pulse lasers: Theoretical analysis

Sukesh Roy, Robert P. Lucht, Thomas A. Reichardt

The physics of short-pulse polarization spectroscopy (PS) and the diagnostic potential for quantitative measurements of species concentration are investigated by direct numerical integration (DNI) of the time-dependent density matrix equations for a multistate system. The effects of laser power, collision rates, and Doppler broadening on the short-pulse PS signal generation process are investigated by systematically varying these parameters in the numerical calculations. It is found that the use of a short-pulse laser (laser pulse width τL<characteristic collision time τC) significantly decreases the collision-rate dependence of the PS signal compared to the long-pulse laser case (τL>τC), even for a nonsaturating pump beam. For a saturating pump beam, the short-pulse PS signal is found to be nearly independent of collision rate. Increasing the collision rate by a factor of 100 (from 108 to 1010 s−1), the calculated PS signal strength decreases by only a factor of 2 for a 100-ps pump laser at high intensity. This insensitivity of the PS signal to the collision rate in the medium enhances greatly the potential for quantitative application of the technique for concentration measurements in reacting flows. The underlying physics of the short-pulse PS is explored by studying the effects of collision rate, Doppler broadening, and the pump laser intensity on the temporal profile of the Zeeman state populations and the coherences between the Zeeman states.

The Journal of Chemical Physics•Jan 8, 2002•21 citations

Multi-axial-mode laser effects in polarization spectroscopy

William C. Giancola, Thomas A. Reichardt, Robert P. Lucht

The effects of multifrequency-mode laser radiation on polarization-spectroscopy signal generation are investigated by direct numerical integration of the time-dependent density-matrix equations. The numerical solution of the density-matrix equations allows us to incorporate a physically reasonable model for pulsed dye-laser radiation in our analysis of the laser–resonance interaction. The laser radiation is modeled as the sum of electric fields from a finite number of modes that are assumed to have random pulse-to-pulse phases and exponentially distributed amplitudes. Calculations are performed for a homogeneously broadened resonance (only collisional broadening) and for a resonance that is both collision and Doppler broadened. The effect of the multimode laser radiation on polarization-spectroscopy line shapes and saturation curves is investigated for different values of the laser bandwidth and mode spacing and resonance collision and Doppler widths. The saturation parameter for the resonance is strongly dependent on the ratio of the laser bandwidth to the resonance collision width when the laser bandwidth is greater than the collision width. The pulse-to-pulse fluctuations in polarization-spectroscopy signal levels are found to decrease substantially for saturating pump intensities. The inclusion of the multimode laser structure into our density-matrix equations represents a significant advance in modeling the nonlinear interaction of laser radiation with atomic or molecular resonances.

Journal of the Optical Society of America B•Oct 1, 2000•19 citations

Theory of collision effects in Doppler-free spectroscopy

P. R. Berman

A theory of the influence of binary collisions on the line shapes associated with Doppler-free spectroscopy is presented. The specific calculation is for two-photon absorption through a real or virtual intermediate state, but the extension of the results to alternative level schemes is included. Collisions are treated quite generally at first, but, ultimately, a simple but reasonable collision model is adopted to properly account for both the "phase-interrupting" and "velocity-changing" aspects of collisions. It is shown that collisional processes can be used to distinguish between the "two-quantum" and "stepwise" contributions to the two-photon excitation rate. Moreover, it is demonstrated that systematic experimental line-shape investigations, in addition to providing tests of current collision theories, can lead to values for collision broadening and shift parameters, excitation transfer rates, magnetic substate relaxation rates, velocity-changing collision rates, and collision kernels. Consequently, Doppler-free spectroscopy can provide a new and important probe of collision effects in atomic and molecular systems.

Physical Review A•Jun 1, 1976•49 citations

Comprehensive theory for line broadening in high-resolution and nonlinear spectroscopies: application to the Na D lines

R. M. Herman, E. W. Weber

A general method for analysing line broadening caused by Doppler, phaseshift, inelastic and velocity-changing collisional effects is proposed for transitions at optical wavelengths. In a unified approach Poisson statistics are used to describe collision probabilities randomly distributed in a time interval which can terminate the optical coherence in a combination of the above effects; markoffian independence is assumed for each collision. Then the dipole moment correlation function is obtained in a form which is virtually exact in accounting for all effects of isotropic forces, and which is correct to second-order terms in the anisotropic interaction potentials. Phenomena as diverse as standard optical pressure broadening, broadening due to velocity-changing collisions in nonlinear spectroscopies, and Dicke narrowing of the Doppler contour are described. The implications of the theory are discussed in detail and applied to the case of the NaD lines perturbed by He buffer gas. Numerical calculations reveal that the substantially different lineshift and broadening parameters in nonlinear and in standard optical spectroscopies can be reasonably well understood within the limitations posed by present uncertainties in the Na 3 2 P-He interaction potentials. However, the large differences in shift and width between the D 2 and D 1 lines in saturation spectroscopy cannot be explained within the present theory.

Journal of Physics B Atomic and Molecular Physics•Apr 28, 1983•8 citations
Polarization intermodulated excitation (POLINEX) spectroscopy is a new nonlinear high resolution speotroscopy. It combines polarization spectroscopy with intermodulated fluorescence speotroscopy. So the POLINEX spectrosoopy has some advantages of them.
In author's former paper, we had used the rate equation approach to analyze how the Doppler background caused by atomic collisions was eliminated and how the Loren-tzian line shape was kept.
In this paper, we use the semiolassioal theory of Lamb to analyze the POLINEX speotroscopy further more. This method is more reasonable. Considering laser beam's polarization, energy level's degeneracy and collision cross relaxation, by means of the equation of motion of density matrix, we have calculated the polarizability of the atomic system submitted to laser beams I1 and I2 to the third order x(3). Then, from x(3) we have evaluated nonlinear components of the absorption coefficient a. So we can obtain the strength and shape of the intermodulated signal in POLINEX spectroscopy.
The conclusion is in conformity with the experimental results. Moreover, it predicts the pressure shift and pressure broadening which can't be predicted by the rate equation approach.
Polarization intermodulated excitation (POLINEX) spectroscopy is a new developing Doppler-free spectroscopic technique which combines the advantages of the polarization spectroscopy and the intermodulated fluorescence speotroscopy. In this technique, a tunable laser beam is circular polarized first and then divided into two parts of nearly same intensities. Two rotating polarizers of different modulated frequencies are used to change the directions of these linear polarized beams periodically with time. When they interact with the atoms, the fluorescence signal are detected via a lock-in amplifier. The POLINEX spectroscopy can effectively eliminate the Doppler-broadened pedestal due to the velocity-changing collisions among atoms as the polarization-modulation is used instead of the amplitude modulation. And that pedestal is a problem in the original saturated spectroscopy and the intermodulated fluorescence spectroscopy. Meanwhile, there is no asymmetry of the line-shape in the polarization spectroscopy, because only the fluorescent or opto-galvanic signal are detected in this new method. In this paper a study of velocity-changing collisions in POLINEX spectroscopy using the rate equation approach is presented. A kernel function is introduced to describe the probability of atom moving out or in the state V (velocity) and m (magnetic quantum number) and the related terms additional to the rate equations. We calculate the total absorption rate and pick out the term concerning the mutual absorption (intermodulated signal). The amplitude of signal is proportional to the difference of the absorption rate when the senses of polarization of two counter-propagating laser beams are same or perpendicular to each other. We obtain the results which show the term related with the Doppler-broadened pedestal being cancelled after the operation of Glebsch-Gordon coefficients. These results coincide with the experiments performed before. Using the density matrix approach we can obtain the same results.
The physics of short-pulse polarization spectroscopy (PS) and the diagnostic potential for quantitative measurements of species concentration are investigated by direct numerical integration (DNI) of the time-dependent density matrix equations for a multistate system. The effects of laser power, collision rates, and Doppler broadening on the short-pulse PS signal generation process are investigated by systematically varying these parameters in the numerical calculations. It is found that the use of a short-pulse laser (laser pulse width τL<characteristic collision time τC) significantly decreases the collision-rate dependence of the PS signal compared to the long-pulse laser case (τL>τC), even for a nonsaturating pump beam. For a saturating pump beam, the short-pulse PS signal is found to be nearly independent of collision rate. Increasing the collision rate by a factor of 100 (from 108 to 1010 s−1), the calculated PS signal strength decreases by only a factor of 2 for a 100-ps pump laser at high intensity. This insensitivity of the PS signal to the collision rate in the medium enhances greatly the potential for quantitative application of the technique for concentration measurements in reacting flows. The underlying physics of the short-pulse PS is explored by studying the effects of collision rate, Doppler broadening, and the pump laser intensity on the temporal profile of the Zeeman state populations and the coherences between the Zeeman states.
The effects of multifrequency-mode laser radiation on polarization-spectroscopy signal generation are investigated by direct numerical integration of the time-dependent density-matrix equations. The numerical solution of the density-matrix equations allows us to incorporate a physically reasonable model for pulsed dye-laser radiation in our analysis of the laser–resonance interaction. The laser radiation is modeled as the sum of electric fields from a finite number of modes that are assumed to have random pulse-to-pulse phases and exponentially distributed amplitudes. Calculations are performed for a homogeneously broadened resonance (only collisional broadening) and for a resonance that is both collision and Doppler broadened. The effect of the multimode laser radiation on polarization-spectroscopy line shapes and saturation curves is investigated for different values of the laser bandwidth and mode spacing and resonance collision and Doppler widths. The saturation parameter for the resonance is strongly dependent on the ratio of the laser bandwidth to the resonance collision width when the laser bandwidth is greater than the collision width. The pulse-to-pulse fluctuations in polarization-spectroscopy signal levels are found to decrease substantially for saturating pump intensities. The inclusion of the multimode laser structure into our density-matrix equations represents a significant advance in modeling the nonlinear interaction of laser radiation with atomic or molecular resonances.
A theory of the influence of binary collisions on the line shapes associated with Doppler-free spectroscopy is presented. The specific calculation is for two-photon absorption through a real or virtual intermediate state, but the extension of the results to alternative level schemes is included. Collisions are treated quite generally at first, but, ultimately, a simple but reasonable collision model is adopted to properly account for both the "phase-interrupting" and "velocity-changing" aspects of collisions. It is shown that collisional processes can be used to distinguish between the "two-quantum" and "stepwise" contributions to the two-photon excitation rate. Moreover, it is demonstrated that systematic experimental line-shape investigations, in addition to providing tests of current collision theories, can lead to values for collision broadening and shift parameters, excitation transfer rates, magnetic substate relaxation rates, velocity-changing collision rates, and collision kernels. Consequently, Doppler-free spectroscopy can provide a new and important probe of collision effects in atomic and molecular systems.
A general method for analysing line broadening caused by Doppler, phaseshift, inelastic and velocity-changing collisional effects is proposed for transitions at optical wavelengths. In a unified approach Poisson statistics are used to describe collision probabilities randomly distributed in a time interval which can terminate the optical coherence in a combination of the above effects; markoffian independence is assumed for each collision. Then the dipole moment correlation function is obtained in a form which is virtually exact in accounting for all effects of isotropic forces, and which is correct to second-order terms in the anisotropic interaction potentials. Phenomena as diverse as standard optical pressure broadening, broadening due to velocity-changing collisions in nonlinear spectroscopies, and Dicke narrowing of the Doppler contour are described. The implications of the theory are discussed in detail and applied to the case of the NaD lines perturbed by He buffer gas. Numerical calculations reveal that the substantially different lineshift and broadening parameters in nonlinear and in standard optical spectroscopies can be reasonably well understood within the limitations posed by present uncertainties in the Na 3 2 P-He interaction potentials. However, the large differences in shift and width between the D 2 and D 1 lines in saturation spectroscopy cannot be explained within the present theory.