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Journal of the Optical Society of America B

Dynamics of the moments of angular momentum distribution during generation of laser-induced polarization spectroscopy (LIPS) signal

Sukesh Roy, Robert P. Lucht, James R. Gord

Published Jan 6, 2011• 0 citations
Publisher

Abstract

The effects of laser-induced anisotropy on the generation of the short-pulse laser-induced polarization spectroscopy (LIPS) signal is investigated by direct numerical integration (DNI) of the time-dependent density matrix equations. The calculations are performed in the short-pulse regime (laser pulse width τL less than characteristic collision time τC) to reduce the influence of collisions on the generation of medium anisotropies. The Zeeman-state structure of the upper and lower energy levels is included in the multistate formulation of the density matrix equations. For a P-branch transition when the isotropic ground-level population is pumped by a circularly polarized light, oriented anisotropy is mainly responsible for the LIPS signal generation; whereas, when the resonance is pumped by a linearly polarized light, aligned anisotropy is mainly responsible. For a Q-branch transition that is pumped by a circularly polarized light, the contributions to the LIPS signal from orientation and alignment are comparable. The effects of saturation on the induced anisotropy is also investigated. The magnitude of the LIPS signal increases by more than a factor of 14 for an initial right circularly polarized-oriented anisotropic distribution in the ground Zeeman states as opposed to an isotropic distribution. An understanding of the effects of anisotropy on the LIPS signal will aid the modeling of the LIPS signal-generation processes and the interpretation of experimental LIPS signals.

DOI
10.1364/josab.28.000208

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The effects of laser-induced anisotropy on the generation of the short-pulse laser-induced polarization spectroscopy (LIPS) signal is investigated by direct numerical integration (DNI) of the time-dependent density matrix equations. The calculations are performed in the short-pulse regime (laser pulse width τL less than characteristic collision time τC) to reduce the influence of collisions on the generation of medium anisotropies. The Zeeman-state structure of the upper and lower energy levels is included in the multistate formulation of the density matrix equations. For a P-branch transition when the isotropic ground-level population is pumped by a circularly polarized light, oriented anisotropy is mainly responsible for the LIPS signal generation; whereas, when the resonance is pumped by a linearly polarized light, aligned anisotropy is mainly responsible. For a Q-branch transition that is pumped by a circularly polarized light, the contributions to the LIPS signal from orientation and alignment are comparable. The effects of saturation on the induced anisotropy is also investigated. The magnitude of the LIPS signal increases by more than a factor of 14 for an initial right circularly polarized-oriented anisotropic distribution in the ground Zeeman states as opposed to an isotropic distribution. An understanding of the effects of anisotropy on the LIPS signal will aid the modeling of the LIPS signal-generation processes and the interpretation of experimental LIPS signals.
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.
The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.
In this study we explored the angular momentum alignment-to-orientation conversion occurring in various alkali metals -- K, Rb, Cs. We used a theoretical model that is based on Optical Bloch equations and uses the density matrix formalism. Our model includes the interaction of all neighboring hyperfine levels, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. Additionally we simulated signals where the ground- or the excited-state coherent processes were switched off allowing us to determine the origins of obtained signals. We also performed experiments on Cs atoms with two laser beams: linearly polarised Cs D1 pump and circularly polarized Cs D2 probe. We used the pump beam to create angular momentum alignment in the ground state and observed the transmission signal of the probe beam as we changed the magnetic field. Full analysis of the experimentally obtained transmission signal from a single circularly polarized probe laser component is provided.
A theoretical analysis of the relative intensities of the Doppler-free signals in saturation spectroscopy, velocity selective optical pumping (VSOP) spectroscopy, polarization spectroscopy and a mixing of saturation and polarization spectroscopies is presented using the approximation of a single cycle of optical pumping in a four-level system. An optical pumping process in the Zeeman sublevels is taken into account owing to the important role of spontaneous emission even if the sublevels are degenerate. Arbitrary polarization combinations are considered for pump and probe beams. The similarities and differences between three kinds of spectroscopy are made clear. Both circular and linear optical anisotropies induced by the pump beam are considered in this theoretical calculation. The magnitude and sign of Doppler-free resonances in each spectroscopy are quite different owing to the polarizations of the pump and probe beams. The four-level system is important as a three-level approximation. The results obtained from the four-level optical pumping theory are in good agreement with experimental reports.
We consider the nonlinear propagation of an intense short pulse of polarized light through a molecular medium with ground- and excited-state absorption, excited-state emission, and fluorescence from the excited state to the ground state and possibly to a lower-lying excited state. We incorporate the effects of saturation, field-induced alignment, and rotational diffusion of the molecules in the medium. Our approach uses a slowly varying envelope approximation for the light propagation and rate equations for the effective parallel and perpendicular (and higher-multipole) population components of the molecular states. The time dependence of the anisotropy of the fluorescence occurring after preparation of the medium by the intense short pulse is determined. We can treat propagation through an optically nonthin medium wherein the intensity of the pulse decreases while propagating through the medium. An example of a 100-ps pulse propagating through a sample of Rhodamine-6G is presented. We compare our method with others used to describe intense-short-pulse propagation in molecular media.