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.

© 2011 Optical Society of America

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2009

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

P. J. Dagdigian and M. H. Alexander, “Dependence of elastic depolarization cross sections on the potential: OH(X2Π)-Ar and NO(X2Π)-Ar,” J. Chem. Phys. 130, 204304 (2009).
[CrossRef] [PubMed]

P. J. Dagdigian and M. H. Alexander, “Tensor cross sections and collisional depolarization of OH(X2Π) in collisions with helium,” J. Chem. Phys. 130, 164315 (2009).
[CrossRef] [PubMed]

P. J. Dagdigian and M. H. Alexander, “Tensor cross sections and the collisional evolution of state multipoles: OH(X2Π)-Ar,” J. Chem. Phys. 130, 094303 (2009).
[CrossRef] [PubMed]

2008

G. Paterson, S. Marinakis, M. Costen, K. G. McKendrick, J. Klos, and R. Tobola, “Orientation and alignment depolarization in OH(X2Π)+Ar/He collisions,” J. Chem. Phys. 129, 074304(2008).
[CrossRef] [PubMed]

2007

S. Marinakis, G. Paterson, J. Klos, M. L. Costen, and K. G. McKendrick, “Inelastic scattering of OH(X2Π) with Ar and He: A combined polarization spectroscopy and quantum scattering study,” Phys. Chem. Chem. Phys. 9, 4414–4426 (2007).
[CrossRef] [PubMed]

2005

Z. S. Li, M. Rupinski, J. Zetterberg, Z. T. Alwahabi, and M. Alden, “Mid-infrared polarization spectroscopy of polyatomic molecules: Detection of nascent CO2 and H2O in atmospheric pressure flames,” Chem. Phys. Lett. 407, 243–248 (2005).
[CrossRef]

2004

X. Chen, B. D. Patterson, and T. B. Settersten, “Time-domain investigation of OH ground-state energy transfer using picosecond two-color polarization spectroscopy,” Chem. Phys. Lett. 388, 358–362 (2004).
[CrossRef]

M. L. Costen, H. J. Crighton, and K. G. McKendrick, “Measurement of orientation and alignment moment relaxation by polarization spectroscopy: Theory and experiment,” J. Chem. Phys. 120, 7910–7926 (2004).
[CrossRef] [PubMed]

2003

T. Dreier and J. Tobai, “Rotational state resolved measurement of relaxation times and ground state recovery rates in small radicals in atmospheric pressure flames using picosecond pump-probe degenerate four-wave mixing,” Laser Phys. 13, 286–292 (2003).

2002

J. Tobai, T. Dreier, and J. W. Daily, “Rotational level dependence of ground state recovery rates for OHX2Π(v′′=0) in atmospheric pressure flames using the picosecond saturating-pump degenerate four-wave mixing probe technique,” J. Chem. Phys. 116, 4030–4038 (2002).
[CrossRef]

S. Roy, R. P. Lucht, and T. A. Reichardt, “Polarization spectroscopy using short-pulse lasers: Theoretical analysis,” J. Chem. Phys. 116, 571–580 (2002).
[CrossRef]

S. Roy, R. P. Lucht, and A. McIlroy, “Mid-infrared polarization spectroscopy of carbon dioxide,” Appl. Phys. B 75, 875–882(2002).
[CrossRef]

2000

E. Hertz, B. Lavorel, O. Faucher, and R. Chaux, “Femtosecond polarization spectroscopy in molecular gas mixtures: Macroscopic interference and concentration measurements,” J. Chem. Phys. 113, 6629–6633 (2000).
[CrossRef]

T. A. Reichardt, W. C. Giancola, and R. P. Lucht, “Experimental investigation of saturated polarization spectroscopy for quantitative concentration measurements,” Appl. Opt. 39, 2002–2008(2000).
[CrossRef]

T. A. Reichardt, F. D. Teodoro, R. L. Farrow, S. Roy, and R. P. Lucht, “Collisional dependence of polarization spectroscopy with a picosecond laser,” J. Chem. Phys. 113, 2263–2269 (2000).
[CrossRef]

1998

T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, “Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems,” J. Chem. Phys. 108, 7713–7739 (1998).
[CrossRef]

T. A. Reichardt and R. P. Lucht, “Theoretical calculation of line shapes and saturation effects in polarization spectroscopy,” J. Chem. Phys. 109, 5830–5843 (1998).
[CrossRef]

T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, “Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems,” J. Chem. Phys. 108, 7713–7738 (1998).
[CrossRef]

1997

M. J. New, P. Ewart, A. Dreizler, and T. Dreier, “Multiplex polarization spectroscopy of OH for flame thermometry,” Appl. Phys. B 65, 633–637 (1997).
[CrossRef]

1996

T. A. Reichardt and R. P. Lucht, “Degenerate four-wave mixing spectroscopy with short-pulse lasers: Theoretical analysis,” J. Opt. Soc. Am. B 13, 1107–1119 (1996).
[CrossRef]

S. Williams, L. A. Rahn, and R. N. Zare, “Effects of different population, orientation, and alignment relaxation rates in resonant four-wave mixing,” J. Chem. Phys. 104, 3947–3955(1996).
[CrossRef]

1995

A. Dreizler, R. Tadday, A. A. Suvernev, M. Himmelhaus, T. Dreier, and P. Foggi, “Measurement of orientational relaxation times of OH in a flame using picosecond time-resolved polarization spectroscopy,” Chem. Phys. Lett. 240, 315–323 (1995).
[CrossRef]

1994

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations I. Weak-field limit,” J. Chem. Phys. 101, 1072–1107 (1994).
[CrossRef]

1993

1992

M. P. Auzinsh, “General restrictions for the relaxation constants of the polarization moments of the density matrix,” Chem. Phys. Lett. 198, 305–310 (1992).
[CrossRef]

1986

K. Danzmann, K. Grützmacher, and B. Wende, “Doppler-free two-photon polarization-spectroscopic measurement of the Stark-broadened profile of the hydrogen Lα line in a dense plasma,” Phys. Rev. Lett. 57, 2151–2153 (1986).
[CrossRef] [PubMed]

1983

C. H. Greene and R. N. Zare, “Determination of product population and alignment using laser-induced fluorescence,” J. Chem. Phys. 78, 6741–6753 (1983).
[CrossRef]

1982

C. H. Greene and R. N. Zare, “Photofragment alignment and orientation,” Annu. Rev. Phys. Chem. 33, 119–150 (1982).
[CrossRef]

1977

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” Proc. SPIE 113, 80–87 (1977).

1973

U. Fano and J. H. Macek, “Impact excitation and polarization of the emitted light,” Rev. Mod. Phys. 45, 553–573 (1973).
[CrossRef]

Alden, M.

Z. S. Li, M. Rupinski, J. Zetterberg, Z. T. Alwahabi, and M. Alden, “Mid-infrared polarization spectroscopy of polyatomic molecules: Detection of nascent CO2 and H2O in atmospheric pressure flames,” Chem. Phys. Lett. 407, 243–248 (2005).
[CrossRef]

K. Nyholm, R. Fritzon, and M. Alden, “Two-dimensional imaging of OH in flames by use of polarization spectroscopy,” Opt. Lett. 18, 1672–1674 (1993).
[CrossRef] [PubMed]

Alexander, M. H.

P. J. Dagdigian and M. H. Alexander, “Dependence of elastic depolarization cross sections on the potential: OH(X2Π)-Ar and NO(X2Π)-Ar,” J. Chem. Phys. 130, 204304 (2009).
[CrossRef] [PubMed]

P. J. Dagdigian and M. H. Alexander, “Tensor cross sections and collisional depolarization of OH(X2Π) in collisions with helium,” J. Chem. Phys. 130, 164315 (2009).
[CrossRef] [PubMed]

P. J. Dagdigian and M. H. Alexander, “Tensor cross sections and the collisional evolution of state multipoles: OH(X2Π)-Ar,” J. Chem. Phys. 130, 094303 (2009).
[CrossRef] [PubMed]

Alwahabi, Z. T.

Z. S. Li, M. Rupinski, J. Zetterberg, Z. T. Alwahabi, and M. Alden, “Mid-infrared polarization spectroscopy of polyatomic molecules: Detection of nascent CO2 and H2O in atmospheric pressure flames,” Chem. Phys. Lett. 407, 243–248 (2005).
[CrossRef]

Aminoff, C. G.

Aoiz, F. J.

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

Auzinsh, M. P.

M. P. Auzinsh, “General restrictions for the relaxation constants of the polarization moments of the density matrix,” Chem. Phys. Lett. 198, 305–310 (1992).
[CrossRef]

Blum, K.

K. Blum, Density Matrix Theory and Applications (Plenum Press, 1981).

Brouard, M.

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

Carlson, N.

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” Proc. SPIE 113, 80–87 (1977).

Chadwick, H.

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

Chang, Y.-P.

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

Chaux, R.

E. Hertz, B. Lavorel, O. Faucher, and R. Chaux, “Femtosecond polarization spectroscopy in molecular gas mixtures: Macroscopic interference and concentration measurements,” J. Chem. Phys. 113, 6629–6633 (2000).
[CrossRef]

Chen, X.

X. Chen, B. D. Patterson, and T. B. Settersten, “Time-domain investigation of OH ground-state energy transfer using picosecond two-color polarization spectroscopy,” Chem. Phys. Lett. 388, 358–362 (2004).
[CrossRef]

Costen, M.

G. Paterson, S. Marinakis, M. Costen, K. G. McKendrick, J. Klos, and R. Tobola, “Orientation and alignment depolarization in OH(X2Π)+Ar/He collisions,” J. Chem. Phys. 129, 074304(2008).
[CrossRef] [PubMed]

Costen, M. L.

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

S. Marinakis, G. Paterson, J. Klos, M. L. Costen, and K. G. McKendrick, “Inelastic scattering of OH(X2Π) with Ar and He: A combined polarization spectroscopy and quantum scattering study,” Phys. Chem. Chem. Phys. 9, 4414–4426 (2007).
[CrossRef] [PubMed]

M. L. Costen, H. J. Crighton, and K. G. McKendrick, “Measurement of orientation and alignment moment relaxation by polarization spectroscopy: Theory and experiment,” J. Chem. Phys. 120, 7910–7926 (2004).
[CrossRef] [PubMed]

Crighton, H. J.

M. L. Costen, H. J. Crighton, and K. G. McKendrick, “Measurement of orientation and alignment moment relaxation by polarization spectroscopy: Theory and experiment,” J. Chem. Phys. 120, 7910–7926 (2004).
[CrossRef] [PubMed]

Dagdigian, P. J.

P. J. Dagdigian and M. H. Alexander, “Dependence of elastic depolarization cross sections on the potential: OH(X2Π)-Ar and NO(X2Π)-Ar,” J. Chem. Phys. 130, 204304 (2009).
[CrossRef] [PubMed]

P. J. Dagdigian and M. H. Alexander, “Tensor cross sections and the collisional evolution of state multipoles: OH(X2Π)-Ar,” J. Chem. Phys. 130, 094303 (2009).
[CrossRef] [PubMed]

P. J. Dagdigian and M. H. Alexander, “Tensor cross sections and collisional depolarization of OH(X2Π) in collisions with helium,” J. Chem. Phys. 130, 164315 (2009).
[CrossRef] [PubMed]

Daily, J. W.

J. Tobai, T. Dreier, and J. W. Daily, “Rotational level dependence of ground state recovery rates for OHX2Π(v′′=0) in atmospheric pressure flames using the picosecond saturating-pump degenerate four-wave mixing probe technique,” J. Chem. Phys. 116, 4030–4038 (2002).
[CrossRef]

Danzmann, K.

K. Danzmann, K. Grützmacher, and B. Wende, “Doppler-free two-photon polarization-spectroscopic measurement of the Stark-broadened profile of the hydrogen Lα line in a dense plasma,” Phys. Rev. Lett. 57, 2151–2153 (1986).
[CrossRef] [PubMed]

Demtröder, W.

W. Demtröder, Laser Spectroscopy (Springer, 1996), pp. 454–466.

Dreier, T.

T. Dreier and J. Tobai, “Rotational state resolved measurement of relaxation times and ground state recovery rates in small radicals in atmospheric pressure flames using picosecond pump-probe degenerate four-wave mixing,” Laser Phys. 13, 286–292 (2003).

J. Tobai, T. Dreier, and J. W. Daily, “Rotational level dependence of ground state recovery rates for OHX2Π(v′′=0) in atmospheric pressure flames using the picosecond saturating-pump degenerate four-wave mixing probe technique,” J. Chem. Phys. 116, 4030–4038 (2002).
[CrossRef]

M. J. New, P. Ewart, A. Dreizler, and T. Dreier, “Multiplex polarization spectroscopy of OH for flame thermometry,” Appl. Phys. B 65, 633–637 (1997).
[CrossRef]

A. Dreizler, R. Tadday, A. A. Suvernev, M. Himmelhaus, T. Dreier, and P. Foggi, “Measurement of orientational relaxation times of OH in a flame using picosecond time-resolved polarization spectroscopy,” Chem. Phys. Lett. 240, 315–323 (1995).
[CrossRef]

Dreizler, A.

M. J. New, P. Ewart, A. Dreizler, and T. Dreier, “Multiplex polarization spectroscopy of OH for flame thermometry,” Appl. Phys. B 65, 633–637 (1997).
[CrossRef]

A. Dreizler, R. Tadday, A. A. Suvernev, M. Himmelhaus, T. Dreier, and P. Foggi, “Measurement of orientational relaxation times of OH in a flame using picosecond time-resolved polarization spectroscopy,” Chem. Phys. Lett. 240, 315–323 (1995).
[CrossRef]

Eckbreth, A. C.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Gordon and Breach, 1996), p. 511.

Ewart, P.

M. J. New, P. Ewart, A. Dreizler, and T. Dreier, “Multiplex polarization spectroscopy of OH for flame thermometry,” Appl. Phys. B 65, 633–637 (1997).
[CrossRef]

Eyles, C. J.

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

Fano, U.

U. Fano and J. H. Macek, “Impact excitation and polarization of the emitted light,” Rev. Mod. Phys. 45, 553–573 (1973).
[CrossRef]

Farrow, R. L.

T. A. Reichardt, F. D. Teodoro, R. L. Farrow, S. Roy, and R. P. Lucht, “Collisional dependence of polarization spectroscopy with a picosecond laser,” J. Chem. Phys. 113, 2263–2269 (2000).
[CrossRef]

Faucher, O.

E. Hertz, B. Lavorel, O. Faucher, and R. Chaux, “Femtosecond polarization spectroscopy in molecular gas mixtures: Macroscopic interference and concentration measurements,” J. Chem. Phys. 113, 6629–6633 (2000).
[CrossRef]

Foggi, P.

A. Dreizler, R. Tadday, A. A. Suvernev, M. Himmelhaus, T. Dreier, and P. Foggi, “Measurement of orientational relaxation times of OH in a flame using picosecond time-resolved polarization spectroscopy,” Chem. Phys. Lett. 240, 315–323 (1995).
[CrossRef]

Fritzon, R.

Giancola, W. C.

Greene, C. H.

C. H. Greene and R. N. Zare, “Determination of product population and alignment using laser-induced fluorescence,” J. Chem. Phys. 78, 6741–6753 (1983).
[CrossRef]

C. H. Greene and R. N. Zare, “Photofragment alignment and orientation,” Annu. Rev. Phys. Chem. 33, 119–150 (1982).
[CrossRef]

Grützmacher, K.

K. Danzmann, K. Grützmacher, and B. Wende, “Doppler-free two-photon polarization-spectroscopic measurement of the Stark-broadened profile of the hydrogen Lα line in a dense plasma,” Phys. Rev. Lett. 57, 2151–2153 (1986).
[CrossRef] [PubMed]

Hänsch, T. W.

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” Proc. SPIE 113, 80–87 (1977).

Hertz, E.

E. Hertz, B. Lavorel, O. Faucher, and R. Chaux, “Femtosecond polarization spectroscopy in molecular gas mixtures: Macroscopic interference and concentration measurements,” J. Chem. Phys. 113, 6629–6633 (2000).
[CrossRef]

Hill, W. T.

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” Proc. SPIE 113, 80–87 (1977).

Himmelhaus, M.

A. Dreizler, R. Tadday, A. A. Suvernev, M. Himmelhaus, T. Dreier, and P. Foggi, “Measurement of orientational relaxation times of OH in a flame using picosecond time-resolved polarization spectroscopy,” Chem. Phys. Lett. 240, 315–323 (1995).
[CrossRef]

Johnson, B. R.

T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, “Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems,” J. Chem. Phys. 108, 7713–7739 (1998).
[CrossRef]

T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, “Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems,” J. Chem. Phys. 108, 7713–7738 (1998).
[CrossRef]

Kaivola, M.

Klos, J.

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

G. Paterson, S. Marinakis, M. Costen, K. G. McKendrick, J. Klos, and R. Tobola, “Orientation and alignment depolarization in OH(X2Π)+Ar/He collisions,” J. Chem. Phys. 129, 074304(2008).
[CrossRef] [PubMed]

S. Marinakis, G. Paterson, J. Klos, M. L. Costen, and K. G. McKendrick, “Inelastic scattering of OH(X2Π) with Ar and He: A combined polarization spectroscopy and quantum scattering study,” Phys. Chem. Chem. Phys. 9, 4414–4426 (2007).
[CrossRef] [PubMed]

Kowalski, F. V.

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” Proc. SPIE 113, 80–87 (1977).

Lamb, W. E.

M. Sargent III, M. O. Scully, and W. E. Lamb Jr., Laser Physics (Addison-Wesley, 1997).

Lavorel, B.

E. Hertz, B. Lavorel, O. Faucher, and R. Chaux, “Femtosecond polarization spectroscopy in molecular gas mixtures: Macroscopic interference and concentration measurements,” J. Chem. Phys. 113, 6629–6633 (2000).
[CrossRef]

Li, Z. S.

Z. S. Li, M. Rupinski, J. Zetterberg, Z. T. Alwahabi, and M. Alden, “Mid-infrared polarization spectroscopy of polyatomic molecules: Detection of nascent CO2 and H2O in atmospheric pressure flames,” Chem. Phys. Lett. 407, 243–248 (2005).
[CrossRef]

Livingstone, R.

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

Lucht, R. P.

S. Roy, R. P. Lucht, and A. McIlroy, “Mid-infrared polarization spectroscopy of carbon dioxide,” Appl. Phys. B 75, 875–882(2002).
[CrossRef]

S. Roy, R. P. Lucht, and T. A. Reichardt, “Polarization spectroscopy using short-pulse lasers: Theoretical analysis,” J. Chem. Phys. 116, 571–580 (2002).
[CrossRef]

T. A. Reichardt, F. D. Teodoro, R. L. Farrow, S. Roy, and R. P. Lucht, “Collisional dependence of polarization spectroscopy with a picosecond laser,” J. Chem. Phys. 113, 2263–2269 (2000).
[CrossRef]

T. A. Reichardt, W. C. Giancola, and R. P. Lucht, “Experimental investigation of saturated polarization spectroscopy for quantitative concentration measurements,” Appl. Opt. 39, 2002–2008(2000).
[CrossRef]

T. A. Reichardt and R. P. Lucht, “Theoretical calculation of line shapes and saturation effects in polarization spectroscopy,” J. Chem. Phys. 109, 5830–5843 (1998).
[CrossRef]

T. A. Reichardt and R. P. Lucht, “Degenerate four-wave mixing spectroscopy with short-pulse lasers: Theoretical analysis,” J. Opt. Soc. Am. B 13, 1107–1119 (1996).
[CrossRef]

Macek, J. H.

U. Fano and J. H. Macek, “Impact excitation and polarization of the emitted light,” Rev. Mod. Phys. 45, 553–573 (1973).
[CrossRef]

Maier, R.

Marinakis, S.

G. Paterson, S. Marinakis, M. Costen, K. G. McKendrick, J. Klos, and R. Tobola, “Orientation and alignment depolarization in OH(X2Π)+Ar/He collisions,” J. Chem. Phys. 129, 074304(2008).
[CrossRef] [PubMed]

S. Marinakis, G. Paterson, J. Klos, M. L. Costen, and K. G. McKendrick, “Inelastic scattering of OH(X2Π) with Ar and He: A combined polarization spectroscopy and quantum scattering study,” Phys. Chem. Chem. Phys. 9, 4414–4426 (2007).
[CrossRef] [PubMed]

McIlroy, A.

S. Roy, R. P. Lucht, and A. McIlroy, “Mid-infrared polarization spectroscopy of carbon dioxide,” Appl. Phys. B 75, 875–882(2002).
[CrossRef]

McKendrick, K. G.

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

G. Paterson, S. Marinakis, M. Costen, K. G. McKendrick, J. Klos, and R. Tobola, “Orientation and alignment depolarization in OH(X2Π)+Ar/He collisions,” J. Chem. Phys. 129, 074304(2008).
[CrossRef] [PubMed]

S. Marinakis, G. Paterson, J. Klos, M. L. Costen, and K. G. McKendrick, “Inelastic scattering of OH(X2Π) with Ar and He: A combined polarization spectroscopy and quantum scattering study,” Phys. Chem. Chem. Phys. 9, 4414–4426 (2007).
[CrossRef] [PubMed]

M. L. Costen, H. J. Crighton, and K. G. McKendrick, “Measurement of orientation and alignment moment relaxation by polarization spectroscopy: Theory and experiment,” J. Chem. Phys. 120, 7910–7926 (2004).
[CrossRef] [PubMed]

New, M. J.

M. J. New, P. Ewart, A. Dreizler, and T. Dreier, “Multiplex polarization spectroscopy of OH for flame thermometry,” Appl. Phys. B 65, 633–637 (1997).
[CrossRef]

Nyholm, K.

Orr-Ewing, A.

A. Orr-Ewing and R. N. Zare, The Chemical Dynamics and Kinetics of Small Radicals (World Scientific, 1995), pp. 936–1063.

Paterson, G.

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

G. Paterson, S. Marinakis, M. Costen, K. G. McKendrick, J. Klos, and R. Tobola, “Orientation and alignment depolarization in OH(X2Π)+Ar/He collisions,” J. Chem. Phys. 129, 074304(2008).
[CrossRef] [PubMed]

S. Marinakis, G. Paterson, J. Klos, M. L. Costen, and K. G. McKendrick, “Inelastic scattering of OH(X2Π) with Ar and He: A combined polarization spectroscopy and quantum scattering study,” Phys. Chem. Chem. Phys. 9, 4414–4426 (2007).
[CrossRef] [PubMed]

Patterson, B. D.

X. Chen, B. D. Patterson, and T. B. Settersten, “Time-domain investigation of OH ground-state energy transfer using picosecond two-color polarization spectroscopy,” Chem. Phys. Lett. 388, 358–362 (2004).
[CrossRef]

Rahn, L. A.

S. Williams, L. A. Rahn, and R. N. Zare, “Effects of different population, orientation, and alignment relaxation rates in resonant four-wave mixing,” J. Chem. Phys. 104, 3947–3955(1996).
[CrossRef]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations I. Weak-field limit,” J. Chem. Phys. 101, 1072–1107 (1994).
[CrossRef]

Reichardt, T. A.

S. Roy, R. P. Lucht, and T. A. Reichardt, “Polarization spectroscopy using short-pulse lasers: Theoretical analysis,” J. Chem. Phys. 116, 571–580 (2002).
[CrossRef]

T. A. Reichardt, F. D. Teodoro, R. L. Farrow, S. Roy, and R. P. Lucht, “Collisional dependence of polarization spectroscopy with a picosecond laser,” J. Chem. Phys. 113, 2263–2269 (2000).
[CrossRef]

T. A. Reichardt, W. C. Giancola, and R. P. Lucht, “Experimental investigation of saturated polarization spectroscopy for quantitative concentration measurements,” Appl. Opt. 39, 2002–2008(2000).
[CrossRef]

T. A. Reichardt and R. P. Lucht, “Theoretical calculation of line shapes and saturation effects in polarization spectroscopy,” J. Chem. Phys. 109, 5830–5843 (1998).
[CrossRef]

T. A. Reichardt and R. P. Lucht, “Degenerate four-wave mixing spectroscopy with short-pulse lasers: Theoretical analysis,” J. Opt. Soc. Am. B 13, 1107–1119 (1996).
[CrossRef]

Roy, S.

S. Roy, R. P. Lucht, and A. McIlroy, “Mid-infrared polarization spectroscopy of carbon dioxide,” Appl. Phys. B 75, 875–882(2002).
[CrossRef]

S. Roy, R. P. Lucht, and T. A. Reichardt, “Polarization spectroscopy using short-pulse lasers: Theoretical analysis,” J. Chem. Phys. 116, 571–580 (2002).
[CrossRef]

T. A. Reichardt, F. D. Teodoro, R. L. Farrow, S. Roy, and R. P. Lucht, “Collisional dependence of polarization spectroscopy with a picosecond laser,” J. Chem. Phys. 113, 2263–2269 (2000).
[CrossRef]

Rupinski, M.

Z. S. Li, M. Rupinski, J. Zetterberg, Z. T. Alwahabi, and M. Alden, “Mid-infrared polarization spectroscopy of polyatomic molecules: Detection of nascent CO2 and H2O in atmospheric pressure flames,” Chem. Phys. Lett. 407, 243–248 (2005).
[CrossRef]

Sargent, M.

M. Sargent III, M. O. Scully, and W. E. Lamb Jr., Laser Physics (Addison-Wesley, 1997).

Scully, M. O.

M. Sargent III, M. O. Scully, and W. E. Lamb Jr., Laser Physics (Addison-Wesley, 1997).

Settersten, T. B.

X. Chen, B. D. Patterson, and T. B. Settersten, “Time-domain investigation of OH ground-state energy transfer using picosecond two-color polarization spectroscopy,” Chem. Phys. Lett. 388, 358–362 (2004).
[CrossRef]

Suvernev, A. A.

A. Dreizler, R. Tadday, A. A. Suvernev, M. Himmelhaus, T. Dreier, and P. Foggi, “Measurement of orientational relaxation times of OH in a flame using picosecond time-resolved polarization spectroscopy,” Chem. Phys. Lett. 240, 315–323 (1995).
[CrossRef]

Tadday, R.

A. Dreizler, R. Tadday, A. A. Suvernev, M. Himmelhaus, T. Dreier, and P. Foggi, “Measurement of orientational relaxation times of OH in a flame using picosecond time-resolved polarization spectroscopy,” Chem. Phys. Lett. 240, 315–323 (1995).
[CrossRef]

Teets, R. E.

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” Proc. SPIE 113, 80–87 (1977).

Teodoro, F. D.

T. A. Reichardt, F. D. Teodoro, R. L. Farrow, S. Roy, and R. P. Lucht, “Collisional dependence of polarization spectroscopy with a picosecond laser,” J. Chem. Phys. 113, 2263–2269 (2000).
[CrossRef]

Tobai, J.

T. Dreier and J. Tobai, “Rotational state resolved measurement of relaxation times and ground state recovery rates in small radicals in atmospheric pressure flames using picosecond pump-probe degenerate four-wave mixing,” Laser Phys. 13, 286–292 (2003).

J. Tobai, T. Dreier, and J. W. Daily, “Rotational level dependence of ground state recovery rates for OHX2Π(v′′=0) in atmospheric pressure flames using the picosecond saturating-pump degenerate four-wave mixing probe technique,” J. Chem. Phys. 116, 4030–4038 (2002).
[CrossRef]

Tobola, R.

G. Paterson, S. Marinakis, M. Costen, K. G. McKendrick, J. Klos, and R. Tobola, “Orientation and alignment depolarization in OH(X2Π)+Ar/He collisions,” J. Chem. Phys. 129, 074304(2008).
[CrossRef] [PubMed]

Vaccaro, P. H.

T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, “Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems,” J. Chem. Phys. 108, 7713–7739 (1998).
[CrossRef]

T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, “Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems,” J. Chem. Phys. 108, 7713–7738 (1998).
[CrossRef]

Wasserman, T. A. W.

T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, “Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems,” J. Chem. Phys. 108, 7713–7739 (1998).
[CrossRef]

T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, “Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems,” J. Chem. Phys. 108, 7713–7738 (1998).
[CrossRef]

Wende, B.

K. Danzmann, K. Grützmacher, and B. Wende, “Doppler-free two-photon polarization-spectroscopic measurement of the Stark-broadened profile of the hydrogen Lα line in a dense plasma,” Phys. Rev. Lett. 57, 2151–2153 (1986).
[CrossRef] [PubMed]

Williams, S.

S. Williams, L. A. Rahn, and R. N. Zare, “Effects of different population, orientation, and alignment relaxation rates in resonant four-wave mixing,” J. Chem. Phys. 104, 3947–3955(1996).
[CrossRef]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations I. Weak-field limit,” J. Chem. Phys. 101, 1072–1107 (1994).
[CrossRef]

Zare, R. N.

S. Williams, L. A. Rahn, and R. N. Zare, “Effects of different population, orientation, and alignment relaxation rates in resonant four-wave mixing,” J. Chem. Phys. 104, 3947–3955(1996).
[CrossRef]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations I. Weak-field limit,” J. Chem. Phys. 101, 1072–1107 (1994).
[CrossRef]

C. H. Greene and R. N. Zare, “Determination of product population and alignment using laser-induced fluorescence,” J. Chem. Phys. 78, 6741–6753 (1983).
[CrossRef]

C. H. Greene and R. N. Zare, “Photofragment alignment and orientation,” Annu. Rev. Phys. Chem. 33, 119–150 (1982).
[CrossRef]

R. N. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley, 1988).

A. Orr-Ewing and R. N. Zare, The Chemical Dynamics and Kinetics of Small Radicals (World Scientific, 1995), pp. 936–1063.

Zetterberg, J.

Z. S. Li, M. Rupinski, J. Zetterberg, Z. T. Alwahabi, and M. Alden, “Mid-infrared polarization spectroscopy of polyatomic molecules: Detection of nascent CO2 and H2O in atmospheric pressure flames,” Chem. Phys. Lett. 407, 243–248 (2005).
[CrossRef]

Annu. Rev. Phys. Chem.

C. H. Greene and R. N. Zare, “Photofragment alignment and orientation,” Annu. Rev. Phys. Chem. 33, 119–150 (1982).
[CrossRef]

Appl. Opt.

Appl. Phys. B

M. J. New, P. Ewart, A. Dreizler, and T. Dreier, “Multiplex polarization spectroscopy of OH for flame thermometry,” Appl. Phys. B 65, 633–637 (1997).
[CrossRef]

S. Roy, R. P. Lucht, and A. McIlroy, “Mid-infrared polarization spectroscopy of carbon dioxide,” Appl. Phys. B 75, 875–882(2002).
[CrossRef]

Chem. Phys. Lett.

Z. S. Li, M. Rupinski, J. Zetterberg, Z. T. Alwahabi, and M. Alden, “Mid-infrared polarization spectroscopy of polyatomic molecules: Detection of nascent CO2 and H2O in atmospheric pressure flames,” Chem. Phys. Lett. 407, 243–248 (2005).
[CrossRef]

A. Dreizler, R. Tadday, A. A. Suvernev, M. Himmelhaus, T. Dreier, and P. Foggi, “Measurement of orientational relaxation times of OH in a flame using picosecond time-resolved polarization spectroscopy,” Chem. Phys. Lett. 240, 315–323 (1995).
[CrossRef]

M. P. Auzinsh, “General restrictions for the relaxation constants of the polarization moments of the density matrix,” Chem. Phys. Lett. 198, 305–310 (1992).
[CrossRef]

X. Chen, B. D. Patterson, and T. B. Settersten, “Time-domain investigation of OH ground-state energy transfer using picosecond two-color polarization spectroscopy,” Chem. Phys. Lett. 388, 358–362 (2004).
[CrossRef]

J. Chem. Phys.

M. L. Costen, H. J. Crighton, and K. G. McKendrick, “Measurement of orientation and alignment moment relaxation by polarization spectroscopy: Theory and experiment,” J. Chem. Phys. 120, 7910–7926 (2004).
[CrossRef] [PubMed]

E. Hertz, B. Lavorel, O. Faucher, and R. Chaux, “Femtosecond polarization spectroscopy in molecular gas mixtures: Macroscopic interference and concentration measurements,” J. Chem. Phys. 113, 6629–6633 (2000).
[CrossRef]

J. Tobai, T. Dreier, and J. W. Daily, “Rotational level dependence of ground state recovery rates for OHX2Π(v′′=0) in atmospheric pressure flames using the picosecond saturating-pump degenerate four-wave mixing probe technique,” J. Chem. Phys. 116, 4030–4038 (2002).
[CrossRef]

G. Paterson, S. Marinakis, M. Costen, K. G. McKendrick, J. Klos, and R. Tobola, “Orientation and alignment depolarization in OH(X2Π)+Ar/He collisions,” J. Chem. Phys. 129, 074304(2008).
[CrossRef] [PubMed]

C. H. Greene and R. N. Zare, “Determination of product population and alignment using laser-induced fluorescence,” J. Chem. Phys. 78, 6741–6753 (1983).
[CrossRef]

P. J. Dagdigian and M. H. Alexander, “Dependence of elastic depolarization cross sections on the potential: OH(X2Π)-Ar and NO(X2Π)-Ar,” J. Chem. Phys. 130, 204304 (2009).
[CrossRef] [PubMed]

P. J. Dagdigian and M. H. Alexander, “Tensor cross sections and collisional depolarization of OH(X2Π) in collisions with helium,” J. Chem. Phys. 130, 164315 (2009).
[CrossRef] [PubMed]

P. J. Dagdigian and M. H. Alexander, “Tensor cross sections and the collisional evolution of state multipoles: OH(X2Π)-Ar,” J. Chem. Phys. 130, 094303 (2009).
[CrossRef] [PubMed]

T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, “Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems,” J. Chem. Phys. 108, 7713–7738 (1998).
[CrossRef]

S. Williams, R. N. Zare, and L. A. Rahn, “Reduction of degenerate four-wave mixing spectra to relative populations I. Weak-field limit,” J. Chem. Phys. 101, 1072–1107 (1994).
[CrossRef]

S. Williams, L. A. Rahn, and R. N. Zare, “Effects of different population, orientation, and alignment relaxation rates in resonant four-wave mixing,” J. Chem. Phys. 104, 3947–3955(1996).
[CrossRef]

T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, “Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems,” J. Chem. Phys. 108, 7713–7739 (1998).
[CrossRef]

T. A. Reichardt and R. P. Lucht, “Theoretical calculation of line shapes and saturation effects in polarization spectroscopy,” J. Chem. Phys. 109, 5830–5843 (1998).
[CrossRef]

S. Roy, R. P. Lucht, and T. A. Reichardt, “Polarization spectroscopy using short-pulse lasers: Theoretical analysis,” J. Chem. Phys. 116, 571–580 (2002).
[CrossRef]

T. A. Reichardt, F. D. Teodoro, R. L. Farrow, S. Roy, and R. P. Lucht, “Collisional dependence of polarization spectroscopy with a picosecond laser,” J. Chem. Phys. 113, 2263–2269 (2000).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem. A

M. L. Costen, R. Livingstone, K. G. McKendrick, G. Paterson, M. Brouard, H. Chadwick, Y.-P. Chang, C. J. Eyles, F. J. Aoiz, and J. Klos, “Elastic depolarization of OH(A) by He and Ar: A comparative study,” J. Phys. Chem. A 113, 15156–15170(2009).
[CrossRef] [PubMed]

Laser Phys.

T. Dreier and J. Tobai, “Rotational state resolved measurement of relaxation times and ground state recovery rates in small radicals in atmospheric pressure flames using picosecond pump-probe degenerate four-wave mixing,” Laser Phys. 13, 286–292 (2003).

Opt. Lett.

Phys. Chem. Chem. Phys.

S. Marinakis, G. Paterson, J. Klos, M. L. Costen, and K. G. McKendrick, “Inelastic scattering of OH(X2Π) with Ar and He: A combined polarization spectroscopy and quantum scattering study,” Phys. Chem. Chem. Phys. 9, 4414–4426 (2007).
[CrossRef] [PubMed]

Phys. Rev. Lett.

K. Danzmann, K. Grützmacher, and B. Wende, “Doppler-free two-photon polarization-spectroscopic measurement of the Stark-broadened profile of the hydrogen Lα line in a dense plasma,” Phys. Rev. Lett. 57, 2151–2153 (1986).
[CrossRef] [PubMed]

Proc. SPIE

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” Proc. SPIE 113, 80–87 (1977).

Rev. Mod. Phys.

U. Fano and J. H. Macek, “Impact excitation and polarization of the emitted light,” Rev. Mod. Phys. 45, 553–573 (1973).
[CrossRef]

Other

R. N. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley, 1988).

A. Orr-Ewing and R. N. Zare, The Chemical Dynamics and Kinetics of Small Radicals (World Scientific, 1995), pp. 936–1063.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Gordon and Breach, 1996), p. 511.

M. Sargent III, M. O. Scully, and W. E. Lamb Jr., Laser Physics (Addison-Wesley, 1997).

K. Blum, Density Matrix Theory and Applications (Plenum Press, 1981).

W. Demtröder, Laser Spectroscopy (Springer, 1996), pp. 454–466.

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Figures (18)

Fig. 1
Fig. 1

Geometry of LIPS signal-generation process.

Fig. 2
Fig. 2

Energy-level diagram for the Zeeman-state structure of the P 1 ( 2 ) transition. Allowed Δ M = 0 transitions are indicated by dashed arrows; Δ M = ± 1 transitions are indicated by solid arrows. Strengths and phases of the transitions are indicated by the numerical value of the x or z components of the geometry-dependent part of the dipole matrix element μ G .

Fig. 3
Fig. 3

Population distribution in the (a) ground Zeeman states at t = 0 sec and (b) excited Zeeman states for the P 1 ( 2 ) transition of OH pumped by a circularly polarized beam. ρ g g 0 is the ground-state population at t = 0 sec .

Fig. 4
Fig. 4

Temporal profiles of the orientation and alignment of the (a) ground level ( J g = 2.5 ) and (b) excited level ( J e = 1.5 ) for the P 1 ( 2 ) transition pumped by a circularly polarized beam. LIPS signal is shown for reference. The intensity of the pump beam is 5 × 10 8 W / m 2 .

Fig. 5
Fig. 5

(a) Population distribution in the excited Zeeman states, (b) temporal profiles of the various moments for the ground level, and (c) temporal profiles of the various moments at the excited level along with the LIPS signal for the P 1 ( 2 ) transition pumped by a linearly polarized beam. The intensity of the pump beam is 5 × 10 8 W / m 2 .

Fig. 6
Fig. 6

Population distribution in the excited Zeeman states for the Q 1 ( 2 ) transition pumped by (a) a linearly polarized beam and (b) a right circularly polarized beam. ρ g g 0 is the ground-state population at t = 0 sec .

Fig. 7
Fig. 7

Temporal profiles of the orientation and the alignment of the excited state for the Q 1 ( 2 ) transition for (a) a linearly polarized pump beam and (b) a right circularly polarized pump beam.

Fig. 8
Fig. 8

Temporal profiles of the LIPS signal for the P 1 ( 8 ) transition pumped by a circularly and linearly polarized pump beam. The intensity of the pump beam is 5 × 10 9 W / m 2 .

Fig. 9
Fig. 9

Population distribution in the excited Zeeman states for the P 1 ( 8 ) transition pumped by (a) a right circularly polarized beam and (b) a linearly polarized beam. ρ g g 0 is the ground-state population at t = 0 sec .

Fig. 10
Fig. 10

Temporal profiles of the orientation and the alignment of the excited state for the P 1 ( 8 ) transition for (a) a right circularly polarized pump beam and (b) a linearly polarized pump beam.

Fig. 11
Fig. 11

Temporal profiles of the LIPS signal for the P 1 ( 2 ) transition pumped by a circularly polarized beam for different intensities.

Fig. 12
Fig. 12

(a) Temporal profiles of the orientation, alignment, and octopole moments of the excited level and (b) population distribution in the excited Zeeman states for the P 1 ( 2 ) transition pumped by a right circularly polarized beam at 5 × 10 9 W / m 2 to 10 10 W / m 2 .

Fig. 13
Fig. 13

Temporal profiles of the orientation, alignment, and octopole moments of the excited state for the P 1 ( 2 ) transition pumped by a right circularly polarized beam at 5 × 10 10 W / m 2 . The LIPS signal is shown for reference.

Fig. 14
Fig. 14

(a) Excited-state population distribution and (b) temporal profiles of orientation, alignment, and octopole moments for the P 1 ( 2 ) transition pumped by a circularly polarized light with an intensity of 10 11 W / m 2 .

Fig. 15
Fig. 15

The (a) aligned, (b) LCP-oriented, and (c) RCP-oriented population distribution among the ground Zeeman states at t = 0 sec . These three initial population distributions are considered to investigate the effect of preexisting anisotropy on the LIPS signal.

Fig. 16
Fig. 16

LIPS signals for the P 1 ( 2 ) transition pumped by a circularly polarized beam where the initial ground-level population distribution is isotropic, aligned, or oriented.

Fig. 17
Fig. 17

Temporal profiles of the excited-level orientation and alignment for the P 1 ( 2 ) transition pumped by a circularly polarized beam, where the initial ground-level population is (a) aligned, (b) LCP oriented, and (c) RCP oriented. The LIPS signal is shown for reference.

Fig. 18
Fig. 18

Temporal profiles of the (a) real and (b) imaginary components of ( μ e g σ g e ) multiplied by the appropriate phase factor exp [ i ( k z y ω t ) ] along the + y axis for the Δ M = + 1 transitions with LCP-oriented ground-level anisotropy.

Equations (17)

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ρ k k ( r , t ) t = i m ( V k m ( r , t ) ρ m k ( r , t ) ρ k m ( r , t ) V m k ( r , t ) ) Γ k ρ k k ( r , t ) + m Γ m k ρ m m ( r , t ) ,
ρ k j ( r , t ) t = ρ k j ( r , t ) ( i ω k j + γ k j ) i m ( V k m ( r , t ) ρ m j ( r , t ) ρ k m ( r , t ) V m j ( r , t ) ) ,
V k m ( r , t ) = μ k m . E ( r , t ) = μ k m . [ E pump ( r , t ) + E pr ( r , t ) ] ,
P ( y , t ) = 1 2 ( Tr [ ρ ( y , t ) μ ] + Tr [ μ ρ ( y , t ) ] ) = 1 2 p k [ μ p k ρ k p ( y , t ) + μ k p ρ p k ( y , t ) ] = 1 2 p k [ μ p k σ k p ( y , t ) exp ( i ω t ) + μ k p σ p k ( y , t ) exp ( i ω t ) ] ,
A 3 ( t ) = m = 1 m = M P ( y = m Δ y , t ) exp [ i ( k y y ω t ) ] .
S 3 = 0 4 t pulse { [ A 3 r ( t ) ] 2 + [ A 3 i ( t ) ] 2 } d t ,
μ e g = ( α e , J e , M e | μ | α g , J g , M g ) = μ R ( α e J e , α g J g ) μ G ( J e M e , J g M g ) ,
μ R ( α e J e , α g J g ) = A e g Γ ( J e , J g ) 3 ε 0 λ e g 3 8 π 2 ,
Γ ( J e , J e + 1 ) = ( J e + 1 ) ( 2 J e + 3 ) Γ ( J e , J e ) = J e ( J e + 1 ) Γ ( J e , J e + 1 ) = J e ( 2 J e 1 ) .
μ G ( J e M e , J e + 1 M e + 1 ) = 1 2 ( J e + M e + 1 ) ( J e + M e + 2 ) ( x ^ + i y ^ ) μ G ( J e M e , J e + 1 M e 1 ) = 1 2 ( J e M e + 1 ) ( J e M e + 2 ) ( x ^ i y ^ ) μ G ( J e M e , J e + 1 M e ) = 1 2 ( J e + 1 ) 2 ( M e ) 2 z ^ .
ρ = J J M M J M | ρ | J M | J M J M | .
ρ = J J K Q [ M M J M | ρ | J M ( 1 ) J M ( J M J M K Q ) × ( 2 K + 1 ) 1 / 2 ] T ( J J ) K Q ,
T ( J J ) K Q = M M ( 1 ) J M ( 2 K + 1 ) 1 / 2 ( J M J M K Q ) × J M | ρ | J M .
ρ K Q = T K Q T r [ ρ ] .
T 00 = ( 0.41 0.41 0.41 0.41 0.41 0.41 ) , T 10 = ( 0.60 0.36 0.12 0.12 0.36 0.60 ) , T 20 = ( 0.55 0.11 0.44 0.44 0.11 0.55 ) , T 30 = ( 0.37 0.52 0.30 0.30 0.52 0.37 ) , T 40 = ( 0.19 0.57 0.38 0.38 0.57 0.19 ) , and T 50 = ( 0.06 0.32 0.63 0.63 0.32 0.06 ) .
T 00 = ( 0.5 0.5 0.5 0.5 ) , T 10 = ( 0.67 0.22 0.22 0.67 ) , T 20 = ( 0.5 0.5 0.5 0.5 ) , and T 30 = ( 0.22 0.67 0.67 0.22 ) .
Orientation J = 2.5 = 0.6 * ( ρ M = 2.5 + ρ M = 2.5 ) + 0.36 * ( ρ M = 1.5 + ρ M = 1.5 ) + 0.12 * ( ρ M = 0.5 + ρ M = 0.5 ) , Orientation J = 1.5 = 0.67 * ( ρ M = 1.5 + ρ M = 1.5 ) + 0.22 * ( ρ M = 0.5 + ρ M = 0.5 ) , Alignment J = 2.5 = 0.55 * ( ρ M = 2.5 + ρ M = 2.5 ) 0.11 * ( ρ M = 1.5 + ρ M = 1.5 ) 0.44 * ( ρ M = 0.5 + ρ M = 0.5 ) , Alignment J = 1.5 = 0.50 * ( ρ M = 1.5 + ρ M = 1.5 ) 0.50 * ( ρ M = 0.5 + ρ M = 0.5 ) , Octopole J = 2.5 = 0.37 * ( ρ M = 2.5 + ρ M = 2.5 ) + 0.52 * ( ρ M = 1.5 ρ M = 1.5 ) + 0.30 * ( ρ M = 0.5 ρ M = 0.5 ) , Octopole J = 1.5 = 0.22 * ( ρ M = 1.5 + ρ M = 1.5 ) + 0.67 * ( ρ M = 0.5 ρ M = 0.5 ) .

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