Abstract

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.

© 2000 Optical Society of America

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2000 (1)

1999 (1)

1998 (1)

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]

1997 (2)

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]

R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a near-adiabatic, surface-mixing (Hencken) burner,” Combust. Flame 109, 323–331 (1997).
[CrossRef]

1996 (1)

C. F. Kaminski, B. Löfstedt, R. Fritzon, and M. Aldén, “Two-photon polarization spectroscopy and (2+3)-photon laser induced fluorescence of N2,” Opt. Commun. 129, 38–43 (1996).
[CrossRef]

1995 (2)

R. Dux, K. Grutzmacher, M. I. de la Rosa, and B. Wende, “Absolute determination of local ground-state densities of atomic hydrogen in nonlocal-thermodynamic-equilibrium environments by two-photon polarization spectroscopy,” Phys. Rev. E 51, 1416–1427 (1995).
[CrossRef]

K. Nyholm, R. Fritzon, N. Georgiev, and M. Aldén, “Two-photon induced polarization spectroscopy applied to the detection of NH3 and CO molecules in cold flows and flames,” Opt. Commun. 114, 76–82 (1995).
[CrossRef]

1994 (3)

E. J. Friedman-Hill, L. A. Rahn, and R. L. Farrow, “On the interpretation and rotational assignment of degenerate four-wave mixing spectra: four-photon line strengths for crossover resonances in NO A2Σ+–X2Π,” J. Chem. Phys. 100, 4065–4076 (1994).
[CrossRef]

K. Nyholm, R. Fritzon, and M. Aldén, “Single-pulse two-dimensional imaging in flames by degenerate four-wave mixing and polarization spectroscopy,” Appl. Phys. B 59, 37–43 (1994).
[CrossRef]

K. Nyholm, “Measurements of OH rotational temperature in flames by using polarization spectroscopy,” Opt. Commun. 111, 66–70 (1994).
[CrossRef]

1993 (2)

1992 (3)

T. T. Kajava, H. M. Lauranto, and R. R. E. Salomaa, “Mode structure fluctuations in a pulsed dye laser,” Appl. Opt. 31, 6987–6992 (1992).
[CrossRef] [PubMed]

R. P. Lucht, R. Trebino, and L. A. Rahn, “Resonant multiwave mixing spectra of gas-phase sodium: nonperturbative calculations,” Phys. Rev. A 45, 8209–8227 (1992).
[CrossRef] [PubMed]

R. L. Farrow and D. J. Rakestraw, “Detection of trace molecular species using degenerate four-wave mixing,” Science 257, 1894–1900 (1992).
[CrossRef] [PubMed]

1989 (1)

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[CrossRef] [PubMed]

1987 (1)

1986 (1)

1985 (2)

D. A. Greenhalgh and S. T. Whittley, “Mode noise in broadband CARS spectroscopy,” Appl. Opt. 24, 907–913 (1985).
[CrossRef] [PubMed]

G. Alber, J. Cooper, and P. Ewart, “Theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 31, 2344–2352 (1985).
[CrossRef] [PubMed]

1984 (1)

1983 (1)

W. Ernst, “Doppler-free polarization spectroscopy of diatomic molecules in flame reactions,” Opt. Commun. 44, 159–164 (1983).
[CrossRef]

1982 (1)

M. Raab, G. Höning, W. Demtröder, and C. R. Vidal, “High resolution laser spectroscopy of CS2,” J. Chem. Phys. 76, 4370–4386 (1982).
[CrossRef]

1981 (1)

V. Baev, G. Gaida, H. Schröder, and P. E. Toschek, “Quantum fluctuations of a multimode laser oscillator,” Opt. Commun. 38, 309–313 (1981).
[CrossRef]

1980 (2)

N. K. Dutta, “Two-photon resonant four-wave mixing with nonmonochromatic waves,” J. Phys. B 13, 411–426 (1980).
[CrossRef]

V. R. Mironenko and V. I. Yudson, “Quantum noise in intracavity laser spectroscopy,” Opt. Commun. 34, 397–403 (1980).
[CrossRef]

1979 (2)

M. Raab, G. Höning, R. Castell, and W. Demtröder, “Doppler-free polarization spectroscopy of the CS2 molecule at λ=6270 Å,” Chem. Phys. Lett. 66, 307–312 (1979).
[CrossRef]

N. K. Dutta, “Effect of pump fluctuations on second harmonic generation and parametric amplifications,” Opt. Quantum Electron. 11, 217–222 (1979).
[CrossRef]

1978 (2)

V. Stert and R. Fischer, “Doppler-free polarization spectroscopy using linearly polarized light,” Appl. Phys. 17, 151–154 (1978).
[CrossRef]

H. Gerhardt, T. Huhle, J. Neukammer, and P. J. West, “High resolution polarization spectroscopy of the 557 nm transition of Kr I,” Opt. Commun. 26, 58–61 (1978).
[CrossRef]

1977 (1)

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” in Advances in Laser Spectroscopy I, A. H. Zewail, ed., Proc. SPIE 113, 80–87 (1977).
[CrossRef]

1976 (1)

C. Wieman and T. W. Hänsch, “Doppler-free polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[CrossRef]

Alber, G.

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[CrossRef] [PubMed]

G. Alber, J. Cooper, and P. Ewart, “Theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 31, 2344–2352 (1985).
[CrossRef] [PubMed]

Alden, M.

Aldén, M.

C. F. Kaminski, B. Löfstedt, R. Fritzon, and M. Aldén, “Two-photon polarization spectroscopy and (2+3)-photon laser induced fluorescence of N2,” Opt. Commun. 129, 38–43 (1996).
[CrossRef]

K. Nyholm, R. Fritzon, N. Georgiev, and M. Aldén, “Two-photon induced polarization spectroscopy applied to the detection of NH3 and CO molecules in cold flows and flames,” Opt. Commun. 114, 76–82 (1995).
[CrossRef]

K. Nyholm, R. Fritzon, and M. Aldén, “Single-pulse two-dimensional imaging in flames by degenerate four-wave mixing and polarization spectroscopy,” Appl. Phys. B 59, 37–43 (1994).
[CrossRef]

Aminoff, C. G.

Baev, V.

V. Baev, G. Gaida, H. Schröder, and P. E. Toschek, “Quantum fluctuations of a multimode laser oscillator,” Opt. Commun. 38, 309–313 (1981).
[CrossRef]

Berglind, T.

Bertagnolli, K. E.

R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a near-adiabatic, surface-mixing (Hencken) burner,” Combust. Flame 109, 323–331 (1997).
[CrossRef]

Carlson, N.

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” in Advances in Laser Spectroscopy I, A. H. Zewail, ed., Proc. SPIE 113, 80–87 (1977).
[CrossRef]

Castell, R.

M. Raab, G. Höning, R. Castell, and W. Demtröder, “Doppler-free polarization spectroscopy of the CS2 molecule at λ=6270 Å,” Chem. Phys. Lett. 66, 307–312 (1979).
[CrossRef]

Charlton, A.

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[CrossRef] [PubMed]

Cooper, J.

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[CrossRef] [PubMed]

G. Alber, J. Cooper, and P. Ewart, “Theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 31, 2344–2352 (1985).
[CrossRef] [PubMed]

de la Rosa, M. I.

R. Dux, K. Grutzmacher, M. I. de la Rosa, and B. Wende, “Absolute determination of local ground-state densities of atomic hydrogen in nonlocal-thermodynamic-equilibrium environments by two-photon polarization spectroscopy,” Phys. Rev. E 51, 1416–1427 (1995).
[CrossRef]

Demtröder, W.

M. Raab, G. Höning, W. Demtröder, and C. R. Vidal, “High resolution laser spectroscopy of CS2,” J. Chem. Phys. 76, 4370–4386 (1982).
[CrossRef]

M. Raab, G. Höning, R. Castell, and W. Demtröder, “Doppler-free polarization spectroscopy of the CS2 molecule at λ=6270 Å,” Chem. Phys. Lett. 66, 307–312 (1979).
[CrossRef]

Dreier, T.

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]

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]

Dutta, N. K.

N. K. Dutta, “Two-photon resonant four-wave mixing with nonmonochromatic waves,” J. Phys. B 13, 411–426 (1980).
[CrossRef]

N. K. Dutta, “Effect of pump fluctuations on second harmonic generation and parametric amplifications,” Opt. Quantum Electron. 11, 217–222 (1979).
[CrossRef]

Dux, R.

R. Dux, K. Grutzmacher, M. I. de la Rosa, and B. Wende, “Absolute determination of local ground-state densities of atomic hydrogen in nonlocal-thermodynamic-equilibrium environments by two-photon polarization spectroscopy,” Phys. Rev. E 51, 1416–1427 (1995).
[CrossRef]

Ernst, W.

W. Ernst, “Doppler-free polarization spectroscopy of diatomic molecules in flame reactions,” Opt. Commun. 44, 159–164 (1983).
[CrossRef]

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]

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[CrossRef] [PubMed]

G. Alber, J. Cooper, and P. Ewart, “Theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 31, 2344–2352 (1985).
[CrossRef] [PubMed]

Farrow, R. L.

E. J. Friedman-Hill, L. A. Rahn, and R. L. Farrow, “On the interpretation and rotational assignment of degenerate four-wave mixing spectra: four-photon line strengths for crossover resonances in NO A2Σ+–X2Π,” J. Chem. Phys. 100, 4065–4076 (1994).
[CrossRef]

R. P. Lucht, R. L. Farrow, and D. J. Rakestraw, “Saturation effects in gas-phase degenerate four-wave mixing spectroscopy: nonperturbative calculations,” J. Opt. Soc. Am. B 10, 1508–1520 (1993).
[CrossRef]

R. L. Farrow and D. J. Rakestraw, “Detection of trace molecular species using degenerate four-wave mixing,” Science 257, 1894–1900 (1992).
[CrossRef] [PubMed]

Fischer, R.

V. Stert and R. Fischer, “Doppler-free polarization spectroscopy using linearly polarized light,” Appl. Phys. 17, 151–154 (1978).
[CrossRef]

Friedman-Hill, E. J.

E. J. Friedman-Hill, L. A. Rahn, and R. L. Farrow, “On the interpretation and rotational assignment of degenerate four-wave mixing spectra: four-photon line strengths for crossover resonances in NO A2Σ+–X2Π,” J. Chem. Phys. 100, 4065–4076 (1994).
[CrossRef]

Fritzon, R.

C. F. Kaminski, B. Löfstedt, R. Fritzon, and M. Aldén, “Two-photon polarization spectroscopy and (2+3)-photon laser induced fluorescence of N2,” Opt. Commun. 129, 38–43 (1996).
[CrossRef]

K. Nyholm, R. Fritzon, N. Georgiev, and M. Aldén, “Two-photon induced polarization spectroscopy applied to the detection of NH3 and CO molecules in cold flows and flames,” Opt. Commun. 114, 76–82 (1995).
[CrossRef]

K. Nyholm, R. Fritzon, and M. Aldén, “Single-pulse two-dimensional imaging in flames by degenerate four-wave mixing and polarization spectroscopy,” Appl. Phys. B 59, 37–43 (1994).
[CrossRef]

Gaida, G.

V. Baev, G. Gaida, H. Schröder, and P. E. Toschek, “Quantum fluctuations of a multimode laser oscillator,” Opt. Commun. 38, 309–313 (1981).
[CrossRef]

Georgiev, N.

K. Nyholm, R. Fritzon, N. Georgiev, and M. Aldén, “Two-photon induced polarization spectroscopy applied to the detection of NH3 and CO molecules in cold flows and flames,” Opt. Commun. 114, 76–82 (1995).
[CrossRef]

Gerhardt, H.

H. Gerhardt, T. Huhle, J. Neukammer, and P. J. West, “High resolution polarization spectroscopy of the 557 nm transition of Kr I,” Opt. Commun. 26, 58–61 (1978).
[CrossRef]

Giancola, W. C.

Greenhalgh, D. A.

Grutzmacher, K.

R. Dux, K. Grutzmacher, M. I. de la Rosa, and B. Wende, “Absolute determination of local ground-state densities of atomic hydrogen in nonlocal-thermodynamic-equilibrium environments by two-photon polarization spectroscopy,” Phys. Rev. E 51, 1416–1427 (1995).
[CrossRef]

Hall, R. J.

Hancock, R. D.

R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a near-adiabatic, surface-mixing (Hencken) burner,” Combust. Flame 109, 323–331 (1997).
[CrossRef]

Hänsch, T. W.

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” in Advances in Laser Spectroscopy I, A. H. Zewail, ed., Proc. SPIE 113, 80–87 (1977).
[CrossRef]

C. Wieman and T. W. Hänsch, “Doppler-free polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[CrossRef]

Hill, W. T.

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” in Advances in Laser Spectroscopy I, A. H. Zewail, ed., Proc. SPIE 113, 80–87 (1977).
[CrossRef]

Höning, G.

M. Raab, G. Höning, W. Demtröder, and C. R. Vidal, “High resolution laser spectroscopy of CS2,” J. Chem. Phys. 76, 4370–4386 (1982).
[CrossRef]

M. Raab, G. Höning, R. Castell, and W. Demtröder, “Doppler-free polarization spectroscopy of the CS2 molecule at λ=6270 Å,” Chem. Phys. Lett. 66, 307–312 (1979).
[CrossRef]

Huhle, T.

H. Gerhardt, T. Huhle, J. Neukammer, and P. J. West, “High resolution polarization spectroscopy of the 557 nm transition of Kr I,” Opt. Commun. 26, 58–61 (1978).
[CrossRef]

Kaivola, M.

Kajava, T. T.

Kaminski, C. F.

C. F. Kaminski, B. Löfstedt, R. Fritzon, and M. Aldén, “Two-photon polarization spectroscopy and (2+3)-photon laser induced fluorescence of N2,” Opt. Commun. 129, 38–43 (1996).
[CrossRef]

Kowalski, F. V.

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” in Advances in Laser Spectroscopy I, A. H. Zewail, ed., Proc. SPIE 113, 80–87 (1977).
[CrossRef]

Kroll, S.

Lanauze, J.

Lauranto, H. M.

Löfstedt, B.

C. F. Kaminski, B. Löfstedt, R. Fritzon, and M. Aldén, “Two-photon polarization spectroscopy and (2+3)-photon laser induced fluorescence of N2,” Opt. Commun. 129, 38–43 (1996).
[CrossRef]

Lucht, R. P.

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, W. C. Giancola, C. M. Shappert, and R. P. Lucht, “Experimental investigation of saturated degenerate four-wave mixing for quantitative concentration measurements,” Appl. Opt. 38, 6951–6961 (1999).
[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]

R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a near-adiabatic, surface-mixing (Hencken) burner,” Combust. Flame 109, 323–331 (1997).
[CrossRef]

R. P. Lucht, R. L. Farrow, and D. J. Rakestraw, “Saturation effects in gas-phase degenerate four-wave mixing spectroscopy: nonperturbative calculations,” J. Opt. Soc. Am. B 10, 1508–1520 (1993).
[CrossRef]

R. P. Lucht, R. Trebino, and L. A. Rahn, “Resonant multiwave mixing spectra of gas-phase sodium: nonperturbative calculations,” Phys. Rev. A 45, 8209–8227 (1992).
[CrossRef] [PubMed]

Maier, R.

Meacher, D. R.

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[CrossRef] [PubMed]

Mironenko, V. R.

V. R. Mironenko and V. I. Yudson, “Quantum noise in intracavity laser spectroscopy,” Opt. Commun. 34, 397–403 (1980).
[CrossRef]

Neukammer, J.

H. Gerhardt, T. Huhle, J. Neukammer, and P. J. West, “High resolution polarization spectroscopy of the 557 nm transition of Kr I,” Opt. Commun. 26, 58–61 (1978).
[CrossRef]

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.

K. Nyholm, R. Fritzon, N. Georgiev, and M. Aldén, “Two-photon induced polarization spectroscopy applied to the detection of NH3 and CO molecules in cold flows and flames,” Opt. Commun. 114, 76–82 (1995).
[CrossRef]

K. Nyholm, “Measurements of OH rotational temperature in flames by using polarization spectroscopy,” Opt. Commun. 111, 66–70 (1994).
[CrossRef]

K. Nyholm, R. Fritzon, and M. Aldén, “Single-pulse two-dimensional imaging in flames by degenerate four-wave mixing and polarization spectroscopy,” Appl. Phys. B 59, 37–43 (1994).
[CrossRef]

K. Nyholm, R. Maier, C. G. Aminoff, and M. Kaivola, “Detection of OH in flames by using polarization spectroscopy,” Appl. Opt. 32, 919–924 (1993).
[CrossRef] [PubMed]

Raab, M.

M. Raab, G. Höning, W. Demtröder, and C. R. Vidal, “High resolution laser spectroscopy of CS2,” J. Chem. Phys. 76, 4370–4386 (1982).
[CrossRef]

M. Raab, G. Höning, R. Castell, and W. Demtröder, “Doppler-free polarization spectroscopy of the CS2 molecule at λ=6270 Å,” Chem. Phys. Lett. 66, 307–312 (1979).
[CrossRef]

Rahn, L. A.

E. J. Friedman-Hill, L. A. Rahn, and R. L. Farrow, “On the interpretation and rotational assignment of degenerate four-wave mixing spectra: four-photon line strengths for crossover resonances in NO A2Σ+–X2Π,” J. Chem. Phys. 100, 4065–4076 (1994).
[CrossRef]

R. P. Lucht, R. Trebino, and L. A. Rahn, “Resonant multiwave mixing spectra of gas-phase sodium: nonperturbative calculations,” Phys. Rev. A 45, 8209–8227 (1992).
[CrossRef] [PubMed]

Rakestraw, D. J.

Raymer, M. G.

Reichardt, T. A.

Salomaa, R. R. E.

Schröder, H.

V. Baev, G. Gaida, H. Schröder, and P. E. Toschek, “Quantum fluctuations of a multimode laser oscillator,” Opt. Commun. 38, 309–313 (1981).
[CrossRef]

Shappert, C. M.

Snyder, J. J.

Stert, V.

V. Stert and R. Fischer, “Doppler-free polarization spectroscopy using linearly polarized light,” Appl. Phys. 17, 151–154 (1978).
[CrossRef]

Teets, R. E.

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” in Advances in Laser Spectroscopy I, A. H. Zewail, ed., Proc. SPIE 113, 80–87 (1977).
[CrossRef]

Toschek, P. E.

V. Baev, G. Gaida, H. Schröder, and P. E. Toschek, “Quantum fluctuations of a multimode laser oscillator,” Opt. Commun. 38, 309–313 (1981).
[CrossRef]

Trebino, R.

R. P. Lucht, R. Trebino, and L. A. Rahn, “Resonant multiwave mixing spectra of gas-phase sodium: nonperturbative calculations,” Phys. Rev. A 45, 8209–8227 (1992).
[CrossRef] [PubMed]

Vidal, C. R.

M. Raab, G. Höning, W. Demtröder, and C. R. Vidal, “High resolution laser spectroscopy of CS2,” J. Chem. Phys. 76, 4370–4386 (1982).
[CrossRef]

Wende, B.

R. Dux, K. Grutzmacher, M. I. de la Rosa, and B. Wende, “Absolute determination of local ground-state densities of atomic hydrogen in nonlocal-thermodynamic-equilibrium environments by two-photon polarization spectroscopy,” Phys. Rev. E 51, 1416–1427 (1995).
[CrossRef]

West, P. J.

H. Gerhardt, T. Huhle, J. Neukammer, and P. J. West, “High resolution polarization spectroscopy of the 557 nm transition of Kr I,” Opt. Commun. 26, 58–61 (1978).
[CrossRef]

Westling, L. A.

Whittley, S. T.

Wieman, C.

C. Wieman and T. W. Hänsch, “Doppler-free polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[CrossRef]

Winefordner, J. D.

Yudson, V. I.

V. R. Mironenko and V. I. Yudson, “Quantum noise in intracavity laser spectroscopy,” Opt. Commun. 34, 397–403 (1980).
[CrossRef]

Zizak, G.

Appl. Opt. (7)

Appl. Phys. (1)

V. Stert and R. Fischer, “Doppler-free polarization spectroscopy using linearly polarized light,” Appl. Phys. 17, 151–154 (1978).
[CrossRef]

Appl. Phys. B (2)

K. Nyholm, R. Fritzon, and M. Aldén, “Single-pulse two-dimensional imaging in flames by degenerate four-wave mixing and polarization spectroscopy,” Appl. Phys. B 59, 37–43 (1994).
[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]

Chem. Phys. Lett. (1)

M. Raab, G. Höning, R. Castell, and W. Demtröder, “Doppler-free polarization spectroscopy of the CS2 molecule at λ=6270 Å,” Chem. Phys. Lett. 66, 307–312 (1979).
[CrossRef]

Combust. Flame (1)

R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a near-adiabatic, surface-mixing (Hencken) burner,” Combust. Flame 109, 323–331 (1997).
[CrossRef]

J. Chem. Phys. (3)

M. Raab, G. Höning, W. Demtröder, and C. R. Vidal, “High resolution laser spectroscopy of CS2,” J. Chem. Phys. 76, 4370–4386 (1982).
[CrossRef]

E. J. Friedman-Hill, L. A. Rahn, and R. L. Farrow, “On the interpretation and rotational assignment of degenerate four-wave mixing spectra: four-photon line strengths for crossover resonances in NO A2Σ+–X2Π,” J. Chem. Phys. 100, 4065–4076 (1994).
[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]

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

N. K. Dutta, “Two-photon resonant four-wave mixing with nonmonochromatic waves,” J. Phys. B 13, 411–426 (1980).
[CrossRef]

Opt. Commun. (7)

V. R. Mironenko and V. I. Yudson, “Quantum noise in intracavity laser spectroscopy,” Opt. Commun. 34, 397–403 (1980).
[CrossRef]

V. Baev, G. Gaida, H. Schröder, and P. E. Toschek, “Quantum fluctuations of a multimode laser oscillator,” Opt. Commun. 38, 309–313 (1981).
[CrossRef]

W. Ernst, “Doppler-free polarization spectroscopy of diatomic molecules in flame reactions,” Opt. Commun. 44, 159–164 (1983).
[CrossRef]

K. Nyholm, “Measurements of OH rotational temperature in flames by using polarization spectroscopy,” Opt. Commun. 111, 66–70 (1994).
[CrossRef]

K. Nyholm, R. Fritzon, N. Georgiev, and M. Aldén, “Two-photon induced polarization spectroscopy applied to the detection of NH3 and CO molecules in cold flows and flames,” Opt. Commun. 114, 76–82 (1995).
[CrossRef]

C. F. Kaminski, B. Löfstedt, R. Fritzon, and M. Aldén, “Two-photon polarization spectroscopy and (2+3)-photon laser induced fluorescence of N2,” Opt. Commun. 129, 38–43 (1996).
[CrossRef]

H. Gerhardt, T. Huhle, J. Neukammer, and P. J. West, “High resolution polarization spectroscopy of the 557 nm transition of Kr I,” Opt. Commun. 26, 58–61 (1978).
[CrossRef]

Opt. Quantum Electron. (1)

N. K. Dutta, “Effect of pump fluctuations on second harmonic generation and parametric amplifications,” Opt. Quantum Electron. 11, 217–222 (1979).
[CrossRef]

Phys. Rev. A (3)

R. P. Lucht, R. Trebino, and L. A. Rahn, “Resonant multiwave mixing spectra of gas-phase sodium: nonperturbative calculations,” Phys. Rev. A 45, 8209–8227 (1992).
[CrossRef] [PubMed]

G. Alber, J. Cooper, and P. Ewart, “Theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 31, 2344–2352 (1985).
[CrossRef] [PubMed]

J. Cooper, A. Charlton, D. R. Meacher, P. Ewart, and G. Alber, “Revised theory of resonant degenerate four-wave mixing with broad-bandwidth lasers,” Phys. Rev. A 40, 5705–5715 (1989).
[CrossRef] [PubMed]

Phys. Rev. E (1)

R. Dux, K. Grutzmacher, M. I. de la Rosa, and B. Wende, “Absolute determination of local ground-state densities of atomic hydrogen in nonlocal-thermodynamic-equilibrium environments by two-photon polarization spectroscopy,” Phys. Rev. E 51, 1416–1427 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

C. Wieman and T. W. Hänsch, “Doppler-free polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[CrossRef]

Proc. SPIE (1)

R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser polarization spectroscopy,” in Advances in Laser Spectroscopy I, A. H. Zewail, ed., Proc. SPIE 113, 80–87 (1977).
[CrossRef]

Science (1)

R. L. Farrow and D. J. Rakestraw, “Detection of trace molecular species using degenerate four-wave mixing,” Science 257, 1894–1900 (1992).
[CrossRef] [PubMed]

Other (10)

R. L. Vander Wal, R. L. Farrow, and D. J. Rakestraw, “High-resolution investigation of degenerate four-wave mixing in the γ(0, 0) band of nitric oxide,” in Twenty-Fourth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pennsylvania, 1993), pp. 1653–1659.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, New York, 1988).

R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992).

W. Demtröder, Laser Spectroscopy (Springer-Verlag, New York, 1996), pp. 454–466.

S. Gordon and B. J. McBride, “Computer program for calculation of complex chemical equilibrium compositions, rocket performance, incident and reflected shocks, and Chapman–Jouguet detonations,” NASA Rep. SP-273 (NASA Glenn Research Center, Cleveland, Ohio, 1976).

E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University, New York, 1951).

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990), Vols. 1 and 2.

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass., 1977).

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of a polarization-spectroscopy experiment. The pump and the probe beams are nearly counterpropagating, and the pump beam is circularly polarized.

Fig. 2
Fig. 2

Schematic diagram of the energy-level structure incorporated in the DNI calculations. The R(1) transition is shown as an example. The solid lines indicate the preferential coupling of the Zeeman states for which ΔM=Ma-Mb=+1 by the circularly polarized pump beams. The dashed lines indicate coupling of levels by collisional transfer.

Fig. 3
Fig. 3

Laser intensity as a function of time for a multiaxial-mode laser pulse. The number of modes included is 25, and the mode spacing is 0.025 cm-1. The laser linewidth for the pulse is 0.2 cm-1.

Fig. 4
Fig. 4

Effect of collisional broadening on the linewidth of the PS line shape for a fixed laser linewidth. Eleven modes are included in the multimode (MM) calculations. The solid, dotted, and dashed curves are the result of single-mode (SM) calculations.

Fig. 5
Fig. 5

Effect of the laser linewidth on the linewidth of the PS line shape for a fixed collisional linewidth. Eleven modes are included in the multimode (MM) calculations. The solid curve is the result of single-mode (SM) calculations.

Fig. 6
Fig. 6

Effect of the saturation on the linewidth of the PS line shape for fixed collisional and laser linewidth. Twenty-one modes are included in the multimode (MM) calculations.

Fig. 7
Fig. 7

Saturation curves for various values of the collisional linewidth and for a fixed value of the laser linewidth. Twenty-one modes are included in the multimode (MM) calculations. The solid, dotted, and dashed curves are the result of single-mode (SM) calculations.

Fig. 8
Fig. 8

Saturation curves for various values of the laser linewidth and for a fixed value of the collisional linewidth. Twenty-one modes are included in the multimode (MM) calculations.

Fig. 9
Fig. 9

Experimental absorption curve for the Q1(8) transition of OH from a lean hydrogen–air flame. The solid curve is a theoretical fit to the experimental absorption curve assuming a Lorentzian laser line shape with a linewidth of 0.2 cm-1.

Fig. 10
Fig. 10

Comparison of measured and calculated PS line shapes for the P1(2) resonance for (a) low pump laser power and (b) high pump laser power.

Fig. 11
Fig. 11

Comparison of measured and calculated PS saturation curves for the P1(2) resonance. The experimental measurements were binned and averaged from single-shot measurements. The theoretical points are the results of single-pulse DNI calculations.

Equations (55)

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ρkk(r, t)t=-i m(Vkmρmk-ρkmVmk)-Γkρkk+mΓmkρmm,
ρkj(r, t)t=-ρkj(iωkj+γkj)-i m(Vkmρmj-ρkmVmj),
Vkm=-μkm·E(r, t)=-μkm·[Eprobe(r, t)+Epump(r, t)],
En(r, t)=12eˆnl{An,l(t)exp[+i(kn,l·r-ωn,lt)]}+12eˆn*l{An,l*(t)exp[-i(kn,l·r-ωn,lt)]},
An,l(t)=A0n,l(t)exp(iϕl),
Vkm=-μkm·12eˆ1l[A1,l(t)exp(-iω1,tt)]+12eˆ1*l[A1,l*(t)exp(+iω1,lt)]=Vkm- exp(-iω1t)+Vkm+ exp(+iω1t),
Vkm-=-12 μkm·eˆ1l[A1,l(t)exp(-iδ1,lt)],
Vkm+=-12 μkm·eˆ1*l[A1,l*(t)exp(+iδ1,lt)].
σab(t)t=-σabγab+iσab(ω1-ωab)-i(ρbb-ρaa)Vab exp(+iω1t)-i m[Vam exp(+iω1t)ρmb]+i sρasVsb exp(+iω1t)=-σabγab+iσab(ω1-ωab)-i(ρbb-ρaa)×[Vab-+Vab+ exp(+2iω1t)]-i m{[Vam-+Vam+ exp(+2iω1t)]ρmb}+i s{ρas[Vsb-+Vsb+ exp(+2iω1t)]}.
σab(t)t=[σabr(t)+iσabi(t)]t=-(σabr+iσabi)γab+i(σabr+iσabi)(ω1-ωab)-i(ρbb-ρaa)×[(Ωab1-)r+i(Ωab1-)i]-im{[(Ωam1-)r+i(Ωam1-)i]ρmb}+is{ρas[(Ωsb1-)r+i(Ωsb1-)i]},
(Ωab1-)r=1(Vab-)r=-(μab·eˆ1)2 l[A1,l(t)exp(-iδ1,lt)]r=-(μab·eˆ1)r2 l[A1,l(t)exp(-iδ1,lt)]r+(μab·eˆ1)i2 l[A1,l(t)exp(-iδ1,lt)]i,
(Ωab1-)i=1(Vab-)i=-(μab·eˆ1)2 l[A1,l(t)exp(-iδ1,lt)]i=-(μab·eˆ1)i2 l[A1,l(t)exp(-iδ1,lt)]r-(μab·eˆ1)r2 l[A1,l(t)exp(-iδ1,lt)]i.
σabr(t)t=-σabrγab-σabi(ω1-ωab)+(ρbb-ρaa)(Ωab1-)i+m[(Ωam1-)rρmbi+(Ωam1-)iρmbr]-s[ρasr(Ωsb1-)i+ρasi(Ωsb1-)r],
σabi(t)t=-σabiγab+σabr(ω1-ωab)-(ρbb-ρaa)×(Ωab1-)r+m[-(Ωam1-)rρmbr+(Ωam1-)iρmbi]+s[ρasr(Ωsb1-)r-ρasi(Ωsb1-)i].
ρbb(t)t=-i s(Vbsρsb-ρbsVsb)-Γbρbb+mΓmbρmm+sΓsbρss,
ρbj(t)t=-ρbj(iωbj+γbj)-i s(Vbsρsj-ρbsvsj).
ρbb(t)t=-i s[Vbsσsb exp(-iω1t)-σbs exp(+iω1t)Vsb]-Γbρbb+mΓmbρmm+sΓsbρss,
ρbj(t)t=-ρbj(iωbj+γbj)-i s[Vbsσsj exp(-iω1t)-σbs exp(+iω1t)Vsj].
Vbs exp(-iω1t)=Vbs+=[(Ωbs1+)r+i(Ωbs1+)i]=[(Ωsb1-)r-i(Ωsb1-)i].
(Ωbs1+)r=(Vbs+)r=-(μbs·eˆ1*)2 l[A1,l*(t)exp(+iδ1,lt)]r=-(μsb*·eˆ1*)r2×l[A01,l(t)exp(-iϕl)exp(+iδ1,lt)]r+(μsb*·eˆ1*)i2×l[A01,l(t)exp(-iϕl)exp(+iδ1,lt)]i=-(μsb·eˆ1)r2 l{A01,l(t)[cos(ϕl)cos(δ1,lt)+sin(ϕl)sin(δ1,lt)]}-(μsb·eˆ1)i2 l{A01,l(t)×[cos(ϕl)sin(δ1,lt)-sin(ϕl)cos(δ1,lt)]},
(Ωsb1-)r=(Vsb-)r=-(μsb·eˆ1)2 l[A1,l(t)exp(-iδ1,lt)]r=(Ωbs1+)r,
(Ωbs1+)i=(Vbs+)i=+(μsb·eˆ1)i2×l{A01,l(t)[cos(ϕl)cos(δ1,lt)+sin(δ1,lt)sin(ϕl)]}-(μsb·eˆ1)r2 l{A01,l(t)[cos(ϕl)sin(δ1,lt)-sin(ϕl)cos(δ1,lt)]},
(Ωsb1-)i=(Vsb-)i=-(Ωbs1+)i.
Vsb exp(+iω1t)=Vsb-=[(Ωsb1-)r+i(Ωsb1-)i],
Vsj exp(+iω1t)=Vsj-=[(Ωsj1-)r+i(Ωsj1-)i].
ρbb(t)t=-i s{(σsbr+iσsbi)[(Ωsb1-)r-i(Ωsb1-)i]-(σsbr-iσsbi)[(Ωsb1-)r+i(Ωsb1-)i]}-Γbρbb+mΓmbρmm+sΓsbρss=s[2σsbi(Ωsb1-)r-2σsbr(Ωsb1-)i]-Γbρbb+mΓmbρmm+sΓsbρss,
ρbjr(t)t=-ρbjrγbj+ρbjiωbj+s[(Ωsb1-)rσsji-(Ωsb1-)iσsjr-σbsr(Ωsj1-)i-σbsi(Ωsj1-)r],
ρbji(t)t=-ρbjiγbj-ρbjrωbj+s[-(Ωsb1-)rσsjr-(Ωsb1-)iσsji+σbsr(Ωsj1-)r-σbsi(Ωsj1-)i].
ρaa(t)t=-i m(Vamρma-ρamVma)-Γaρaa+mΓmaρaa+sΓsaρss,
ρas(t)t=-ρas(iωas+γas)-i m(Vamρms-ρamVms).
ρaa(t)t=-i m[Vamσma exp(+iω1t)-σam exp(-iω1t)Vma]-Γaρaa+mΓmaρmm+sΓsaρss=-i m(Vam-σma-σamVma+)-Γaρaa+mΓmaρmm+sΓsaρss=m[2σamr(Ωam1-)i-2σami(Ωam1-)r]-Γaρaa+mΓmaρmm+sΓsaρss,
ρasr(t)t=-ρasrγas+ρasiωas+m[(Ωam1-)rσmsi+(Ωam1-)iσmsr+σami(Ωsm1-)r-σamr(Ωsm1-)i],
ρasi(t)t=-ρasiγas-ρasrωas+m[-(Ωam1-)rσmsr+(Ωam1-)iσmsi+σamr(Ωsm1-)r+σami(Ωsm1-)i],
γab=12(Γa+Γb)+γabdeph,
eˆ1=12(xˆ+iyˆ).
Ωab-1(t)=-(μab·eˆ1)2 l[A1,l(t)exp(-iδ1,lt)]=-[μab·(xˆ+iyˆ)]22 l[A1,l(t)exp(-iδ1,lt)]
Eprobe(z, t)
=12 l{A0pr,l[exp(-iωlt+iklz+iϕl)+exp(+iωlt-iklz-iϕl)]}xˆ=lA02,l(xˆ+iyˆ)22 exp(-iωlt+iklz+iϕl)+(xˆ-iyˆ)22 exp(+iωlt-iklz-iϕl)+lA03,l(xˆ-iyˆ)22 exp(-iωlt+iklz+iϕl)+(xˆ+iyˆ)22 exp(+iωlt-iklz-iϕl).
E2(L, t)=(xˆ+iyˆ)22 l[A02,l exp(-iωlt+iϕl)×exp(-α2,lL)exp(-iΔk2,lL)]+c.c.=(xˆ+iyˆ)22 l[AL2,l exp(-iω2t)]+c.c.=12 l[AL2,l exp(-iω2t)]+c.c.,
E3(L, t)=(xˆ-iyˆ)22 l[A03,l exp(-iωlt+iϕl)×exp(-α3,lL)exp(-iΔk3,lL)]+c.c.=(xˆ-iyˆ)22 l[AL3,l exp(-iω3t)]+c.c.=12 l[AL3,l exp(-iω3t)]+c.c.,
AL2,l=A02,l exp(-α2,lL){[cos(Δk2,lL)cos(Φl)+sin(Δk2,lL)sin(Φl)]+i[cos(Δk2,lL)sin(Φl)-sin(Δk2lL)cos(Φl)]},
AL3,l=A03,l exp(-α3,lL){[cos(Δk3,lL)cos(Φl)+sin(Δk3,lL)sin(Φl)]+i[cos(Δk3,lL)sin(Φl)-sin(Δk3lL)cos(Φl)]},
Φn,l=ϕl-δn,lt,n=1, 2, 3,
AL2,l=AL2,l (xˆ+iyˆ)2,AL3,l=AL3,l (xˆ-iyˆ)2,
α2,l=2πε0λ0ΔωH11+[2(ω2+δ2,l-ω0)/ΔωH]2×ab[(nb-na)/μab·eˆ2|2],
Δk2,l=α2,l 2(ω2+δ2,l-ω0)ΔωH,
It=12cε0AtransmittedAtransmitted*=cε02|(AL2r+AL3r)sin θ+(-AL2i+AL3i)cos θ+i[(AL2r-AL3r)cos θ+(AL2i+AL3i)sin θ]|2,
AL2r=lA02,l[cos(Δk2,lL)cos(Φl)+sin(Δk2,lL)sin(Φl)],
AL2i=lA02,l[cos(Δk2,lL)sin(Φl)-sin(Δk2,lL)cos(Φl)],
α3,l-α2,l=C1,liab(nbi-nai)×(|μab·eˆ3|2-|μab·eˆ2|2)11+x2i,l2,
x2i,l=2(ω2i+δ2,l-ω0)ΔωH=2(ω3i+δ3,l-ω0)ΔωH,
A¯0,l=1Nl 2I0cε0 exp-4 ln(2)δlΔωL2,
A0,l=A¯0,lξl,
ξl=-ln(1-ζl),
δtcomp=π10δ1,1,

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