Abstract

A nearly degenerate, four-wave mixing (ND4WM) setup with noisy light called I(2)ND4WM() is investigated both experimentally and theoretically through factorized-time-correlation (FTC) diagram analysis. This third order nonlinear signal is of interest because the phenomenon of color-locking appears very directly in the measured signal. Color locking is a fundamental aspect of noisy-light spectroscopies that often plays a critical but subtle role in production of the signal. For I(2)ND4WM(), color-locking results in complete cancellation of the spectrally broad noise carried by the noisy light used to create it. When combined with FTC diagram analysis the qualitative features of the I(2)ND4WM() can be understood. In addition to the striking noise cancellation, the qualitative features addressed in this work include the time profile, dynamic range, and polarization dependence of the signal. For comparison the spectrally broad I(2)ND4WM(+) signal is presented.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2003

D. J. Ulness, "On the role of classical field time correlations in noisy light spectroscopy: color locking and a spectral filter analogy," J. Phys. Chem. A 107, 8111-8123 (2003).
[CrossRef]

D. B. Turner and D. J. Ulness, "Factorized time correlation diagram analysis of Raman induced Kerr effect spectroscopy using noisy light," J. Chem. Phys. 119, 10745-10752 (2003).
[CrossRef]

D. P. Biebighauser, J. Gregiore, and D. J. Ulness, "General counting formulae for factorized time correlation diagram analysis," Physica A 320, 1-10 (2003).
[CrossRef]

2002

Y. Zhang, C. Gan, K. Lu, C. Li, and X. Hou, "Raman-enhanced polarization beats in Markovian stochastic fields," Opt. Commun. 205, 163-186 (2002).
[CrossRef]

D. P. Biebighauser, D. B. Turner, and D. J. Ulness, "Factorized time correlation diagram analysis of paired causal systems excited by twin stochastic driving functions," Phys. Rev. E 65, 026142 (2002).
[CrossRef]

2001

Y. Zhang, C. B. de Araújo, and E. E. Eyler, "Higher-order correlation on polarization beats in Markovian stochastic fields," Phys. Rev. A 63, 043802 (2001).
[CrossRef]

V. P. Kozich, L. S. de Menezes, and C. B. de Araujo, "Stimulated effects in one-photon resonant interferometric four-wave mixing with incoherent light," Opt. Lett. 26, 262-264 (2001).
[CrossRef]

L. S. Meneze, C. B. de Araújo, M. A. R. C. Alencar, P. F. Athayde-Filho, J. Miller, and A. M. Simas, "Ultrafast dynamics of mesoionic liquid solutions studied with incoherent light," Chem. Phys. Lett. 347, 163-166 (2001).
[CrossRef]

J. M. Dawlaty and D. J. Ulness, "Effects of noise on parameter recovery from Raman spectrograms," J. Raman Spectrosc. 32, 211-218 (2001).
[CrossRef]

A. A. Al-ghamdi, "Fluorescence anisotropy by use of optical Kerr gating with incoherent laser light," Appl. Opt. 40, 2485-2489 (2001).
[CrossRef]

2000

V. P. Kozich, L. S. de Menezes, and C. B. de Araujo, "Interferometric effects in time-delayed degenerate four wave mixing with broadband noisy light," J. Opt. Soc. Am. B 17, 973-976 (2000).
[CrossRef]

S. V. Rao, N. K. M. Naga Srinivas, D. N. Rao, L. Giribabu, B. G. Maiya, R. Philip, and G. R. Kumar, "Excited state dynamics in tetra tolyl porphyrins studied using degenerate four wave mixing with incoherent light and ps pulses," Opt. Commun. 182, 255-264 (2000).
[CrossRef]

J. C. Kirkwood and A. C. Albrecht, "Down-conversion of electronic frequencies and their dephasing dynamics: interferometric four-wave-mixing spectroscopy with broadband light," Phys. Rev. A 61, 033802 (2000).
[CrossRef]

Y. Zhang, X. Hou, K. Lu, and H. Wu, "Sixth-order correlations on Raman-enhanced polarization beats with phase-conjugation geometry," Opt. Commun. 184, 265-276 (2000).
[CrossRef]

Y. Zhang, T. T. Tang, L. Q. Sun, and P. M. Fu, "Effects of fourth-order coherence on ultrafast modulation spectroscopy," Phys. Rev. A 61, 023809 (2000).
[CrossRef]

Y. Zhang, L. Q. Sun, T. T. Tang, and P. M. Fu, "Effects of field correlation on polarization beats," Phys. Rev. A 61, 053819 (2000).
[CrossRef]

1999

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Raman spectrograms for high sensitivity probing of nonlinear hyperpolarizabilities and C-H stretching frequency shifts in acetonitrile-water liquid mixtures," Asian J. Phys. 7, 405-420 (1999).

J. C. Kirkwood, A. C. Albrecht, and D. J. Ulness, "Fifth-order nonlinear Raman processes in molecular liquids using quasi-cw noisy light. I. Theory," J. Chem. Phys. 111, 253-271 (1999).
[CrossRef]

D. A. Blank, L. J. Kaufman, and G. R. Fleming, "Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades," J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

1998

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
[CrossRef]

J. C. Kirkwood, D. J. Ulness, and A. C. Albrecht, "Electronically nonresonant coherent Raman scattering using incoherent light: Two Brownian oscillator approaches," J. Chem. Phys. 108, 9425-9435 (1998).
[CrossRef]

J. C. Kirkwood, D. J. Ulness, M. J. Stimson, and A. C. Albrecht, "On the mechanism of vibrational dephasing in liquid benzene by coherent anti-Stokes Raman scattering using incoherent light," Chem. Phys. Lett. 293, 167-172 (1998).
[CrossRef]

M. Pfeiffer and A. Lau, "Femtosecond fifth-order nonlinear response of nuclear motion in liquids investigated by incoherent laser light. Part I. Theory," J. Chem. Phys. 108, 4159-4172 (1998).
[CrossRef]

S. V. Rao and D. N. Rao, "Excited state dynamics of C60 studied using incoherent light," Chem. Phys. Lett. 283, 227-230 (1998).
[CrossRef]

1997

D. N. Rao, S. V. Rao, F. J. Aranda, D. V. G. L. N. Rao, M. Nakashima, and J. A. Akkara, "Ultrafast relaxation times of metalloporphyrins by time-resolved degenerate four-wave mixing with incoherent light," J. Opt. Soc. Am. B 14, 2710-2715 (1997).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Theory of coherent Raman scattering with quasi-cw noisy light for a general lineshape function," J. Chem. Phys. 107, 7127-7137 (1997).
[CrossRef]

D. J. Ulness and A. C. Albrecht, "A theory of time resolved coherent Raman scattering with spectrally tailored noisy light," J. Raman Spectrosc. 28, 571-578 (1997).
[CrossRef]

M. J. Stimson, D. J. Ulness, and A. C. Albrecht, "Time resolved coherent Raman spectroscopy controlled by spectrally tailored noisy light," J. Raman Spectrosc. 28, 579-587 (1997).
[CrossRef]

1996

A. Kummrow and A. Lau, "Dynamics in condensed molecular systems studied by incoherent light," Appl. Phys. B: Lasers Opt. 63, 209-223 (1996).
[CrossRef]

D. J. Ulness and A. C. Albrecht, "Four-wave mixing in a Bloch two-level system with incoherent laser light having a Lorentzian spectral density: analytic solution and a diagrammatic approach," Phys. Rev. A 53, 1081-1095 (1996).
[CrossRef] [PubMed]

1993

X. Mi, Z. Yu, Q. Jiang, and P. Fu, "Time-delayed Raman-enhanced nondegenerate four-wave-mixing with a broadband laser source," Phys. Rev. A 48, 3203-3208 (1993).
[CrossRef] [PubMed]

1992

P. Fu, Z. Yu, X. Mi, Q. Jiang, and Z. Zhang, "Theoretical study of the suppression of thermal background in the Raman-enhanced nondegenerate four-wave-mixing spectrum by a time-delayed method," Phys. Rev. A 46, 1530-1539 (1992).
[CrossRef] [PubMed]

1991

M. A. Dugan and A. C. Albrecht, "Radiation-matter oscillations and spectral line narrowing in field-correlated four-wave mixing. I. Theory," Phys. Rev. A 43, 3877-3921 (1991).
[CrossRef] [PubMed]

1987

T. Hattori, A. Terasaki, and T. Kobayashi, "Coherent Stokes Raman scattering with incoherent light for vibrational-dephasing-time measurement," Phys. Rev. A 35, 715-723 (1987).
[CrossRef] [PubMed]

1986

S. Mukamel and E. Hanamura, "Four-wave mixing using partially coherent fields in systems with spatial correlations," Phys. Rev. A 33, 1099-1108 (1986).
[CrossRef] [PubMed]

1984

E. Hanamura, "Coherent and incoherent laser spectroscopy of spatial and temporal fluctuations," Solid State Commun. 51, 697-700 (1984).
[CrossRef]

N. Morita and T. Yajima, "Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light," Phys. Rev. A 30, 2525-2536 (1984).
[CrossRef]

N. Nakatsuka, M. Tomita, M. Fujiwara, and S. Asaka, "Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass," Phys. Rev. A 29, 2286-2289 (1984).
[CrossRef]

R. Beach and S. R. Hartmann, "Incoherent photon echoes," Phys. Rev. Lett. 53, 663-666 (1984).
[CrossRef]

Akkara, J. A.

Albrecht, A. C.

J. C. Kirkwood and A. C. Albrecht, "Down-conversion of electronic frequencies and their dephasing dynamics: interferometric four-wave-mixing spectroscopy with broadband light," Phys. Rev. A 61, 033802 (2000).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Raman spectrograms for high sensitivity probing of nonlinear hyperpolarizabilities and C-H stretching frequency shifts in acetonitrile-water liquid mixtures," Asian J. Phys. 7, 405-420 (1999).

J. C. Kirkwood, A. C. Albrecht, and D. J. Ulness, "Fifth-order nonlinear Raman processes in molecular liquids using quasi-cw noisy light. I. Theory," J. Chem. Phys. 111, 253-271 (1999).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
[CrossRef]

J. C. Kirkwood, D. J. Ulness, and A. C. Albrecht, "Electronically nonresonant coherent Raman scattering using incoherent light: Two Brownian oscillator approaches," J. Chem. Phys. 108, 9425-9435 (1998).
[CrossRef]

J. C. Kirkwood, D. J. Ulness, M. J. Stimson, and A. C. Albrecht, "On the mechanism of vibrational dephasing in liquid benzene by coherent anti-Stokes Raman scattering using incoherent light," Chem. Phys. Lett. 293, 167-172 (1998).
[CrossRef]

M. J. Stimson, D. J. Ulness, and A. C. Albrecht, "Time resolved coherent Raman spectroscopy controlled by spectrally tailored noisy light," J. Raman Spectrosc. 28, 579-587 (1997).
[CrossRef]

D. J. Ulness and A. C. Albrecht, "A theory of time resolved coherent Raman scattering with spectrally tailored noisy light," J. Raman Spectrosc. 28, 571-578 (1997).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Theory of coherent Raman scattering with quasi-cw noisy light for a general lineshape function," J. Chem. Phys. 107, 7127-7137 (1997).
[CrossRef]

D. J. Ulness and A. C. Albrecht, "Four-wave mixing in a Bloch two-level system with incoherent laser light having a Lorentzian spectral density: analytic solution and a diagrammatic approach," Phys. Rev. A 53, 1081-1095 (1996).
[CrossRef] [PubMed]

M. A. Dugan and A. C. Albrecht, "Radiation-matter oscillations and spectral line narrowing in field-correlated four-wave mixing. I. Theory," Phys. Rev. A 43, 3877-3921 (1991).
[CrossRef] [PubMed]

D. Lee and A. C. Albrecht, "A unified view of Raman, resonance Raman, and fluorescence spectroscopy (and their analogues in two-photon absorption," in Advances in Infrared and Raman Spectroscopy, R.J.Clark and R.E.Hester, eds. (Wiley, New York, 1985).

Alencar, M. A. R. C.

L. S. Meneze, C. B. de Araújo, M. A. R. C. Alencar, P. F. Athayde-Filho, J. Miller, and A. M. Simas, "Ultrafast dynamics of mesoionic liquid solutions studied with incoherent light," Chem. Phys. Lett. 347, 163-166 (2001).
[CrossRef]

Al-ghamdi, A. A.

Aranda, F. J.

Asaka, S.

N. Nakatsuka, M. Tomita, M. Fujiwara, and S. Asaka, "Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass," Phys. Rev. A 29, 2286-2289 (1984).
[CrossRef]

Athayde-Filho, P. F.

L. S. Meneze, C. B. de Araújo, M. A. R. C. Alencar, P. F. Athayde-Filho, J. Miller, and A. M. Simas, "Ultrafast dynamics of mesoionic liquid solutions studied with incoherent light," Chem. Phys. Lett. 347, 163-166 (2001).
[CrossRef]

Beach, R.

R. Beach and S. R. Hartmann, "Incoherent photon echoes," Phys. Rev. Lett. 53, 663-666 (1984).
[CrossRef]

Biebighauser, D. P.

D. P. Biebighauser, J. Gregiore, and D. J. Ulness, "General counting formulae for factorized time correlation diagram analysis," Physica A 320, 1-10 (2003).
[CrossRef]

D. P. Biebighauser, D. B. Turner, and D. J. Ulness, "Factorized time correlation diagram analysis of paired causal systems excited by twin stochastic driving functions," Phys. Rev. E 65, 026142 (2002).
[CrossRef]

Blank, D. A.

D. A. Blank, L. J. Kaufman, and G. R. Fleming, "Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades," J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

Dawlaty, J. M.

J. M. Dawlaty and D. J. Ulness, "Effects of noise on parameter recovery from Raman spectrograms," J. Raman Spectrosc. 32, 211-218 (2001).
[CrossRef]

de Araujo, C. B.

de Araújo, C. B.

Y. Zhang, C. B. de Araújo, and E. E. Eyler, "Higher-order correlation on polarization beats in Markovian stochastic fields," Phys. Rev. A 63, 043802 (2001).
[CrossRef]

L. S. Meneze, C. B. de Araújo, M. A. R. C. Alencar, P. F. Athayde-Filho, J. Miller, and A. M. Simas, "Ultrafast dynamics of mesoionic liquid solutions studied with incoherent light," Chem. Phys. Lett. 347, 163-166 (2001).
[CrossRef]

de Menezes, L. S.

Dugan, M. A.

M. A. Dugan and A. C. Albrecht, "Radiation-matter oscillations and spectral line narrowing in field-correlated four-wave mixing. I. Theory," Phys. Rev. A 43, 3877-3921 (1991).
[CrossRef] [PubMed]

Eyler, E. E.

Y. Zhang, C. B. de Araújo, and E. E. Eyler, "Higher-order correlation on polarization beats in Markovian stochastic fields," Phys. Rev. A 63, 043802 (2001).
[CrossRef]

Fleming, G. R.

D. A. Blank, L. J. Kaufman, and G. R. Fleming, "Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades," J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

Fu, P.

X. Mi, Z. Yu, Q. Jiang, and P. Fu, "Time-delayed Raman-enhanced nondegenerate four-wave-mixing with a broadband laser source," Phys. Rev. A 48, 3203-3208 (1993).
[CrossRef] [PubMed]

P. Fu, Z. Yu, X. Mi, Q. Jiang, and Z. Zhang, "Theoretical study of the suppression of thermal background in the Raman-enhanced nondegenerate four-wave-mixing spectrum by a time-delayed method," Phys. Rev. A 46, 1530-1539 (1992).
[CrossRef] [PubMed]

Fu, P. M.

Y. Zhang, T. T. Tang, L. Q. Sun, and P. M. Fu, "Effects of fourth-order coherence on ultrafast modulation spectroscopy," Phys. Rev. A 61, 023809 (2000).
[CrossRef]

Y. Zhang, L. Q. Sun, T. T. Tang, and P. M. Fu, "Effects of field correlation on polarization beats," Phys. Rev. A 61, 053819 (2000).
[CrossRef]

Fujiwara, M.

N. Nakatsuka, M. Tomita, M. Fujiwara, and S. Asaka, "Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass," Phys. Rev. A 29, 2286-2289 (1984).
[CrossRef]

Gan, C.

Y. Zhang, C. Gan, K. Lu, C. Li, and X. Hou, "Raman-enhanced polarization beats in Markovian stochastic fields," Opt. Commun. 205, 163-186 (2002).
[CrossRef]

Giribabu, L.

S. V. Rao, N. K. M. Naga Srinivas, D. N. Rao, L. Giribabu, B. G. Maiya, R. Philip, and G. R. Kumar, "Excited state dynamics in tetra tolyl porphyrins studied using degenerate four wave mixing with incoherent light and ps pulses," Opt. Commun. 182, 255-264 (2000).
[CrossRef]

Gregiore, J.

D. P. Biebighauser, J. Gregiore, and D. J. Ulness, "General counting formulae for factorized time correlation diagram analysis," Physica A 320, 1-10 (2003).
[CrossRef]

Hanamura, E.

S. Mukamel and E. Hanamura, "Four-wave mixing using partially coherent fields in systems with spatial correlations," Phys. Rev. A 33, 1099-1108 (1986).
[CrossRef] [PubMed]

E. Hanamura, "Coherent and incoherent laser spectroscopy of spatial and temporal fluctuations," Solid State Commun. 51, 697-700 (1984).
[CrossRef]

Hartmann, S. R.

R. Beach and S. R. Hartmann, "Incoherent photon echoes," Phys. Rev. Lett. 53, 663-666 (1984).
[CrossRef]

Hattori, T.

T. Hattori, A. Terasaki, and T. Kobayashi, "Coherent Stokes Raman scattering with incoherent light for vibrational-dephasing-time measurement," Phys. Rev. A 35, 715-723 (1987).
[CrossRef] [PubMed]

Hou, X.

Y. Zhang, C. Gan, K. Lu, C. Li, and X. Hou, "Raman-enhanced polarization beats in Markovian stochastic fields," Opt. Commun. 205, 163-186 (2002).
[CrossRef]

Y. Zhang, X. Hou, K. Lu, and H. Wu, "Sixth-order correlations on Raman-enhanced polarization beats with phase-conjugation geometry," Opt. Commun. 184, 265-276 (2000).
[CrossRef]

Jiang, Q.

X. Mi, Z. Yu, Q. Jiang, and P. Fu, "Time-delayed Raman-enhanced nondegenerate four-wave-mixing with a broadband laser source," Phys. Rev. A 48, 3203-3208 (1993).
[CrossRef] [PubMed]

P. Fu, Z. Yu, X. Mi, Q. Jiang, and Z. Zhang, "Theoretical study of the suppression of thermal background in the Raman-enhanced nondegenerate four-wave-mixing spectrum by a time-delayed method," Phys. Rev. A 46, 1530-1539 (1992).
[CrossRef] [PubMed]

Kaufman, L. J.

D. A. Blank, L. J. Kaufman, and G. R. Fleming, "Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades," J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

Kirkwood, J. C.

J. C. Kirkwood and A. C. Albrecht, "Down-conversion of electronic frequencies and their dephasing dynamics: interferometric four-wave-mixing spectroscopy with broadband light," Phys. Rev. A 61, 033802 (2000).
[CrossRef]

J. C. Kirkwood, A. C. Albrecht, and D. J. Ulness, "Fifth-order nonlinear Raman processes in molecular liquids using quasi-cw noisy light. I. Theory," J. Chem. Phys. 111, 253-271 (1999).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Raman spectrograms for high sensitivity probing of nonlinear hyperpolarizabilities and C-H stretching frequency shifts in acetonitrile-water liquid mixtures," Asian J. Phys. 7, 405-420 (1999).

J. C. Kirkwood, D. J. Ulness, M. J. Stimson, and A. C. Albrecht, "On the mechanism of vibrational dephasing in liquid benzene by coherent anti-Stokes Raman scattering using incoherent light," Chem. Phys. Lett. 293, 167-172 (1998).
[CrossRef]

J. C. Kirkwood, D. J. Ulness, and A. C. Albrecht, "Electronically nonresonant coherent Raman scattering using incoherent light: Two Brownian oscillator approaches," J. Chem. Phys. 108, 9425-9435 (1998).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Theory of coherent Raman scattering with quasi-cw noisy light for a general lineshape function," J. Chem. Phys. 107, 7127-7137 (1997).
[CrossRef]

Kobayashi, T.

T. Hattori, A. Terasaki, and T. Kobayashi, "Coherent Stokes Raman scattering with incoherent light for vibrational-dephasing-time measurement," Phys. Rev. A 35, 715-723 (1987).
[CrossRef] [PubMed]

T. Kobayashi "Measurement of the femtosecond dynamics of nonlinear optical responses," in Modern Nonlinear Optics Part 3, M.Evans and S.Kielich, eds. Adv. Chem. Phys.85, 55-105 (1994).

Kozich, V. P.

Kumar, G. R.

S. V. Rao, N. K. M. Naga Srinivas, D. N. Rao, L. Giribabu, B. G. Maiya, R. Philip, and G. R. Kumar, "Excited state dynamics in tetra tolyl porphyrins studied using degenerate four wave mixing with incoherent light and ps pulses," Opt. Commun. 182, 255-264 (2000).
[CrossRef]

Kummrow, A.

A. Kummrow and A. Lau, "Dynamics in condensed molecular systems studied by incoherent light," Appl. Phys. B: Lasers Opt. 63, 209-223 (1996).
[CrossRef]

Lau, A.

M. Pfeiffer and A. Lau, "Femtosecond fifth-order nonlinear response of nuclear motion in liquids investigated by incoherent laser light. Part I. Theory," J. Chem. Phys. 108, 4159-4172 (1998).
[CrossRef]

A. Kummrow and A. Lau, "Dynamics in condensed molecular systems studied by incoherent light," Appl. Phys. B: Lasers Opt. 63, 209-223 (1996).
[CrossRef]

Lee, D.

D. Lee and A. C. Albrecht, "A unified view of Raman, resonance Raman, and fluorescence spectroscopy (and their analogues in two-photon absorption," in Advances in Infrared and Raman Spectroscopy, R.J.Clark and R.E.Hester, eds. (Wiley, New York, 1985).

Li, C.

Y. Zhang, C. Gan, K. Lu, C. Li, and X. Hou, "Raman-enhanced polarization beats in Markovian stochastic fields," Opt. Commun. 205, 163-186 (2002).
[CrossRef]

Lu, K.

Y. Zhang, C. Gan, K. Lu, C. Li, and X. Hou, "Raman-enhanced polarization beats in Markovian stochastic fields," Opt. Commun. 205, 163-186 (2002).
[CrossRef]

Y. Zhang, X. Hou, K. Lu, and H. Wu, "Sixth-order correlations on Raman-enhanced polarization beats with phase-conjugation geometry," Opt. Commun. 184, 265-276 (2000).
[CrossRef]

Maiya, B. G.

S. V. Rao, N. K. M. Naga Srinivas, D. N. Rao, L. Giribabu, B. G. Maiya, R. Philip, and G. R. Kumar, "Excited state dynamics in tetra tolyl porphyrins studied using degenerate four wave mixing with incoherent light and ps pulses," Opt. Commun. 182, 255-264 (2000).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

Mehta, C. L.

C. L. Mehta, "Coherence and statistics of radiation," in Lectures in Theoretical Physics, W.E.Britin, ed. (University of Colorado, Boulder, Colo. 1965), Vol. VIIC.

Meneze, L. S.

L. S. Meneze, C. B. de Araújo, M. A. R. C. Alencar, P. F. Athayde-Filho, J. Miller, and A. M. Simas, "Ultrafast dynamics of mesoionic liquid solutions studied with incoherent light," Chem. Phys. Lett. 347, 163-166 (2001).
[CrossRef]

Mi, X.

X. Mi, Z. Yu, Q. Jiang, and P. Fu, "Time-delayed Raman-enhanced nondegenerate four-wave-mixing with a broadband laser source," Phys. Rev. A 48, 3203-3208 (1993).
[CrossRef] [PubMed]

P. Fu, Z. Yu, X. Mi, Q. Jiang, and Z. Zhang, "Theoretical study of the suppression of thermal background in the Raman-enhanced nondegenerate four-wave-mixing spectrum by a time-delayed method," Phys. Rev. A 46, 1530-1539 (1992).
[CrossRef] [PubMed]

Miller, J.

L. S. Meneze, C. B. de Araújo, M. A. R. C. Alencar, P. F. Athayde-Filho, J. Miller, and A. M. Simas, "Ultrafast dynamics of mesoionic liquid solutions studied with incoherent light," Chem. Phys. Lett. 347, 163-166 (2001).
[CrossRef]

Morita, N.

N. Morita and T. Yajima, "Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light," Phys. Rev. A 30, 2525-2536 (1984).
[CrossRef]

Mukamel, S.

S. Mukamel and E. Hanamura, "Four-wave mixing using partially coherent fields in systems with spatial correlations," Phys. Rev. A 33, 1099-1108 (1986).
[CrossRef] [PubMed]

Naga Srinivas, N. K. M.

S. V. Rao, N. K. M. Naga Srinivas, D. N. Rao, L. Giribabu, B. G. Maiya, R. Philip, and G. R. Kumar, "Excited state dynamics in tetra tolyl porphyrins studied using degenerate four wave mixing with incoherent light and ps pulses," Opt. Commun. 182, 255-264 (2000).
[CrossRef]

Nakashima, M.

Nakatsuka, N.

N. Nakatsuka, M. Tomita, M. Fujiwara, and S. Asaka, "Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass," Phys. Rev. A 29, 2286-2289 (1984).
[CrossRef]

Pfeiffer, M.

M. Pfeiffer and A. Lau, "Femtosecond fifth-order nonlinear response of nuclear motion in liquids investigated by incoherent laser light. Part I. Theory," J. Chem. Phys. 108, 4159-4172 (1998).
[CrossRef]

Philip, R.

S. V. Rao, N. K. M. Naga Srinivas, D. N. Rao, L. Giribabu, B. G. Maiya, R. Philip, and G. R. Kumar, "Excited state dynamics in tetra tolyl porphyrins studied using degenerate four wave mixing with incoherent light and ps pulses," Opt. Commun. 182, 255-264 (2000).
[CrossRef]

Rao, D. N.

S. V. Rao, N. K. M. Naga Srinivas, D. N. Rao, L. Giribabu, B. G. Maiya, R. Philip, and G. R. Kumar, "Excited state dynamics in tetra tolyl porphyrins studied using degenerate four wave mixing with incoherent light and ps pulses," Opt. Commun. 182, 255-264 (2000).
[CrossRef]

S. V. Rao and D. N. Rao, "Excited state dynamics of C60 studied using incoherent light," Chem. Phys. Lett. 283, 227-230 (1998).
[CrossRef]

D. N. Rao, S. V. Rao, F. J. Aranda, D. V. G. L. N. Rao, M. Nakashima, and J. A. Akkara, "Ultrafast relaxation times of metalloporphyrins by time-resolved degenerate four-wave mixing with incoherent light," J. Opt. Soc. Am. B 14, 2710-2715 (1997).
[CrossRef]

Rao, D. V. G. L. N.

Rao, S. V.

S. V. Rao, N. K. M. Naga Srinivas, D. N. Rao, L. Giribabu, B. G. Maiya, R. Philip, and G. R. Kumar, "Excited state dynamics in tetra tolyl porphyrins studied using degenerate four wave mixing with incoherent light and ps pulses," Opt. Commun. 182, 255-264 (2000).
[CrossRef]

S. V. Rao and D. N. Rao, "Excited state dynamics of C60 studied using incoherent light," Chem. Phys. Lett. 283, 227-230 (1998).
[CrossRef]

D. N. Rao, S. V. Rao, F. J. Aranda, D. V. G. L. N. Rao, M. Nakashima, and J. A. Akkara, "Ultrafast relaxation times of metalloporphyrins by time-resolved degenerate four-wave mixing with incoherent light," J. Opt. Soc. Am. B 14, 2710-2715 (1997).
[CrossRef]

Simas, A. M.

L. S. Meneze, C. B. de Araújo, M. A. R. C. Alencar, P. F. Athayde-Filho, J. Miller, and A. M. Simas, "Ultrafast dynamics of mesoionic liquid solutions studied with incoherent light," Chem. Phys. Lett. 347, 163-166 (2001).
[CrossRef]

Stimson, M. J.

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Raman spectrograms for high sensitivity probing of nonlinear hyperpolarizabilities and C-H stretching frequency shifts in acetonitrile-water liquid mixtures," Asian J. Phys. 7, 405-420 (1999).

J. C. Kirkwood, D. J. Ulness, M. J. Stimson, and A. C. Albrecht, "On the mechanism of vibrational dephasing in liquid benzene by coherent anti-Stokes Raman scattering using incoherent light," Chem. Phys. Lett. 293, 167-172 (1998).
[CrossRef]

M. J. Stimson, D. J. Ulness, and A. C. Albrecht, "Time resolved coherent Raman spectroscopy controlled by spectrally tailored noisy light," J. Raman Spectrosc. 28, 579-587 (1997).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Theory of coherent Raman scattering with quasi-cw noisy light for a general lineshape function," J. Chem. Phys. 107, 7127-7137 (1997).
[CrossRef]

Sun, L. Q.

Y. Zhang, T. T. Tang, L. Q. Sun, and P. M. Fu, "Effects of fourth-order coherence on ultrafast modulation spectroscopy," Phys. Rev. A 61, 023809 (2000).
[CrossRef]

Y. Zhang, L. Q. Sun, T. T. Tang, and P. M. Fu, "Effects of field correlation on polarization beats," Phys. Rev. A 61, 053819 (2000).
[CrossRef]

Tang, T. T.

Y. Zhang, L. Q. Sun, T. T. Tang, and P. M. Fu, "Effects of field correlation on polarization beats," Phys. Rev. A 61, 053819 (2000).
[CrossRef]

Y. Zhang, T. T. Tang, L. Q. Sun, and P. M. Fu, "Effects of fourth-order coherence on ultrafast modulation spectroscopy," Phys. Rev. A 61, 023809 (2000).
[CrossRef]

Terasaki, A.

T. Hattori, A. Terasaki, and T. Kobayashi, "Coherent Stokes Raman scattering with incoherent light for vibrational-dephasing-time measurement," Phys. Rev. A 35, 715-723 (1987).
[CrossRef] [PubMed]

Tomita, M.

N. Nakatsuka, M. Tomita, M. Fujiwara, and S. Asaka, "Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass," Phys. Rev. A 29, 2286-2289 (1984).
[CrossRef]

Turner, D. B.

D. B. Turner and D. J. Ulness, "Factorized time correlation diagram analysis of Raman induced Kerr effect spectroscopy using noisy light," J. Chem. Phys. 119, 10745-10752 (2003).
[CrossRef]

D. P. Biebighauser, D. B. Turner, and D. J. Ulness, "Factorized time correlation diagram analysis of paired causal systems excited by twin stochastic driving functions," Phys. Rev. E 65, 026142 (2002).
[CrossRef]

Ulness, D. J.

D. P. Biebighauser, J. Gregiore, and D. J. Ulness, "General counting formulae for factorized time correlation diagram analysis," Physica A 320, 1-10 (2003).
[CrossRef]

D. B. Turner and D. J. Ulness, "Factorized time correlation diagram analysis of Raman induced Kerr effect spectroscopy using noisy light," J. Chem. Phys. 119, 10745-10752 (2003).
[CrossRef]

D. J. Ulness, "On the role of classical field time correlations in noisy light spectroscopy: color locking and a spectral filter analogy," J. Phys. Chem. A 107, 8111-8123 (2003).
[CrossRef]

D. P. Biebighauser, D. B. Turner, and D. J. Ulness, "Factorized time correlation diagram analysis of paired causal systems excited by twin stochastic driving functions," Phys. Rev. E 65, 026142 (2002).
[CrossRef]

J. M. Dawlaty and D. J. Ulness, "Effects of noise on parameter recovery from Raman spectrograms," J. Raman Spectrosc. 32, 211-218 (2001).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Raman spectrograms for high sensitivity probing of nonlinear hyperpolarizabilities and C-H stretching frequency shifts in acetonitrile-water liquid mixtures," Asian J. Phys. 7, 405-420 (1999).

J. C. Kirkwood, A. C. Albrecht, and D. J. Ulness, "Fifth-order nonlinear Raman processes in molecular liquids using quasi-cw noisy light. I. Theory," J. Chem. Phys. 111, 253-271 (1999).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
[CrossRef]

J. C. Kirkwood, D. J. Ulness, and A. C. Albrecht, "Electronically nonresonant coherent Raman scattering using incoherent light: Two Brownian oscillator approaches," J. Chem. Phys. 108, 9425-9435 (1998).
[CrossRef]

J. C. Kirkwood, D. J. Ulness, M. J. Stimson, and A. C. Albrecht, "On the mechanism of vibrational dephasing in liquid benzene by coherent anti-Stokes Raman scattering using incoherent light," Chem. Phys. Lett. 293, 167-172 (1998).
[CrossRef]

M. J. Stimson, D. J. Ulness, and A. C. Albrecht, "Time resolved coherent Raman spectroscopy controlled by spectrally tailored noisy light," J. Raman Spectrosc. 28, 579-587 (1997).
[CrossRef]

D. J. Ulness and A. C. Albrecht, "A theory of time resolved coherent Raman scattering with spectrally tailored noisy light," J. Raman Spectrosc. 28, 571-578 (1997).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Theory of coherent Raman scattering with quasi-cw noisy light for a general lineshape function," J. Chem. Phys. 107, 7127-7137 (1997).
[CrossRef]

D. J. Ulness and A. C. Albrecht, "Four-wave mixing in a Bloch two-level system with incoherent laser light having a Lorentzian spectral density: analytic solution and a diagrammatic approach," Phys. Rev. A 53, 1081-1095 (1996).
[CrossRef] [PubMed]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

Wu, H.

Y. Zhang, X. Hou, K. Lu, and H. Wu, "Sixth-order correlations on Raman-enhanced polarization beats with phase-conjugation geometry," Opt. Commun. 184, 265-276 (2000).
[CrossRef]

Yajima, T.

N. Morita and T. Yajima, "Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light," Phys. Rev. A 30, 2525-2536 (1984).
[CrossRef]

Yu, Z.

X. Mi, Z. Yu, Q. Jiang, and P. Fu, "Time-delayed Raman-enhanced nondegenerate four-wave-mixing with a broadband laser source," Phys. Rev. A 48, 3203-3208 (1993).
[CrossRef] [PubMed]

P. Fu, Z. Yu, X. Mi, Q. Jiang, and Z. Zhang, "Theoretical study of the suppression of thermal background in the Raman-enhanced nondegenerate four-wave-mixing spectrum by a time-delayed method," Phys. Rev. A 46, 1530-1539 (1992).
[CrossRef] [PubMed]

Zhang, Y.

Y. Zhang, C. Gan, K. Lu, C. Li, and X. Hou, "Raman-enhanced polarization beats in Markovian stochastic fields," Opt. Commun. 205, 163-186 (2002).
[CrossRef]

Y. Zhang, C. B. de Araújo, and E. E. Eyler, "Higher-order correlation on polarization beats in Markovian stochastic fields," Phys. Rev. A 63, 043802 (2001).
[CrossRef]

Y. Zhang, L. Q. Sun, T. T. Tang, and P. M. Fu, "Effects of field correlation on polarization beats," Phys. Rev. A 61, 053819 (2000).
[CrossRef]

Y. Zhang, T. T. Tang, L. Q. Sun, and P. M. Fu, "Effects of fourth-order coherence on ultrafast modulation spectroscopy," Phys. Rev. A 61, 023809 (2000).
[CrossRef]

Y. Zhang, X. Hou, K. Lu, and H. Wu, "Sixth-order correlations on Raman-enhanced polarization beats with phase-conjugation geometry," Opt. Commun. 184, 265-276 (2000).
[CrossRef]

Zhang, Z.

P. Fu, Z. Yu, X. Mi, Q. Jiang, and Z. Zhang, "Theoretical study of the suppression of thermal background in the Raman-enhanced nondegenerate four-wave-mixing spectrum by a time-delayed method," Phys. Rev. A 46, 1530-1539 (1992).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. B: Lasers Opt.

A. Kummrow and A. Lau, "Dynamics in condensed molecular systems studied by incoherent light," Appl. Phys. B: Lasers Opt. 63, 209-223 (1996).
[CrossRef]

Asian J. Phys.

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Raman spectrograms for high sensitivity probing of nonlinear hyperpolarizabilities and C-H stretching frequency shifts in acetonitrile-water liquid mixtures," Asian J. Phys. 7, 405-420 (1999).

Chem. Phys. Lett.

J. C. Kirkwood, D. J. Ulness, M. J. Stimson, and A. C. Albrecht, "On the mechanism of vibrational dephasing in liquid benzene by coherent anti-Stokes Raman scattering using incoherent light," Chem. Phys. Lett. 293, 167-172 (1998).
[CrossRef]

L. S. Meneze, C. B. de Araújo, M. A. R. C. Alencar, P. F. Athayde-Filho, J. Miller, and A. M. Simas, "Ultrafast dynamics of mesoionic liquid solutions studied with incoherent light," Chem. Phys. Lett. 347, 163-166 (2001).
[CrossRef]

S. V. Rao and D. N. Rao, "Excited state dynamics of C60 studied using incoherent light," Chem. Phys. Lett. 283, 227-230 (1998).
[CrossRef]

J. Chem. Phys.

D. J. Ulness, J. C. Kirkwood, M. J. Stimson, and A. C. Albrecht, "Theory of coherent Raman scattering with quasi-cw noisy light for a general lineshape function," J. Chem. Phys. 107, 7127-7137 (1997).
[CrossRef]

M. Pfeiffer and A. Lau, "Femtosecond fifth-order nonlinear response of nuclear motion in liquids investigated by incoherent laser light. Part I. Theory," J. Chem. Phys. 108, 4159-4172 (1998).
[CrossRef]

D. B. Turner and D. J. Ulness, "Factorized time correlation diagram analysis of Raman induced Kerr effect spectroscopy using noisy light," J. Chem. Phys. 119, 10745-10752 (2003).
[CrossRef]

J. C. Kirkwood, D. J. Ulness, and A. C. Albrecht, "Electronically nonresonant coherent Raman scattering using incoherent light: Two Brownian oscillator approaches," J. Chem. Phys. 108, 9425-9435 (1998).
[CrossRef]

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
[CrossRef]

J. C. Kirkwood, A. C. Albrecht, and D. J. Ulness, "Fifth-order nonlinear Raman processes in molecular liquids using quasi-cw noisy light. I. Theory," J. Chem. Phys. 111, 253-271 (1999).
[CrossRef]

D. A. Blank, L. J. Kaufman, and G. R. Fleming, "Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades," J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem. A

D. J. Ulness, "On the role of classical field time correlations in noisy light spectroscopy: color locking and a spectral filter analogy," J. Phys. Chem. A 107, 8111-8123 (2003).
[CrossRef]

J. Raman Spectrosc.

D. J. Ulness and A. C. Albrecht, "A theory of time resolved coherent Raman scattering with spectrally tailored noisy light," J. Raman Spectrosc. 28, 571-578 (1997).
[CrossRef]

M. J. Stimson, D. J. Ulness, and A. C. Albrecht, "Time resolved coherent Raman spectroscopy controlled by spectrally tailored noisy light," J. Raman Spectrosc. 28, 579-587 (1997).
[CrossRef]

J. M. Dawlaty and D. J. Ulness, "Effects of noise on parameter recovery from Raman spectrograms," J. Raman Spectrosc. 32, 211-218 (2001).
[CrossRef]

Opt. Commun.

Y. Zhang, C. Gan, K. Lu, C. Li, and X. Hou, "Raman-enhanced polarization beats in Markovian stochastic fields," Opt. Commun. 205, 163-186 (2002).
[CrossRef]

Y. Zhang, X. Hou, K. Lu, and H. Wu, "Sixth-order correlations on Raman-enhanced polarization beats with phase-conjugation geometry," Opt. Commun. 184, 265-276 (2000).
[CrossRef]

S. V. Rao, N. K. M. Naga Srinivas, D. N. Rao, L. Giribabu, B. G. Maiya, R. Philip, and G. R. Kumar, "Excited state dynamics in tetra tolyl porphyrins studied using degenerate four wave mixing with incoherent light and ps pulses," Opt. Commun. 182, 255-264 (2000).
[CrossRef]

Opt. Lett.

Phys. Rev. A

Y. Zhang, T. T. Tang, L. Q. Sun, and P. M. Fu, "Effects of fourth-order coherence on ultrafast modulation spectroscopy," Phys. Rev. A 61, 023809 (2000).
[CrossRef]

Y. Zhang, C. B. de Araújo, and E. E. Eyler, "Higher-order correlation on polarization beats in Markovian stochastic fields," Phys. Rev. A 63, 043802 (2001).
[CrossRef]

Y. Zhang, L. Q. Sun, T. T. Tang, and P. M. Fu, "Effects of field correlation on polarization beats," Phys. Rev. A 61, 053819 (2000).
[CrossRef]

D. J. Ulness and A. C. Albrecht, "Four-wave mixing in a Bloch two-level system with incoherent laser light having a Lorentzian spectral density: analytic solution and a diagrammatic approach," Phys. Rev. A 53, 1081-1095 (1996).
[CrossRef] [PubMed]

M. A. Dugan and A. C. Albrecht, "Radiation-matter oscillations and spectral line narrowing in field-correlated four-wave mixing. I. Theory," Phys. Rev. A 43, 3877-3921 (1991).
[CrossRef] [PubMed]

T. Hattori, A. Terasaki, and T. Kobayashi, "Coherent Stokes Raman scattering with incoherent light for vibrational-dephasing-time measurement," Phys. Rev. A 35, 715-723 (1987).
[CrossRef] [PubMed]

P. Fu, Z. Yu, X. Mi, Q. Jiang, and Z. Zhang, "Theoretical study of the suppression of thermal background in the Raman-enhanced nondegenerate four-wave-mixing spectrum by a time-delayed method," Phys. Rev. A 46, 1530-1539 (1992).
[CrossRef] [PubMed]

X. Mi, Z. Yu, Q. Jiang, and P. Fu, "Time-delayed Raman-enhanced nondegenerate four-wave-mixing with a broadband laser source," Phys. Rev. A 48, 3203-3208 (1993).
[CrossRef] [PubMed]

N. Morita and T. Yajima, "Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light," Phys. Rev. A 30, 2525-2536 (1984).
[CrossRef]

N. Nakatsuka, M. Tomita, M. Fujiwara, and S. Asaka, "Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass," Phys. Rev. A 29, 2286-2289 (1984).
[CrossRef]

J. C. Kirkwood and A. C. Albrecht, "Down-conversion of electronic frequencies and their dephasing dynamics: interferometric four-wave-mixing spectroscopy with broadband light," Phys. Rev. A 61, 033802 (2000).
[CrossRef]

S. Mukamel and E. Hanamura, "Four-wave mixing using partially coherent fields in systems with spatial correlations," Phys. Rev. A 33, 1099-1108 (1986).
[CrossRef] [PubMed]

Phys. Rev. E

D. P. Biebighauser, D. B. Turner, and D. J. Ulness, "Factorized time correlation diagram analysis of paired causal systems excited by twin stochastic driving functions," Phys. Rev. E 65, 026142 (2002).
[CrossRef]

Phys. Rev. Lett.

R. Beach and S. R. Hartmann, "Incoherent photon echoes," Phys. Rev. Lett. 53, 663-666 (1984).
[CrossRef]

Physica A

D. P. Biebighauser, J. Gregiore, and D. J. Ulness, "General counting formulae for factorized time correlation diagram analysis," Physica A 320, 1-10 (2003).
[CrossRef]

Solid State Commun.

E. Hanamura, "Coherent and incoherent laser spectroscopy of spatial and temporal fluctuations," Solid State Commun. 51, 697-700 (1984).
[CrossRef]

Other

D. Lee and A. C. Albrecht, "A unified view of Raman, resonance Raman, and fluorescence spectroscopy (and their analogues in two-photon absorption," in Advances in Infrared and Raman Spectroscopy, R.J.Clark and R.E.Hester, eds. (Wiley, New York, 1985).

C. L. Mehta, "Coherence and statistics of radiation," in Lectures in Theoretical Physics, W.E.Britin, ed. (University of Colorado, Boulder, Colo. 1965), Vol. VIIC.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

T. Kobayashi "Measurement of the femtosecond dynamics of nonlinear optical responses," in Modern Nonlinear Optics Part 3, M.Evans and S.Kielich, eds. Adv. Chem. Phys.85, 55-105 (1994).

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Figures (5)

Fig. 1
Fig. 1

Subset of the WMEL diagrams for I ( 2 ) ND 4 WM ( ) . Diagrams P1 and P2 represent terms in the density operator expansion in which a population is created after the second field action. Diagrams R1 and R2 represent pathways in which only an excited state coherence is achieved after the second step. Consistent with standard convention, solid (dashed) arrows represent ket-side (bra-side) field actions. The labels B, B , and M identify the beam from which the field originates.

Fig. 2
Fig. 2

Complete set of FTC diagrams for I ( 2 ) ND 4 WM ( ) obtained from the subset of WMEL diagrams in Fig. 1. The horizontal lines represent timelines for the two (independent) chromophores of the bichromophoric model. The tick marks on each of the timelines represent field actions, and the arrow (line) segments connecting tick marks indicate τ-dependent (τ-independent) correlation between field events. The diagrams of column A dominate the behavior of the signal because their topology allows for the greatest accumulation (see text and associated references for more detail).

Fig. 3
Fig. 3

Closer look at FTC diagram IA from Fig. 2. Here, if on a given chromophore frequency ω 1 acts to promote the ket to one of the excited states, then by color-locking, precisely frequency ω 1 must then act to promote the bra to that very same excited state. This leads to complete cancellation of the noise since the electric polarization that is developed by the final action of the narrowband beam will always be at precisely the frequency of the narrowband beam regardless of the value of ω 1 . Across the entire ensemble all frequencies present in the noisy beam are represented (indicated in the figure by the curve encompassing the excited-state manifold), but since color-locking prevents ω 1 , ω 2 coherences, the spectral width of the noisy beam is not present in the I ( 2 ) ND 4 WM ( ) signal (see text for more detail).

Fig. 4
Fig. 4

Spectrogram showing the striking cancellation of the noise for the I ( 2 ) ND 4 WM ( ) signal. The very large peak-to-background contrast ratio is also evident The noisy source is Kiton Red, the narrowband source is Rhodamine 610 set to 595 nm , and the sample is cresyl violet. This is a case where all beams reach an electronic resonance. The other cases mentioned in the text exhibit qualitatively similar spectrograms. The insets show a temporal (vertical) and spectral (horizontal) slice of the spectrogram. The spectral width of the signal is limited by the resolution of the monochromator as implied by the spectral width’s being identical to that of neon lines used for calibration. The temporal width is given by a convolution of the autocorrelation of the noisy light and the dephasing decay response of the sample.

Fig. 5
Fig. 5

Spectrogram for I ( 2 ) ND 4 WM ( + ) from water with the same noisy and narrowband source as in Fig. 4. Now color-locking does not force noise cancellation; consequently, the signal has a broad spectral profile. This is in sharp contrast to the I ( 2 ) ND 4 WM ( ) signal shown in Fig. 4.

Equations (18)

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I ( ω S ) = P s * ( ω S ) P t ( ω S ) = N 2 μ 2 d t d s exp ( i ω S t ) exp ( i ω S s ) ( P 1 * P 1 + P 1 * P 2 + P 2 * P 1 + P 2 * P 2 ) ,
P ( 3 ) ( t ) = N Tr [ μ ̂ ρ ̂ ( 3 ) ( t ) ] = N μ [ ρ g m ( 3 ) ( t ) + ρ m g ( 3 ) ( t ) ] ,
p ̃ ( ω i ) p ̃ ( ω j ) = δ ( ω i ω j ) J ( ω j ) ,
ρ m g ( 3 ) ( t ) = 2 i ρ o ( μ ) 3 t d t 3 t 3 d t 2 t 2 d t 1 E ( z , t 3 ) × E ( z , t 2 ) E ( z , t 1 ) × exp [ γ m m ( t 3 t 2 ) γ m g ( t t 3 + t 2 t 1 ) ] × { exp [ i ω m g ( t t 3 + t 2 t 1 ) ] + exp [ i ω m g ( t t 3 t 2 + t 1 ) ] } .
ρ m g ( 3 ) ( s ) = Eq. ( A 1 ) with t 1 s 1 , t 2 s 2 , t 3 s 3 , t s .
E B ( z , t ) = E B 2 p ( t ) exp ( i ω ¯ t + i k B z ) + E B 2 p * ( t ) exp ( i ω ¯ t i k B z ) ,
E B ( z , t ) = E B 2 p ( t τ ) exp [ i ω ¯ ( t τ ) + i k B z ] + E B 2 p * ( t τ ) exp [ i ω ¯ ( t τ ) i k B z ] ,
E M ( z , t ) = E M 2 exp ( i ω M t + i k M z ) + E M 2 exp ( i M t i k M z ) .
[ E M ( z , t 3 ) E B ( z , t 2 ) E B ( z , t 1 ) ] P 1 E B 2 E M 8 p * ( t 3 τ ) p ( t 1 ) exp [ i ω ¯ ( t 3 + t 1 τ ) i ω M t 2 + i k S z ] .
[ E M ( z , s 3 ) E B ( z , s 2 ) E B ( z , s 1 ) ] P 1 * E B 2 E M 8 p ( s 3 τ ) p * ( s 1 ) exp [ + i ω ¯ ( s 3 + s 1 τ ) + i ω M s 2 i k S z ] .
P 1 = i Λ t d t 3 t 3 d t 2 t 2 d t 1 p * ( t 3 τ ) p ( t 1 ) × exp [ i ω ¯ ( t 3 + t 1 τ ) i ω M t 2 + i k S z ] × exp [ γ m m ( t 3 t 2 ) ] exp [ γ m g ( t t 3 + t 2 t 1 ) ] exp [ i ω m g ( t t 3 + t 2 t 1 ) ] ,
P 1 * = i Λ s d s 3 s 3 d s 2 s 2 d s 1 p ( s 3 τ ) p * ( s 1 ) × exp [ + i ω ¯ ( s 3 + s 1 τ ) + i ω M s 2 i k S z ] × exp [ γ m m ( s 3 s 2 ) ] exp [ γ m g ( s s 3 + s 2 s 1 ) ] exp [ + i ω m g ( s s 3 + s 2 s 1 ) ] ,
P ( 3 ) ( t ) = N Tr [ μ ̂ ρ ̂ ( 3 ) ( t ) ] = N μ [ ρ g m ( 3 ) ( t ) + ρ m g ( 3 ) ( t ) ] .
P ( 3 ) ( t ) = N μ [ P 1 + P 2 ] .
P * ( 3 ) ( s ) = N Tr [ μ ρ ( 3 ) ( s ) ] = N μ [ P 1 * + P 2 * ] .
I ( ω S ) = P s * ( ω S ) P t ( ω S ) = N 2 μ 2 d t d s exp ( i ω S t ) exp ( i ω S s ) ( P 1 * P 1 + P 1 * P 2 + P 2 * P 1 + P 2 * P 2 ) .
I P 1 * P 1 = d Ω p * ( t 3 τ ) p ( t 1 ) p ( s 3 τ ) p * ( s 1 ) exp [ i ω ¯ ( t 3 + t 1 τ ) i ω M t 2 ] × exp [ γ m m ( t 3 t 2 + s 3 s 2 ) ] exp [ γ m g ( t t 3 + t 2 t 1 + s s 3 + s 2 s 1 ) ] × exp [ i ω m g ( t t 3 + t 2 t 1 s + s 3 s 2 + s 1 ) ] × exp [ + i ω ¯ ( s 3 + s 1 τ ) + i ω M s 2 ] exp ( i ω S t ) exp ( i ω S s ) ,
d Ω d t d s s d s 3 s 3 d s 2 s 2 d s 1 × t d t 3 t 3 d t 2 t 2 d t 1 .

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