Abstract

A novel optimized heterodyne method that recovers the complete electric field of any four-wave mixing signal at its point of origin is demonstrated. A tracer pulse is sent along the signal path and characterized at the sample by frequency-resolved optical gating. Spectral interferometry is used to determine the phase difference between the tracer and a reference pulse, the absorptive change in tracer phase in the sample, and the reference-signal phase difference. Together, these measurements allow calculation of the signal phase at the sample. The phase of three pulse-scattering signals from solutions of the infrared dye IR 144 in methanol determines the absolute signal-emission time within 0.5 fs.

© 1998 Optical Society of America

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1997

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

S. Matsuo and T. Tahara, “Phase stabilized optical heterodyne detection of impulsive stimulated Raman scattering,” Chem. Phys. Lett. 265, 636–642 (1997).
[CrossRef]

J.-P. Likforman, M. Joffre, and V. Thierry-Mieg, “Measurement of photon echoes by use of femtosecond Fourier-transform spectral interferometry,” Opt. Lett. 22, 1104–1106 (1997).
[CrossRef] [PubMed]

M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Spectral interferometry as an alternative to time domain heterodyning,” Opt. Lett. 22, 1338–1340 (1997).
[CrossRef]

X. Chen, W. J. Walecki, O. Buccafusca, D. N. Fittinghoff, and A. L. Smirl, “Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells,” Phys. Rev. B 56, 9738–9743 (1997).
[CrossRef]

1996

L. Xu, C. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21, 2008–2010 (1996).
[CrossRef] [PubMed]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses: erratum,” Opt. Lett. 21, 1313 (1996).
[CrossRef] [PubMed]

T. Joo, Y. Jia, J.-Y. Yu, M. J. Lang, and G. R. Fleming, “Third order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104, 6089–6108 (1996).
[CrossRef]

T. Joo, Y. Jia, J.-Y. Yu, D. M. Jonas, and G. R. Fleming, “Dynamics in isolated bacterial light harvesting antenna (LH2) of Rhodobacter sphaeroides at room temperature,” J. Phys. Chem. 100, 2399–2409 (1996).
[CrossRef]

K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1996).
[CrossRef]

L. Lepetit and M. Joffre, “Two-dimensional nonlinear optics using Fourier-transform spectral interferometry,” Opt. Lett. 21, 564–566 (1996).
[CrossRef] [PubMed]

S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, “Wigner spectrograms for femtosecond pulse-shaped heterodyne and autocorrelation measurements,” IEEE J. Quantum Electron. 32, 1278–1288 (1996).
[CrossRef]

1995

E. Tokunaga, A. Terasaki, and T. Kobayashi, “Femtosecond phase spectroscopy by use of frequency-domain interference,” J. Opt. Soc. Am. B 12, 753–771 (1995).
[CrossRef]

L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995).
[CrossRef]

X. J. Chang, P. Cong, and J. D. Simon, “Optical heterodyne detection of impulsive stimulated Raman scattering in liquids,” J. Phys. Chem. 99, 7857–7859 (1995).
[CrossRef]

W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-locked heterodyne-detected stimulated photon echo. A unique tool to study solute-solvent interactions,” Chem. Phys. Lett. 238, 1–8 (1995).
[CrossRef]

M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, “Time-resolved femtosecond photon echo probes bimodal solvent dynamics,” Phys. Rev. Lett. 74, 674–677 (1995).
[CrossRef] [PubMed]

P. Vöhringer, D. C. Arnett, T.-S. Yang, and N. F. Scherer, “Time-gated photon echo spectroscopy in liquids,” Chem. Phys. Lett. 237, 387–398 (1995).
[CrossRef]

T. Joo, Y. Jia, and G. R. Fleming, “Ultrafast liquid dynamics studied by third and fifth order three pulse photon echoes,” J. Chem. Phys. 102, 4063–4068 (1995).
[CrossRef]

P. Vöhringer and N. F. Scherer, “Transient grating optical heterodyne detected impulsive stimulated Raman scattering,” J. Phys. Chem. 99, 2684–2695 (1995).
[CrossRef]

K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, and A. Sullivan, “Direct measurement of the phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
[CrossRef] [PubMed]

1994

H. Nakatsuka, N. Tsurmachi, and T. Fuji, “Interferometric observation of femtosecond free induction decay,” Opt. Lett. 19, 1867–1869 (1994).
[CrossRef] [PubMed]

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

J. Paye, “How to measure the amplitude and phase of an ultrashort light pulse with an autocorrelator and a spectrometer,” IEEE J. Quantum Electron. 30, 2693–2697 (1994).
[CrossRef]

1993

1992

S. Qian and J. M. Morris, “Wigner distribution decomposition and cross-terms deleted representation,” Signal Process. 27, 125–144 (1992).
[CrossRef]

W. T. Pollard and R. A. Mathies, “Analysis of femtosecond dynamic absorption spectra of nonstationary states,” Ann. Rev. Phys. Chem. 43, 497–523 (1992).
[CrossRef]

1991

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

1989

1985

1979

M. D. Levenson and G. L. Eesley, “Polarization selective optical heterodyne detection for dramatically improved sensitivity in laser spectroscopy,” Appl. Phys. 19, 1–17 (1979).
[CrossRef]

1961

W. B. Mims, K. Nassau, and J. D. McGee, “Spectral diffusion in electron resonance lines,” Phys. Rev. 123, 2059–2069 (1961).
[CrossRef]

1957

I. Solomon, “Multiple echoes in solids,” Phys. Rev. 110, 61–65 (1957).
[CrossRef]

1950

E. L. Hahn, “Spin echoes,” Phys. Rev. 80, 580–594 (1950).
[CrossRef]

Arnett, D. C.

P. Vöhringer, D. C. Arnett, T.-S. Yang, and N. F. Scherer, “Time-gated photon echo spectroscopy in liquids,” Chem. Phys. Lett. 237, 387–398 (1995).
[CrossRef]

Barthelmy, A.

Bigot, J.-Y.

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

Bowie, J. L.

Brabec, T.

Buccafusca, O.

X. Chen, W. J. Walecki, O. Buccafusca, D. N. Fittinghoff, and A. L. Smirl, “Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells,” Phys. Rev. B 56, 9738–9743 (1997).
[CrossRef]

Carlson, R. J.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

Chang, X. J.

X. J. Chang, P. Cong, and J. D. Simon, “Optical heterodyne detection of impulsive stimulated Raman scattering in liquids,” J. Phys. Chem. 99, 7857–7859 (1995).
[CrossRef]

Chemla, D. S.

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

Chen, X.

X. Chen, W. J. Walecki, O. Buccafusca, D. N. Fittinghoff, and A. L. Smirl, “Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells,” Phys. Rev. B 56, 9738–9743 (1997).
[CrossRef]

Chériaux, G.

Chu, K. C.

Cina, J. A.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

Ciordas-Ciurdariu, C.

S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, “Wigner spectrograms for femtosecond pulse-shaped heterodyne and autocorrelation measurements,” IEEE J. Quantum Electron. 32, 1278–1288 (1996).
[CrossRef]

Cong, P.

X. J. Chang, P. Cong, and J. D. Simon, “Optical heterodyne detection of impulsive stimulated Raman scattering in liquids,” J. Phys. Chem. 99, 7857–7859 (1995).
[CrossRef]

de Boeij, W. P.

M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Spectral interferometry as an alternative to time domain heterodyning,” Opt. Lett. 22, 1338–1340 (1997).
[CrossRef]

W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-locked heterodyne-detected stimulated photon echo. A unique tool to study solute-solvent interactions,” Chem. Phys. Lett. 238, 1–8 (1995).
[CrossRef]

De Silvestri, S.

DeLong, K. W.

Dienes, A.

Du, M.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

Duppen, K.

M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, “Time-resolved femtosecond photon echo probes bimodal solvent dynamics,” Phys. Rev. Lett. 74, 674–677 (1995).
[CrossRef] [PubMed]

Eesley, G. L.

M. D. Levenson and G. L. Eesley, “Polarization selective optical heterodyne detection for dramatically improved sensitivity in laser spectroscopy,” Appl. Phys. 19, 1–17 (1979).
[CrossRef]

Emde, M. F.

Fittinghoff, D. N.

X. Chen, W. J. Walecki, O. Buccafusca, D. N. Fittinghoff, and A. L. Smirl, “Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells,” Phys. Rev. B 56, 9738–9743 (1997).
[CrossRef]

K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1996).
[CrossRef]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses: erratum,” Opt. Lett. 21, 1313 (1996).
[CrossRef] [PubMed]

Fleming, G. R.

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

T. Joo, Y. Jia, J.-Y. Yu, M. J. Lang, and G. R. Fleming, “Third order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104, 6089–6108 (1996).
[CrossRef]

T. Joo, Y. Jia, J.-Y. Yu, D. M. Jonas, and G. R. Fleming, “Dynamics in isolated bacterial light harvesting antenna (LH2) of Rhodobacter sphaeroides at room temperature,” J. Phys. Chem. 100, 2399–2409 (1996).
[CrossRef]

T. Joo, Y. Jia, and G. R. Fleming, “Ultrafast liquid dynamics studied by third and fifth order three pulse photon echoes,” J. Chem. Phys. 102, 4063–4068 (1995).
[CrossRef]

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

Fuji, T.

Grant, R. S.

Hahn, E. L.

E. L. Hahn, “Spin echoes,” Phys. Rev. 80, 580–594 (1950).
[CrossRef]

Hänsch, T. W.

Heritage, J. P.

Ippen, E. P.

Jennings, R. T.

Jia, Y.

T. Joo, Y. Jia, J.-Y. Yu, M. J. Lang, and G. R. Fleming, “Third order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104, 6089–6108 (1996).
[CrossRef]

T. Joo, Y. Jia, J.-Y. Yu, D. M. Jonas, and G. R. Fleming, “Dynamics in isolated bacterial light harvesting antenna (LH2) of Rhodobacter sphaeroides at room temperature,” J. Phys. Chem. 100, 2399–2409 (1996).
[CrossRef]

T. Joo, Y. Jia, and G. R. Fleming, “Ultrafast liquid dynamics studied by third and fifth order three pulse photon echoes,” J. Chem. Phys. 102, 4063–4068 (1995).
[CrossRef]

Joffre, M.

Jonas, D. M.

T. Joo, Y. Jia, J.-Y. Yu, D. M. Jonas, and G. R. Fleming, “Dynamics in isolated bacterial light harvesting antenna (LH2) of Rhodobacter sphaeroides at room temperature,” J. Phys. Chem. 100, 2399–2409 (1996).
[CrossRef]

Joo, T.

T. Joo, Y. Jia, J.-Y. Yu, D. M. Jonas, and G. R. Fleming, “Dynamics in isolated bacterial light harvesting antenna (LH2) of Rhodobacter sphaeroides at room temperature,” J. Phys. Chem. 100, 2399–2409 (1996).
[CrossRef]

T. Joo, Y. Jia, J.-Y. Yu, M. J. Lang, and G. R. Fleming, “Third order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104, 6089–6108 (1996).
[CrossRef]

T. Joo, Y. Jia, and G. R. Fleming, “Ultrafast liquid dynamics studied by third and fifth order three pulse photon echoes,” J. Chem. Phys. 102, 4063–4068 (1995).
[CrossRef]

Kane, D. J.

Khidekel, V.

S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, “Wigner spectrograms for femtosecond pulse-shaped heterodyne and autocorrelation measurements,” IEEE J. Quantum Electron. 32, 1278–1288 (1996).
[CrossRef]

Kobayashi, T.

Krausz, F.

Krumbügel, M. A.

Lang, M. J.

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

T. Joo, Y. Jia, J.-Y. Yu, M. J. Lang, and G. R. Fleming, “Third order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104, 6089–6108 (1996).
[CrossRef]

Larsen, D. S.

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

Lepetit, L.

Levenson, M. D.

M. D. Levenson and G. L. Eesley, “Polarization selective optical heterodyne detection for dramatically improved sensitivity in laser spectroscopy,” Appl. Phys. 19, 1–17 (1979).
[CrossRef]

Likforman, J.-P.

Liu, K. X.

Mathies, R. A.

W. T. Pollard and R. A. Mathies, “Analysis of femtosecond dynamic absorption spectra of nonstationary states,” Ann. Rev. Phys. Chem. 43, 497–523 (1992).
[CrossRef]

Matro, A.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

Matsuo, S.

S. Matsuo and T. Tahara, “Phase stabilized optical heterodyne detection of impulsive stimulated Raman scattering,” Chem. Phys. Lett. 265, 636–642 (1997).
[CrossRef]

McGee, J. D.

W. B. Mims, K. Nassau, and J. D. McGee, “Spectral diffusion in electron resonance lines,” Phys. Rev. 123, 2059–2069 (1961).
[CrossRef]

Mims, W. B.

W. B. Mims, K. Nassau, and J. D. McGee, “Spectral diffusion in electron resonance lines,” Phys. Rev. 123, 2059–2069 (1961).
[CrossRef]

Morris, J. M.

S. Qian and J. M. Morris, “Wigner distribution decomposition and cross-terms deleted representation,” Signal Process. 27, 125–144 (1992).
[CrossRef]

Mukamel, S.

S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, “Wigner spectrograms for femtosecond pulse-shaped heterodyne and autocorrelation measurements,” IEEE J. Quantum Electron. 32, 1278–1288 (1996).
[CrossRef]

Mycek, M.-A.

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

Nakatsuka, H.

Nassau, K.

W. B. Mims, K. Nassau, and J. D. McGee, “Spectral diffusion in electron resonance lines,” Phys. Rev. 123, 2059–2069 (1961).
[CrossRef]

Paye, J.

J. Paye, “How to measure the amplitude and phase of an ultrashort light pulse with an autocorrelator and a spectrometer,” IEEE J. Quantum Electron. 30, 2693–2697 (1994).
[CrossRef]

Pollard, W. T.

W. T. Pollard and R. A. Mathies, “Analysis of femtosecond dynamic absorption spectra of nonstationary states,” Ann. Rev. Phys. Chem. 43, 497–523 (1992).
[CrossRef]

Poppe, A.

Pshenichnikov, M. S.

M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Spectral interferometry as an alternative to time domain heterodyning,” Opt. Lett. 22, 1338–1340 (1997).
[CrossRef]

M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, “Time-resolved femtosecond photon echo probes bimodal solvent dynamics,” Phys. Rev. Lett. 74, 674–677 (1995).
[CrossRef] [PubMed]

W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-locked heterodyne-detected stimulated photon echo. A unique tool to study solute-solvent interactions,” Chem. Phys. Lett. 238, 1–8 (1995).
[CrossRef]

Qian, S.

S. Qian and J. M. Morris, “Wigner distribution decomposition and cross-terms deleted representation,” Signal Process. 27, 125–144 (1992).
[CrossRef]

Reynaud, F.

Rice, S. A.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

Romero-Rochin, V.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

Ruggiero, A. J.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

Salin, F.

Schäfer, W.

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

Scherer, N. F.

P. Vöhringer and N. F. Scherer, “Transient grating optical heterodyne detected impulsive stimulated Raman scattering,” J. Phys. Chem. 99, 2684–2695 (1995).
[CrossRef]

P. Vöhringer, D. C. Arnett, T.-S. Yang, and N. F. Scherer, “Time-gated photon echo spectroscopy in liquids,” Chem. Phys. Lett. 237, 387–398 (1995).
[CrossRef]

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

Simon, J. D.

X. J. Chang, P. Cong, and J. D. Simon, “Optical heterodyne detection of impulsive stimulated Raman scattering in liquids,” J. Phys. Chem. 99, 7857–7859 (1995).
[CrossRef]

Smirl, A. L.

X. Chen, W. J. Walecki, O. Buccafusca, D. N. Fittinghoff, and A. L. Smirl, “Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells,” Phys. Rev. B 56, 9738–9743 (1997).
[CrossRef]

Solomon, I.

I. Solomon, “Multiple echoes in solids,” Phys. Rev. 110, 61–65 (1957).
[CrossRef]

Spielmann, C.

Sullivan, A.

Sweetser, J. N.

Tahara, T.

S. Matsuo and T. Tahara, “Phase stabilized optical heterodyne detection of impulsive stimulated Raman scattering,” Chem. Phys. Lett. 265, 636–642 (1997).
[CrossRef]

Terasaki, A.

Thierry-Mieg, V.

Tokmakoff, A.

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

Tokunaga, E.

Trebino, R.

Tsurmachi, N.

Vöhringer, P.

P. Vöhringer, D. C. Arnett, T.-S. Yang, and N. F. Scherer, “Time-gated photon echo spectroscopy in liquids,” Chem. Phys. Lett. 237, 387–398 (1995).
[CrossRef]

P. Vöhringer and N. F. Scherer, “Transient grating optical heterodyne detected impulsive stimulated Raman scattering,” J. Phys. Chem. 99, 2684–2695 (1995).
[CrossRef]

Walecki, W. J.

X. Chen, W. J. Walecki, O. Buccafusca, D. N. Fittinghoff, and A. L. Smirl, “Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells,” Phys. Rev. B 56, 9738–9743 (1997).
[CrossRef]

Walmsley, I. A.

Weiner, A. M.

Weiss, S.

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

White, W. E.

Wiersma, D. A.

M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Spectral interferometry as an alternative to time domain heterodyning,” Opt. Lett. 22, 1338–1340 (1997).
[CrossRef]

M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, “Time-resolved femtosecond photon echo probes bimodal solvent dynamics,” Phys. Rev. Lett. 74, 674–677 (1995).
[CrossRef] [PubMed]

W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-locked heterodyne-detected stimulated photon echo. A unique tool to study solute-solvent interactions,” Chem. Phys. Lett. 238, 1–8 (1995).
[CrossRef]

Xu, L.

Yang, T.-S.

P. Vöhringer, D. C. Arnett, T.-S. Yang, and N. F. Scherer, “Time-gated photon echo spectroscopy in liquids,” Chem. Phys. Lett. 237, 387–398 (1995).
[CrossRef]

Yu, J.-Y.

T. Joo, Y. Jia, J.-Y. Yu, M. J. Lang, and G. R. Fleming, “Third order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104, 6089–6108 (1996).
[CrossRef]

T. Joo, Y. Jia, J.-Y. Yu, D. M. Jonas, and G. R. Fleming, “Dynamics in isolated bacterial light harvesting antenna (LH2) of Rhodobacter sphaeroides at room temperature,” J. Phys. Chem. 100, 2399–2409 (1996).
[CrossRef]

Ann. Rev. Phys. Chem.

W. T. Pollard and R. A. Mathies, “Analysis of femtosecond dynamic absorption spectra of nonstationary states,” Ann. Rev. Phys. Chem. 43, 497–523 (1992).
[CrossRef]

Appl. Phys.

M. D. Levenson and G. L. Eesley, “Polarization selective optical heterodyne detection for dramatically improved sensitivity in laser spectroscopy,” Appl. Phys. 19, 1–17 (1979).
[CrossRef]

Chem. Phys. Lett.

W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Phase-locked heterodyne-detected stimulated photon echo. A unique tool to study solute-solvent interactions,” Chem. Phys. Lett. 238, 1–8 (1995).
[CrossRef]

P. Vöhringer, D. C. Arnett, T.-S. Yang, and N. F. Scherer, “Time-gated photon echo spectroscopy in liquids,” Chem. Phys. Lett. 237, 387–398 (1995).
[CrossRef]

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

S. Matsuo and T. Tahara, “Phase stabilized optical heterodyne detection of impulsive stimulated Raman scattering,” Chem. Phys. Lett. 265, 636–642 (1997).
[CrossRef]

IEEE J. Quantum Electron.

J. Paye, “How to measure the amplitude and phase of an ultrashort light pulse with an autocorrelator and a spectrometer,” IEEE J. Quantum Electron. 30, 2693–2697 (1994).
[CrossRef]

K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1996).
[CrossRef]

S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, “Wigner spectrograms for femtosecond pulse-shaped heterodyne and autocorrelation measurements,” IEEE J. Quantum Electron. 32, 1278–1288 (1996).
[CrossRef]

J. Chem. Phys.

T. Joo, Y. Jia, J.-Y. Yu, M. J. Lang, and G. R. Fleming, “Third order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104, 6089–6108 (1996).
[CrossRef]

T. Joo, Y. Jia, and G. R. Fleming, “Ultrafast liquid dynamics studied by third and fifth order three pulse photon echoes,” J. Chem. Phys. 102, 4063–4068 (1995).
[CrossRef]

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence detected wave packet interferometry: time resolved spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487–1511 (1991).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. Chem.

P. Vöhringer and N. F. Scherer, “Transient grating optical heterodyne detected impulsive stimulated Raman scattering,” J. Phys. Chem. 99, 2684–2695 (1995).
[CrossRef]

X. J. Chang, P. Cong, and J. D. Simon, “Optical heterodyne detection of impulsive stimulated Raman scattering in liquids,” J. Phys. Chem. 99, 7857–7859 (1995).
[CrossRef]

T. Joo, Y. Jia, J.-Y. Yu, D. M. Jonas, and G. R. Fleming, “Dynamics in isolated bacterial light harvesting antenna (LH2) of Rhodobacter sphaeroides at room temperature,” J. Phys. Chem. 100, 2399–2409 (1996).
[CrossRef]

Opt. Lett.

H. Nakatsuka, N. Tsurmachi, and T. Fuji, “Interferometric observation of femtosecond free induction decay,” Opt. Lett. 19, 1867–1869 (1994).
[CrossRef] [PubMed]

K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, and A. Sullivan, “Direct measurement of the phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
[CrossRef] [PubMed]

F. Reynaud, F. Salin, and A. Barthelmy, “Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,” Opt. Lett. 14, 275–277 (1989).
[CrossRef] [PubMed]

L. Xu, C. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21, 2008–2010 (1996).
[CrossRef] [PubMed]

J.-P. Likforman, M. Joffre, and V. Thierry-Mieg, “Measurement of photon echoes by use of femtosecond Fourier-transform spectral interferometry,” Opt. Lett. 22, 1104–1106 (1997).
[CrossRef] [PubMed]

M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, “Spectral interferometry as an alternative to time domain heterodyning,” Opt. Lett. 22, 1338–1340 (1997).
[CrossRef]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses: erratum,” Opt. Lett. 21, 1313 (1996).
[CrossRef] [PubMed]

L. Lepetit and M. Joffre, “Two-dimensional nonlinear optics using Fourier-transform spectral interferometry,” Opt. Lett. 21, 564–566 (1996).
[CrossRef] [PubMed]

Phys. Rev.

E. L. Hahn, “Spin echoes,” Phys. Rev. 80, 580–594 (1950).
[CrossRef]

I. Solomon, “Multiple echoes in solids,” Phys. Rev. 110, 61–65 (1957).
[CrossRef]

W. B. Mims, K. Nassau, and J. D. McGee, “Spectral diffusion in electron resonance lines,” Phys. Rev. 123, 2059–2069 (1961).
[CrossRef]

Phys. Rev. B

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

X. Chen, W. J. Walecki, O. Buccafusca, D. N. Fittinghoff, and A. L. Smirl, “Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells,” Phys. Rev. B 56, 9738–9743 (1997).
[CrossRef]

Phys. Rev. Lett.

M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, “Time-resolved femtosecond photon echo probes bimodal solvent dynamics,” Phys. Rev. Lett. 74, 674–677 (1995).
[CrossRef] [PubMed]

Signal Process.

S. Qian and J. M. Morris, “Wigner distribution decomposition and cross-terms deleted representation,” Signal Process. 27, 125–144 (1992).
[CrossRef]

Other

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

D. W. Robinson, “Phase unwrapping methods” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Philadelphia, 1993).

The spectral phases are identical in the sense of a FROG measurement. There are experimental uncertainties in the delay, and there could be nearly constant differences in the spectral phases. Near 800 nm, a path difference of ~30 μm between a fused-silica beam splitter and compensating block would produce both a 45-fs delay and a nearly constant spectral phase difference of π (see Ref. 31). Such constant phase differences might be eliminated by tilting the compensating blocks.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, New York, 1997).

U. Brackmann, Lamdachrome Laser Dyes (Lambda Physik, Gottingen, 1986).

For ω≫0, (1/2)∫e(t)exp[−iΦ(t)]exp(iωt)dt is a rotating-wave approximation to E⁁(ω), while (1/2)∫e(t)exp[iΦ(t)] exp(iωt)dt is a rotating-wave approximation for ω≪0. Near ω=0, the two rotating-wave approximations to E⁁(ω) interfere so that Φ(ω=0)=0, ±π is continuous with Φ(ω)=−Φ(−ω)mod(2π).

N. Bloembergen, Nonlinear Optics (Addison-Wesley, New York, 1992). See the discussion at the beginning of Chap. 4. Within the rotating-wave approximation defined in Note 30, if constant spectral phases Φ1, Φ2, and Φ3 are added to the excitation pulses, the phase of the nonlinear polarization in direction s1k1+s2k2+s3k3 (where si= ±1) is increased by s1Φ1+s2Φ2+s3Φ3. In the direction k3+k2−k1, a constant phase Φ0 added to all three excitation pulses adds the same constant phase Φ0 to the third-order polarization and emitted field. This is canceled in the spectral interferogram because the reference pulse has the same constant phase Φ0.

M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Philadelphia, 1993), pp. 141–193.

J. K. M. Sanders and B. K. Hunter, Modern NMR Spectroscopy: A Guide for Chemists (Oxford U. Press, Oxford, UK, 1987).

S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford U. Press, New York, 1995).

J. L. Hall, H. G. Robinson, T. Baer, and L. Hollberg, “The lineshapes of sub-Doppler resonances observable with FM side-band (optical heterodyne) techniques,” in Advances in Laser Spectroscopy, F. T. Arecchi, F. Strumia, and H. Walther, eds. (Plenum, New York, 1983).

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Figures (6)

Fig. 1
Fig. 1

Experimental layout. A five-beam interferometer creates three excitation pulses, a tracer, and a reference. BS, 50-50 beam splitter; BS’, 66-33 beam splitter; CB, fused-silica compensating block; F, neutral-density filter; L, 10-cm lens; M, mask to block beams other than tracer and echo; T, tracer; R, reference; D, photodiode; S, 0.2-mm sample cell. For clarity the compensating block common to beams 1 and 3 has been displaced from its experimental location at the beam crossing. The lens view shows the positions of the beams on the lens before the sample. ks=kt=k3+k2-k1. Dispersion is matched along the excitation and tracer paths. The tracer is used to characterize the reference-pulse phase, absorptive phase shifts in the sample, and the dispersion of the optics after the signal leaves the sample. In an experiment the tracer is blocked and the four-wave mixing signal emitted along the tracer wave vector is detected through interference with the reference pulse.

Fig. 2
Fig. 2

Spectral interferogram of the signal and reference pulses with a signal-reference delay of 760 fs. The fringe spacing Δω provides the delay tdelay=2π/Δω between pulses. A frequency-dependent delay indicates a difference in chirp. Excitation pulse delays were t1=-14.7 fs and t2=t3=0.

Fig. 3
Fig. 3

Pulse characteristics. Top panel: Spectrum I(ω) of the excitation and tracer pulses through pure methanol and phase ϕ(ω) recovered by second-harmonic FROG (dots) in a KDP wedge. The solid curve through the phase points is a fourth-order expansion of the phase. Middle panel: Spectrum and phase of the tracer pulse after passage through the 0.2-mm sample cell containing 0.55-mM IR144 in methanol. The spectrum is shifted to lower frequencies by absorption, and the shape of the phase curve is changed. Bottom panel: Spectrum and phase of a four-wave mixing signal observed with pulse 1 arriving at the sample 20.0 fs before pulses 2 and 3. The signal spectrum is centered between that of the excitation pulses as they enter and exit the sample. The delay dϕ/dω indicated the signal is emitted 12 fs after pulses 2 and 3 and is chirped, with low frequencies emitted near zero delay.

Fig. 4
Fig. 4

Contour plot of the intensity I(t, τ) of the signals as a function of τ and the time t after the third pulse for T=0. (τ is the delay between pulses 1 and 2. T is the delay between the last two pulses.) The darkened curve denotes the half-maximum contour. The spacing between the contours is 10% of the maximum value, with the bottom line representing 10%. The diamonds show the average time of signal emission.

Fig. 5
Fig. 5

Contour plot of the signal spectrum I(ω) as a function of τ for T=0. The darkened curve marks the half-maximum contour. The spacing between the contours is 10% of the maximum value, with the bottom curve representing 10%. The diamonds show the average frequency of the signal spectrum.

Fig. 6
Fig. 6

Panels show W(t, ω), the Wigner transform of the signal, for six values of τ at T=0. For τ=-10 fs and τ=0, the signal shows a significant upchirp (frequency increasing with time). For later values of τ, the spectral phase of the signal gradually straightens out and the upchirp decreases.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

Eˆ(ω)=-+E(t)exp(iωt)dt=e(ω)exp[iϕ(ω)]
I(ω)|Eˆ(ω)|2 =[e(ω)]2,
I(ω)|E^sig(ω)+E^ref(ω)|2esig2(ω)+2 sin2(δωtdelay/2)(δωtdelay/2)2 esig(ω)eref(ω)cos[Δϕ(ω)]+eref2(ω).
ϕsignal(ω)=Δϕsr(ω)-Δϕtr(ω)+ϕtracer(ω).
Eˆ(t)=1π 0E^sig(ω)exp(-iωt)dω,

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