Abstract

Ultrafast science is inherently, due to the lack of fast enough detectors and electronics, based on nonlinear interactions. Typically, however, nonlinear measurements require significant powers and often operate in a limited spectral range. Here we overcome the difficulties of ultraweak ultrafast measurements by precision time-domain localization of spectral components. We utilize this for linear self-referenced characterization of pulse trains having ∼ 1 photon per pulse, a regime in which nonlinear techniques are impractical, at a temporal resolution of ∼ 10 fs. This technique does not only set a new scale of sensitivity in ultrashort pulse characterization, but is also applicable in any spectral range from the near-infrared to the deep UV.

© 2011 OSA

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2010 (2)

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nature Photon. (2010).
[Crossref]

C. Dorrer and J. Bromage, “High-sensitivity optical pulse characterization using Sagnac electro-optic spectral shearing interferometry,” Opt. Lett. 35, 1353–1355 (2010).
[Crossref] [PubMed]

2009 (2)

S. Moon and D. Kim, “Reflectometric fiber dispersion measurement using a supercontinuum pulse source,” IEEE Photon. Technol. Lett. 21, 1262 –1264 (2009).
[Crossref]

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1, 308–437 (2009).
[Crossref]

2008 (3)

2007 (1)

D. Reid and J. Harvey, “Linear Spectrograms Using Electrooptic Modulators,” IEEE Photon. Technol. Lett. 19, 535–537 (2007).
[Crossref]

2006 (1)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nature Methods 3, 793–796 (2006).
[Crossref] [PubMed]

2004 (2)

S. Diddams, J. Bergquist, S. Jefferts, and C. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306, 1318 (2004).
[Crossref] [PubMed]

P. Kockaert, M. Haelterman, P. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quant. Electron. 10, 206–212 (2004).
[Crossref]

2003 (1)

2002 (3)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J 82, 2775–2783 (2002).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Coherent Transient Enhancement of Optically Induced Resonant Transitions,” Phys. Rev. Lett. 88, 123004 (2002).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature (London) 418, 512–514 (2002).
[Crossref]

2001 (1)

M. Beck, C. Dorrer, and I. Walmsley, “Joint quantum measurement using unbalanced array detection,” Phys. Rev. Lett. 87, 253601 (2001).
[Crossref] [PubMed]

2000 (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Scie. Instr. 71, 1929–1960 (2000).
[Crossref]

1999 (2)

H. Cramer, Mathematical methods of statistics (Princeton Univ Pr, 1999).

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-stokes raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[Crossref]

1998 (1)

1997 (2)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Scie. Inst. 68, 3277–3295 (1997).
[Crossref]

D. Meshulach, D. Yelin, and Y. Silberberg, “Real-time spatialspectral interference measurements of ultrashort optical pulses,” J. Opt. Soc. Am. B Opt. Phys. 14, 2095–2098 (1997).
[Crossref]

1996 (2)

1995 (1)

K. Mori, T. Morioka, and M. Saruwatari, “Ultrawide spectral range group-velocity dispersion measurement utilizing supercontinuum in an optical fiber pumped by a 1.5 mu;m compact laser source,” IEEE Trans. Instr. Measur. 44, 712 –715 (1995).
[Crossref]

1993 (1)

1991 (1)

1979 (1)

K. Weber and K. Niemax, “Self-broadening and shift of Doppler-free two-photon lines of Rb,” Opt. Commun. 31, 52–56 (1979).
[Crossref]

Allan, D. W.

D. W. Allan, J. H. Shoaf, and D. Halford, “Statistics of Time and Frequency Data Analysis,” in “Time and Frequency: Theory and Fundamentals,” B. E. Blair, ed. (1974), pp. 151–+.

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nature Methods 3, 793–796 (2006).
[Crossref] [PubMed]

Beck, M.

M. Beck, C. Dorrer, and I. Walmsley, “Joint quantum measurement using unbalanced array detection,” Phys. Rev. Lett. 87, 253601 (2001).
[Crossref] [PubMed]

Bergquist, J.

S. Diddams, J. Bergquist, S. Jefferts, and C. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306, 1318 (2004).
[Crossref] [PubMed]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science313, 1642–1645 (2006).
[Crossref] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science313, 1642–1645 (2006).
[Crossref] [PubMed]

Bowie, J. L.

Bromage, J.

Chilla, J. L. A.

Cramer, H.

H. Cramer, Mathematical methods of statistics (Princeton Univ Pr, 1999).

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science313, 1642–1645 (2006).
[Crossref] [PubMed]

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Scie. Inst. 68, 3277–3295 (1997).
[Crossref]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbüugel, 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]

Diddams, S.

S. Diddams, J. Bergquist, S. Jefferts, and C. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306, 1318 (2004).
[Crossref] [PubMed]

S. Prein, S. Diddams, and J. Diels, “Complete characterization of femtosecond pulses using an all-electronic detector,” Opt. Commun. 123, 567–573 (1996).
[Crossref]

Diels, J.

S. Prein, S. Diddams, and J. Diels, “Complete characterization of femtosecond pulses using an all-electronic detector,” Opt. Commun. 123, 567–573 (1996).
[Crossref]

Dorrer, C.

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, “Coherent Transient Enhancement of Optically Induced Resonant Transitions,” Phys. Rev. Lett. 88, 123004 (2002).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature (London) 418, 512–514 (2002).
[Crossref]

Emplit, P.

P. Kockaert, M. Haelterman, P. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quant. Electron. 10, 206–212 (2004).
[Crossref]

Fejer, M. M.

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Scie. Inst. 68, 3277–3295 (1997).
[Crossref]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbüugel, 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]

Fontaine, N. K.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nature Photon. (2010).
[Crossref]

Froehly, C.

P. Kockaert, M. Haelterman, P. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quant. Electron. 10, 206–212 (2004).
[Crossref]

Haelterman, M.

P. Kockaert, M. Haelterman, P. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quant. Electron. 10, 206–212 (2004).
[Crossref]

Halford, D.

D. W. Allan, J. H. Shoaf, and D. Halford, “Statistics of Time and Frequency Data Analysis,” in “Time and Frequency: Theory and Fundamentals,” B. E. Blair, ed. (1974), pp. 151–+.

Harvey, J.

D. Reid and J. Harvey, “Linear Spectrograms Using Electrooptic Modulators,” IEEE Photon. Technol. Lett. 19, 535–537 (2007).
[Crossref]

Heritage, J. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nature Photon. (2010).
[Crossref]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science313, 1642–1645 (2006).
[Crossref] [PubMed]

Holtom, G. R.

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-stokes raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[Crossref]

Iaconis, C.

Jefferts, S.

S. Diddams, J. Bergquist, S. Jefferts, and C. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306, 1318 (2004).
[Crossref] [PubMed]

Jennings, R. T.

Jin, J.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[Crossref] [PubMed]

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Scie. Inst. 68, 3277–3295 (1997).
[Crossref]

R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10, 1101–1111 (1993).
[Crossref]

Kang, I.

Kim, D.

S. Moon and D. Kim, “Reflectometric fiber dispersion measurement using a supercontinuum pulse source,” IEEE Photon. Technol. Lett. 21, 1262 –1264 (2009).
[Crossref]

Kim, S.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[Crossref] [PubMed]

Kim, S. W.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[Crossref] [PubMed]

Kim, Y.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[Crossref] [PubMed]

Kim, Y. J.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[Crossref] [PubMed]

Kockaert, P.

P. Kockaert, M. Haelterman, P. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quant. Electron. 10, 206–212 (2004).
[Crossref]

Krumbügel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Scie. Inst. 68, 3277–3295 (1997).
[Crossref]

Krumbüugel, M. A.

Langrock, C.

Larson, D. R.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J 82, 2775–2783 (2002).
[Crossref] [PubMed]

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science313, 1642–1645 (2006).
[Crossref] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science313, 1642–1645 (2006).
[Crossref] [PubMed]

Martinez, O. E.

Meshulach, D.

D. Meshulach, D. Yelin, and Y. Silberberg, “Real-time spatialspectral interference measurements of ultrashort optical pulses,” J. Opt. Soc. Am. B Opt. Phys. 14, 2095–2098 (1997).
[Crossref]

Miao, H.

Moon, S.

S. Moon and D. Kim, “Reflectometric fiber dispersion measurement using a supercontinuum pulse source,” IEEE Photon. Technol. Lett. 21, 1262 –1264 (2009).
[Crossref]

Mori, K.

K. Mori, T. Morioka, and M. Saruwatari, “Ultrawide spectral range group-velocity dispersion measurement utilizing supercontinuum in an optical fiber pumped by a 1.5 mu;m compact laser source,” IEEE Trans. Instr. Measur. 44, 712 –715 (1995).
[Crossref]

Morioka, T.

K. Mori, T. Morioka, and M. Saruwatari, “Ultrawide spectral range group-velocity dispersion measurement utilizing supercontinuum in an optical fiber pumped by a 1.5 mu;m compact laser source,” IEEE Trans. Instr. Measur. 44, 712 –715 (1995).
[Crossref]

Niemax, K.

K. Weber and K. Niemax, “Self-broadening and shift of Doppler-free two-photon lines of Rb,” Opt. Commun. 31, 52–56 (1979).
[Crossref]

Oates, C.

S. Diddams, J. Bergquist, S. Jefferts, and C. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306, 1318 (2004).
[Crossref] [PubMed]

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science313, 1642–1645 (2006).
[Crossref] [PubMed]

Oron, D.

N. Dudovich, D. Oron, and Y. Silberberg, “Coherent Transient Enhancement of Optically Induced Resonant Transitions,” Phys. Rev. Lett. 88, 123004 (2002).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature (London) 418, 512–514 (2002).
[Crossref]

Park, I. Y.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[Crossref] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science313, 1642–1645 (2006).
[Crossref] [PubMed]

Prein, S.

S. Prein, S. Diddams, and J. Diels, “Complete characterization of femtosecond pulses using an all-electronic detector,” Opt. Commun. 123, 567–573 (1996).
[Crossref]

Quochi, F.

Reid, D.

D. Reid and J. Harvey, “Linear Spectrograms Using Electrooptic Modulators,” IEEE Photon. Technol. Lett. 19, 535–537 (2007).
[Crossref]

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Scie. Inst. 68, 3277–3295 (1997).
[Crossref]

Roussev, R. V.

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nature Methods 3, 793–796 (2006).
[Crossref] [PubMed]

Saruwatari, M.

K. Mori, T. Morioka, and M. Saruwatari, “Ultrawide spectral range group-velocity dispersion measurement utilizing supercontinuum in an optical fiber pumped by a 1.5 mu;m compact laser source,” IEEE Trans. Instr. Measur. 44, 712 –715 (1995).
[Crossref]

Scott, R. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nature Photon. (2010).
[Crossref]

Shoaf, J. H.

D. W. Allan, J. H. Shoaf, and D. Halford, “Statistics of Time and Frequency Data Analysis,” in “Time and Frequency: Theory and Fundamentals,” B. E. Blair, ed. (1974), pp. 151–+.

Silberberg, Y.

N. Dudovich, D. Oron, and Y. Silberberg, “Coherent Transient Enhancement of Optically Induced Resonant Transitions,” Phys. Rev. Lett. 88, 123004 (2002).
[Crossref] [PubMed]

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N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nature Photon. (2010).
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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science313, 1642–1645 (2006).
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A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-stokes raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
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D. Meshulach, D. Yelin, and Y. Silberberg, “Real-time spatialspectral interference measurements of ultrashort optical pulses,” J. Opt. Soc. Am. B Opt. Phys. 14, 2095–2098 (1997).
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Yoo, S. J. B.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nature Photon. (2010).
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Nature (London) (1)

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M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nature Methods 3, 793–796 (2006).
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Nature Photon. (1)

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nature Photon. (2010).
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M. Beck, C. Dorrer, and I. Walmsley, “Joint quantum measurement using unbalanced array detection,” Phys. Rev. Lett. 87, 253601 (2001).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Coherent Transient Enhancement of Optically Induced Resonant Transitions,” Phys. Rev. Lett. 88, 123004 (2002).
[Crossref] [PubMed]

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-stokes raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
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Rev. Scie. Inst. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Scie. Inst. 68, 3277–3295 (1997).
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Figures (4)

Fig. 1
Fig. 1

Experimental setup. The characterized pulse is passed through a 4f pulse shaper selecting a spectral component, and is detected by a single photon counting APD. One replica of the original pulse is used as a trigger signal for the TCSPC module, while the other, serving as an additional reference, is directed into the signal detector. The inset shows a sample histogram with the two peaks corresponding to the signal and the reference pulses.

Fig. 2
Fig. 2

Allan variance. The plot shows the standard deviation of the measured pulse arrival time as a function of the integration time. Two replicas of the same pulse separated by a constant delay were used as the signal and the reference, each attenuated to 1 MHz detection rate. The arrival time of the signal pulse was measured by finding the absolute position of the peak in the histogram (magenta) and by finding its position relative to the reference pulse (blue). The dashed black line represents the shot noise limit as given by Eq. (1). At short integration times, the relative timing standard deviation scales as 2 / N 45 ps, which is 15% larger than the shot noise limit.

Fig. 3
Fig. 3

Characterization of a 85 fs transform limited pulse and a pulse chirped by a 152 mm long F3 glass slab. (a) Density plot of a typical raw measurement trace featuring two peaks, the reference and the signal. The inset shows a cross section of the signal peak with FWHM of about 70 ps. (b) Measured delays of the spectral components for the transform limited and the chirped pulse (represented by the blue and red dots, respectively). The dashed black and cyan lines show the delays derived from the FROG measurements, and the dashed green line represents Sellmeier equation. The gray solid curve in the lower part of the plot shows the spectrum of the pulses in arbitrary units.

Fig. 4
Fig. 4

Measurement of the spectral delay of pulses passed through a Rb cell. (a) Measured delays of spectral components at 100°C (blue) and 210°C (red). The integration time was 4s per point at 100°C and 8s per point at 210°C. (b) A magnified view of the same (markers) fitted with a resonance delay profile (lines). (c) Normalized spectrum of the transmitted pulse at 100°C (blue) and 210°C (red) measured at a resolution of 0.05 nm. (The dashed black line shows the resonant absorbtion profile corresponding to the fit of 210°C spectral delay data.)

Equations (1)

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σ min 2 = Δ 2 N ( i ( f ( t i + Δ / 2 ) f ( t i + Δ / 2 ) ) 2 t i Δ / 2 t i + Δ / 2 f ( t ) dt ) 1

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