Abstract

Femtosecond time-resolved signals often display oscillations arising from the nuclear and electronic wave packet motions. Fourier power spectrum is generally used to retrieve the frequency spectrum. We have shown by numerical simulations and coherent phonon spectrum of single walled carbon nanotubes (SWCNT) that the Fourier power spectrum may not be appropriate to obtain the spectrum, when the peaks overlap with varying phases. Linear prediction singular value decomposition (LPSVD) can be a good alternative for this case. We present a robust way to perform LPSVD analysis and demonstrate the method for the chirality assignment of SWCNT through the time-domain coherent phonon spectroscopy.

© 2014 Optical Society of America

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  1. F. W. Wise, M. J. Rosker, and C. L. Tang, “Oscillatory femtosecond relaxation of photoexcited organic molecules,” J. Chem. Phys. 86(5), 2827–2832 (1987).
    [Crossref]
  2. I. A. Walmsley, M. Mitsunaga, and C. L. Tang, “Theory of quantum beats in optical transmission-correlation and pump-probe experiments for a general Raman configuration,” Phys. Rev. A 38(9), 4681–4689 (1988).
    [Crossref] [PubMed]
  3. C. J. Bardeen, Q. Wang, and C. V. Shank, “Femtosecond chirped pulse excitation of vibrational wave packets in LD690 and bacteriorhodopsin,” J. Phys. Chem. A 102(17), 2759–2766 (1998).
    [Crossref]
  4. T. Joo, Y. W. Jia, J. Y. Yu, M. J. Lang, and G. R. Fleming, “Third-order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104(16), 6089–6108 (1996).
    [Crossref]
  5. J. L. Lacoume, M. Gharbi, C. Latombe, and J. Nicolas, “Close frequency resolution by maximum entropy spectral estimators,” IEEE Trans. Acoust. Speech Signal Process. 32(5), 977–984 (1984).
    [Crossref]
  6. J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proc. IEEE 57(8), 1408–1418 (1969).
    [Crossref]
  7. H. Barkhuijsen, R. De Beer, W. M. M. J. Bovee, and D. Van Ormondt, “Retrieval of frequencies, amplitudes, damping factors, and phases from time-domain signals using a linear least-squares procedure,” J. Magn. Reson. 61, 465–481 (1985).
  8. G. L. Millhauser and J. H. Freed, “Linear prediction and resolution enhancement of complex line shapes in two-dimensional electron-spin-echo spectroscopy,” J. Chem. Phys. 85(1), 63–67 (1986).
    [Crossref]
  9. F. W. Wise, M. J. Rosker, G. L. Millhauser, and C. L. Tang, “Application of linear prediction least-squares fitting to time-resolved optical spectroscopy,” IEEE J. Quantum Electron. 23(7), 1116–1121 (1987).
    [Crossref]
  10. J. L. Galazzo and J. E. Bailey, “Application of linear prediction singular value decomposition for processing in vivo NMR data with low signal-to-noise ratio,” Biotechnol. Tech. 3(1), 13–18 (1989).
    [Crossref]
  11. S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298(5602), 2361–2366 (2002).
    [Crossref] [PubMed]
  12. H. Barkhuijsen, R. de Beer, and D. van Ormondt, “Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals,” J. Magn. Reson. 73, 553–557 (1987).
  13. A. E. Johnson and A. B. Myers, “A comparison of time- and frequency-domain resonance Raman spectroscopy in triiodide,” J. Chem. Phys. 104(7), 2497–2507 (1996).
    [Crossref]
  14. M. S. Dresselhaus, G. Dresselhaus, R. Saito, and A. Jorio, “Raman spectroscopy of carbon nanotubes,” Phys. Rep. 409(2), 47–99 (2005).
    [Crossref]
  15. W. T. Pollard, S.-Y. Lee, and R. A. Mathies, “Wave packet theory of dynamic absorption spectra in femtosecond pump–probe experiments,” J. Chem. Phys. 92(7), 4012–4029 (1990).
    [Crossref]
  16. Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
    [Crossref] [PubMed]
  17. I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
    [Crossref] [PubMed]
  18. H. M. Lawler, D. Areshkin, J. W. Mintmire, and C. T. White, “Radial-breathing mode frequencies for single-walled carbon nanotubes of arbitrary chirality: First-principles calculations,” Phys. Rev. B 72(23), 233403 (2005).
    [Crossref]
  19. H. Telg, J. Maultzsch, S. Reich, F. Hennrich, and C. Thomsen, “Chirality distribution and transition energies of carbon nanotubes,” Phys. Rev. Lett. 93(17), 177401 (2004).
    [Crossref] [PubMed]
  20. D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, “Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots,” Phys. Rev. B 77(23), 235321 (2008).
    [Crossref]

2012 (1)

I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
[Crossref] [PubMed]

2008 (1)

D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, “Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots,” Phys. Rev. B 77(23), 235321 (2008).
[Crossref]

2006 (1)

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

2005 (2)

M. S. Dresselhaus, G. Dresselhaus, R. Saito, and A. Jorio, “Raman spectroscopy of carbon nanotubes,” Phys. Rep. 409(2), 47–99 (2005).
[Crossref]

H. M. Lawler, D. Areshkin, J. W. Mintmire, and C. T. White, “Radial-breathing mode frequencies for single-walled carbon nanotubes of arbitrary chirality: First-principles calculations,” Phys. Rev. B 72(23), 233403 (2005).
[Crossref]

2004 (1)

H. Telg, J. Maultzsch, S. Reich, F. Hennrich, and C. Thomsen, “Chirality distribution and transition energies of carbon nanotubes,” Phys. Rev. Lett. 93(17), 177401 (2004).
[Crossref] [PubMed]

2002 (1)

S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298(5602), 2361–2366 (2002).
[Crossref] [PubMed]

1998 (1)

C. J. Bardeen, Q. Wang, and C. V. Shank, “Femtosecond chirped pulse excitation of vibrational wave packets in LD690 and bacteriorhodopsin,” J. Phys. Chem. A 102(17), 2759–2766 (1998).
[Crossref]

1996 (2)

T. Joo, Y. W. Jia, J. Y. Yu, M. J. Lang, and G. R. Fleming, “Third-order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104(16), 6089–6108 (1996).
[Crossref]

A. E. Johnson and A. B. Myers, “A comparison of time- and frequency-domain resonance Raman spectroscopy in triiodide,” J. Chem. Phys. 104(7), 2497–2507 (1996).
[Crossref]

1990 (1)

W. T. Pollard, S.-Y. Lee, and R. A. Mathies, “Wave packet theory of dynamic absorption spectra in femtosecond pump–probe experiments,” J. Chem. Phys. 92(7), 4012–4029 (1990).
[Crossref]

1989 (1)

J. L. Galazzo and J. E. Bailey, “Application of linear prediction singular value decomposition for processing in vivo NMR data with low signal-to-noise ratio,” Biotechnol. Tech. 3(1), 13–18 (1989).
[Crossref]

1988 (1)

I. A. Walmsley, M. Mitsunaga, and C. L. Tang, “Theory of quantum beats in optical transmission-correlation and pump-probe experiments for a general Raman configuration,” Phys. Rev. A 38(9), 4681–4689 (1988).
[Crossref] [PubMed]

1987 (3)

F. W. Wise, M. J. Rosker, and C. L. Tang, “Oscillatory femtosecond relaxation of photoexcited organic molecules,” J. Chem. Phys. 86(5), 2827–2832 (1987).
[Crossref]

F. W. Wise, M. J. Rosker, G. L. Millhauser, and C. L. Tang, “Application of linear prediction least-squares fitting to time-resolved optical spectroscopy,” IEEE J. Quantum Electron. 23(7), 1116–1121 (1987).
[Crossref]

H. Barkhuijsen, R. de Beer, and D. van Ormondt, “Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals,” J. Magn. Reson. 73, 553–557 (1987).

1986 (1)

G. L. Millhauser and J. H. Freed, “Linear prediction and resolution enhancement of complex line shapes in two-dimensional electron-spin-echo spectroscopy,” J. Chem. Phys. 85(1), 63–67 (1986).
[Crossref]

1985 (1)

H. Barkhuijsen, R. De Beer, W. M. M. J. Bovee, and D. Van Ormondt, “Retrieval of frequencies, amplitudes, damping factors, and phases from time-domain signals using a linear least-squares procedure,” J. Magn. Reson. 61, 465–481 (1985).

1984 (1)

J. L. Lacoume, M. Gharbi, C. Latombe, and J. Nicolas, “Close frequency resolution by maximum entropy spectral estimators,” IEEE Trans. Acoust. Speech Signal Process. 32(5), 977–984 (1984).
[Crossref]

1969 (1)

J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proc. IEEE 57(8), 1408–1418 (1969).
[Crossref]

Areshkin, D.

H. M. Lawler, D. Areshkin, J. W. Mintmire, and C. T. White, “Radial-breathing mode frequencies for single-walled carbon nanotubes of arbitrary chirality: First-principles calculations,” Phys. Rev. B 72(23), 233403 (2005).
[Crossref]

Bachilo, S. M.

S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298(5602), 2361–2366 (2002).
[Crossref] [PubMed]

Baik, S.-H.

I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
[Crossref] [PubMed]

Bailey, J. E.

J. L. Galazzo and J. E. Bailey, “Application of linear prediction singular value decomposition for processing in vivo NMR data with low signal-to-noise ratio,” Biotechnol. Tech. 3(1), 13–18 (1989).
[Crossref]

Bardeen, C. J.

C. J. Bardeen, Q. Wang, and C. V. Shank, “Femtosecond chirped pulse excitation of vibrational wave packets in LD690 and bacteriorhodopsin,” J. Phys. Chem. A 102(17), 2759–2766 (1998).
[Crossref]

Barkhuijsen, H.

H. Barkhuijsen, R. de Beer, and D. van Ormondt, “Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals,” J. Magn. Reson. 73, 553–557 (1987).

H. Barkhuijsen, R. De Beer, W. M. M. J. Bovee, and D. Van Ormondt, “Retrieval of frequencies, amplitudes, damping factors, and phases from time-domain signals using a linear least-squares procedure,” J. Magn. Reson. 61, 465–481 (1985).

Barsan, M. M.

D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, “Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots,” Phys. Rev. B 77(23), 235321 (2008).
[Crossref]

Bovee, W. M. M. J.

H. Barkhuijsen, R. De Beer, W. M. M. J. Bovee, and D. Van Ormondt, “Retrieval of frequencies, amplitudes, damping factors, and phases from time-domain signals using a linear least-squares procedure,” J. Magn. Reson. 61, 465–481 (1985).

Butler, I. S.

D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, “Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots,” Phys. Rev. B 77(23), 235321 (2008).
[Crossref]

Capon, J.

J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proc. IEEE 57(8), 1408–1418 (1969).
[Crossref]

Cooney, R. R.

D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, “Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots,” Phys. Rev. B 77(23), 235321 (2008).
[Crossref]

de Beer, R.

H. Barkhuijsen, R. de Beer, and D. van Ormondt, “Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals,” J. Magn. Reson. 73, 553–557 (1987).

H. Barkhuijsen, R. De Beer, W. M. M. J. Bovee, and D. Van Ormondt, “Retrieval of frequencies, amplitudes, damping factors, and phases from time-domain signals using a linear least-squares procedure,” J. Magn. Reson. 61, 465–481 (1985).

Dias, E. A.

D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, “Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots,” Phys. Rev. B 77(23), 235321 (2008).
[Crossref]

Doorn, S. K.

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

Dresselhaus, G.

M. S. Dresselhaus, G. Dresselhaus, R. Saito, and A. Jorio, “Raman spectroscopy of carbon nanotubes,” Phys. Rep. 409(2), 47–99 (2005).
[Crossref]

Dresselhaus, M. S.

M. S. Dresselhaus, G. Dresselhaus, R. Saito, and A. Jorio, “Raman spectroscopy of carbon nanotubes,” Phys. Rep. 409(2), 47–99 (2005).
[Crossref]

Eom, I.

I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
[Crossref] [PubMed]

Fleming, G. R.

T. Joo, Y. W. Jia, J. Y. Yu, M. J. Lang, and G. R. Fleming, “Third-order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104(16), 6089–6108 (1996).
[Crossref]

Freed, J. H.

G. L. Millhauser and J. H. Freed, “Linear prediction and resolution enhancement of complex line shapes in two-dimensional electron-spin-echo spectroscopy,” J. Chem. Phys. 85(1), 63–67 (1986).
[Crossref]

Galazzo, J. L.

J. L. Galazzo and J. E. Bailey, “Application of linear prediction singular value decomposition for processing in vivo NMR data with low signal-to-noise ratio,” Biotechnol. Tech. 3(1), 13–18 (1989).
[Crossref]

Gharbi, M.

J. L. Lacoume, M. Gharbi, C. Latombe, and J. Nicolas, “Close frequency resolution by maximum entropy spectral estimators,” IEEE Trans. Acoust. Speech Signal Process. 32(5), 977–984 (1984).
[Crossref]

Han, H.-S.

I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
[Crossref] [PubMed]

Hároz, E. H.

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

Hauge, R. H.

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298(5602), 2361–2366 (2002).
[Crossref] [PubMed]

Hennrich, F.

H. Telg, J. Maultzsch, S. Reich, F. Hennrich, and C. Thomsen, “Chirality distribution and transition energies of carbon nanotubes,” Phys. Rev. Lett. 93(17), 177401 (2004).
[Crossref] [PubMed]

Jeong, D.-Y.

I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
[Crossref] [PubMed]

Jia, Y. W.

T. Joo, Y. W. Jia, J. Y. Yu, M. J. Lang, and G. R. Fleming, “Third-order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104(16), 6089–6108 (1996).
[Crossref]

Johnson, A. E.

A. E. Johnson and A. B. Myers, “A comparison of time- and frequency-domain resonance Raman spectroscopy in triiodide,” J. Chem. Phys. 104(7), 2497–2507 (1996).
[Crossref]

Joo, T.

I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
[Crossref] [PubMed]

T. Joo, Y. W. Jia, J. Y. Yu, M. J. Lang, and G. R. Fleming, “Third-order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104(16), 6089–6108 (1996).
[Crossref]

Jorio, A.

M. S. Dresselhaus, G. Dresselhaus, R. Saito, and A. Jorio, “Raman spectroscopy of carbon nanotubes,” Phys. Rep. 409(2), 47–99 (2005).
[Crossref]

Kambhampati, P.

D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, “Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots,” Phys. Rev. B 77(23), 235321 (2008).
[Crossref]

Kim, J. H.

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

Kittrell, C.

S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298(5602), 2361–2366 (2002).
[Crossref] [PubMed]

Kono, J.

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

Lacoume, J. L.

J. L. Lacoume, M. Gharbi, C. Latombe, and J. Nicolas, “Close frequency resolution by maximum entropy spectral estimators,” IEEE Trans. Acoust. Speech Signal Process. 32(5), 977–984 (1984).
[Crossref]

Lang, M. J.

T. Joo, Y. W. Jia, J. Y. Yu, M. J. Lang, and G. R. Fleming, “Third-order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104(16), 6089–6108 (1996).
[Crossref]

Latombe, C.

J. L. Lacoume, M. Gharbi, C. Latombe, and J. Nicolas, “Close frequency resolution by maximum entropy spectral estimators,” IEEE Trans. Acoust. Speech Signal Process. 32(5), 977–984 (1984).
[Crossref]

Lawler, H. M.

H. M. Lawler, D. Areshkin, J. W. Mintmire, and C. T. White, “Radial-breathing mode frequencies for single-walled carbon nanotubes of arbitrary chirality: First-principles calculations,” Phys. Rev. B 72(23), 233403 (2005).
[Crossref]

Lee, S.-Y.

W. T. Pollard, S.-Y. Lee, and R. A. Mathies, “Wave packet theory of dynamic absorption spectra in femtosecond pump–probe experiments,” J. Chem. Phys. 92(7), 4012–4029 (1990).
[Crossref]

Lim, Y. S.

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

Lim, Y.-S.

I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
[Crossref] [PubMed]

Mathies, R. A.

W. T. Pollard, S.-Y. Lee, and R. A. Mathies, “Wave packet theory of dynamic absorption spectra in femtosecond pump–probe experiments,” J. Chem. Phys. 92(7), 4012–4029 (1990).
[Crossref]

Maultzsch, J.

H. Telg, J. Maultzsch, S. Reich, F. Hennrich, and C. Thomsen, “Chirality distribution and transition energies of carbon nanotubes,” Phys. Rev. Lett. 93(17), 177401 (2004).
[Crossref] [PubMed]

Millhauser, G. L.

F. W. Wise, M. J. Rosker, G. L. Millhauser, and C. L. Tang, “Application of linear prediction least-squares fitting to time-resolved optical spectroscopy,” IEEE J. Quantum Electron. 23(7), 1116–1121 (1987).
[Crossref]

G. L. Millhauser and J. H. Freed, “Linear prediction and resolution enhancement of complex line shapes in two-dimensional electron-spin-echo spectroscopy,” J. Chem. Phys. 85(1), 63–67 (1986).
[Crossref]

Mintmire, J. W.

H. M. Lawler, D. Areshkin, J. W. Mintmire, and C. T. White, “Radial-breathing mode frequencies for single-walled carbon nanotubes of arbitrary chirality: First-principles calculations,” Phys. Rev. B 72(23), 233403 (2005).
[Crossref]

Mitsunaga, M.

I. A. Walmsley, M. Mitsunaga, and C. L. Tang, “Theory of quantum beats in optical transmission-correlation and pump-probe experiments for a general Raman configuration,” Phys. Rev. A 38(9), 4681–4689 (1988).
[Crossref] [PubMed]

Myers, A. B.

A. E. Johnson and A. B. Myers, “A comparison of time- and frequency-domain resonance Raman spectroscopy in triiodide,” J. Chem. Phys. 104(7), 2497–2507 (1996).
[Crossref]

Nicolas, J.

J. L. Lacoume, M. Gharbi, C. Latombe, and J. Nicolas, “Close frequency resolution by maximum entropy spectral estimators,” IEEE Trans. Acoust. Speech Signal Process. 32(5), 977–984 (1984).
[Crossref]

Park, S.

I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
[Crossref] [PubMed]

Pollard, W. T.

W. T. Pollard, S.-Y. Lee, and R. A. Mathies, “Wave packet theory of dynamic absorption spectra in femtosecond pump–probe experiments,” J. Chem. Phys. 92(7), 4012–4029 (1990).
[Crossref]

Reich, S.

H. Telg, J. Maultzsch, S. Reich, F. Hennrich, and C. Thomsen, “Chirality distribution and transition energies of carbon nanotubes,” Phys. Rev. Lett. 93(17), 177401 (2004).
[Crossref] [PubMed]

Rosker, M. J.

F. W. Wise, M. J. Rosker, and C. L. Tang, “Oscillatory femtosecond relaxation of photoexcited organic molecules,” J. Chem. Phys. 86(5), 2827–2832 (1987).
[Crossref]

F. W. Wise, M. J. Rosker, G. L. Millhauser, and C. L. Tang, “Application of linear prediction least-squares fitting to time-resolved optical spectroscopy,” IEEE J. Quantum Electron. 23(7), 1116–1121 (1987).
[Crossref]

Sagar, D. M.

D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, “Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots,” Phys. Rev. B 77(23), 235321 (2008).
[Crossref]

Saito, R.

M. S. Dresselhaus, G. Dresselhaus, R. Saito, and A. Jorio, “Raman spectroscopy of carbon nanotubes,” Phys. Rep. 409(2), 47–99 (2005).
[Crossref]

Sewall, S. L.

D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, “Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots,” Phys. Rev. B 77(23), 235321 (2008).
[Crossref]

Shank, C. V.

C. J. Bardeen, Q. Wang, and C. V. Shank, “Femtosecond chirped pulse excitation of vibrational wave packets in LD690 and bacteriorhodopsin,” J. Phys. Chem. A 102(17), 2759–2766 (1998).
[Crossref]

Shaver, J.

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

Smalley, R. E.

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298(5602), 2361–2366 (2002).
[Crossref] [PubMed]

Strano, M. S.

S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298(5602), 2361–2366 (2002).
[Crossref] [PubMed]

Tang, C. L.

I. A. Walmsley, M. Mitsunaga, and C. L. Tang, “Theory of quantum beats in optical transmission-correlation and pump-probe experiments for a general Raman configuration,” Phys. Rev. A 38(9), 4681–4689 (1988).
[Crossref] [PubMed]

F. W. Wise, M. J. Rosker, and C. L. Tang, “Oscillatory femtosecond relaxation of photoexcited organic molecules,” J. Chem. Phys. 86(5), 2827–2832 (1987).
[Crossref]

F. W. Wise, M. J. Rosker, G. L. Millhauser, and C. L. Tang, “Application of linear prediction least-squares fitting to time-resolved optical spectroscopy,” IEEE J. Quantum Electron. 23(7), 1116–1121 (1987).
[Crossref]

Telg, H.

H. Telg, J. Maultzsch, S. Reich, F. Hennrich, and C. Thomsen, “Chirality distribution and transition energies of carbon nanotubes,” Phys. Rev. Lett. 93(17), 177401 (2004).
[Crossref] [PubMed]

Thomsen, C.

H. Telg, J. Maultzsch, S. Reich, F. Hennrich, and C. Thomsen, “Chirality distribution and transition energies of carbon nanotubes,” Phys. Rev. Lett. 93(17), 177401 (2004).
[Crossref] [PubMed]

van Ormondt, D.

H. Barkhuijsen, R. de Beer, and D. van Ormondt, “Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals,” J. Magn. Reson. 73, 553–557 (1987).

H. Barkhuijsen, R. De Beer, W. M. M. J. Bovee, and D. Van Ormondt, “Retrieval of frequencies, amplitudes, damping factors, and phases from time-domain signals using a linear least-squares procedure,” J. Magn. Reson. 61, 465–481 (1985).

Walmsley, I. A.

I. A. Walmsley, M. Mitsunaga, and C. L. Tang, “Theory of quantum beats in optical transmission-correlation and pump-probe experiments for a general Raman configuration,” Phys. Rev. A 38(9), 4681–4689 (1988).
[Crossref] [PubMed]

Wang, Q.

C. J. Bardeen, Q. Wang, and C. V. Shank, “Femtosecond chirped pulse excitation of vibrational wave packets in LD690 and bacteriorhodopsin,” J. Phys. Chem. A 102(17), 2759–2766 (1998).
[Crossref]

Weisman, R. B.

S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298(5602), 2361–2366 (2002).
[Crossref] [PubMed]

White, C. T.

H. M. Lawler, D. Areshkin, J. W. Mintmire, and C. T. White, “Radial-breathing mode frequencies for single-walled carbon nanotubes of arbitrary chirality: First-principles calculations,” Phys. Rev. B 72(23), 233403 (2005).
[Crossref]

Wise, F. W.

F. W. Wise, M. J. Rosker, and C. L. Tang, “Oscillatory femtosecond relaxation of photoexcited organic molecules,” J. Chem. Phys. 86(5), 2827–2832 (1987).
[Crossref]

F. W. Wise, M. J. Rosker, G. L. Millhauser, and C. L. Tang, “Application of linear prediction least-squares fitting to time-resolved optical spectroscopy,” IEEE J. Quantum Electron. 23(7), 1116–1121 (1987).
[Crossref]

Yee, K. J.

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

Yee, K.-J.

I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
[Crossref] [PubMed]

Yu, J. Y.

T. Joo, Y. W. Jia, J. Y. Yu, M. J. Lang, and G. R. Fleming, “Third-order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104(16), 6089–6108 (1996).
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F. W. Wise, M. J. Rosker, G. L. Millhauser, and C. L. Tang, “Application of linear prediction least-squares fitting to time-resolved optical spectroscopy,” IEEE J. Quantum Electron. 23(7), 1116–1121 (1987).
[Crossref]

IEEE Trans. Acoust. Speech Signal Process. (1)

J. L. Lacoume, M. Gharbi, C. Latombe, and J. Nicolas, “Close frequency resolution by maximum entropy spectral estimators,” IEEE Trans. Acoust. Speech Signal Process. 32(5), 977–984 (1984).
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G. L. Millhauser and J. H. Freed, “Linear prediction and resolution enhancement of complex line shapes in two-dimensional electron-spin-echo spectroscopy,” J. Chem. Phys. 85(1), 63–67 (1986).
[Crossref]

F. W. Wise, M. J. Rosker, and C. L. Tang, “Oscillatory femtosecond relaxation of photoexcited organic molecules,” J. Chem. Phys. 86(5), 2827–2832 (1987).
[Crossref]

T. Joo, Y. W. Jia, J. Y. Yu, M. J. Lang, and G. R. Fleming, “Third-order nonlinear time domain probes of solvation dynamics,” J. Chem. Phys. 104(16), 6089–6108 (1996).
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W. T. Pollard, S.-Y. Lee, and R. A. Mathies, “Wave packet theory of dynamic absorption spectra in femtosecond pump–probe experiments,” J. Chem. Phys. 92(7), 4012–4029 (1990).
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A. E. Johnson and A. B. Myers, “A comparison of time- and frequency-domain resonance Raman spectroscopy in triiodide,” J. Chem. Phys. 104(7), 2497–2507 (1996).
[Crossref]

J. Magn. Reson. (2)

H. Barkhuijsen, R. de Beer, and D. van Ormondt, “Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals,” J. Magn. Reson. 73, 553–557 (1987).

H. Barkhuijsen, R. De Beer, W. M. M. J. Bovee, and D. Van Ormondt, “Retrieval of frequencies, amplitudes, damping factors, and phases from time-domain signals using a linear least-squares procedure,” J. Magn. Reson. 61, 465–481 (1985).

J. Phys. Chem. A (1)

C. J. Bardeen, Q. Wang, and C. V. Shank, “Femtosecond chirped pulse excitation of vibrational wave packets in LD690 and bacteriorhodopsin,” J. Phys. Chem. A 102(17), 2759–2766 (1998).
[Crossref]

Nano Lett. (2)

Y. S. Lim, K. J. Yee, J. H. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn, R. H. Hauge, and R. E. Smalley, “Coherent lattice vibrations in single-walled carbon nanotubes,” Nano Lett. 6(12), 2696–2700 (2006).
[Crossref] [PubMed]

I. Eom, S. Park, H.-S. Han, K.-J. Yee, S.-H. Baik, D.-Y. Jeong, T. Joo, and Y.-S. Lim, “Coherent electronic and phononic oscillations in single-walled carbon nanotubes,” Nano Lett. 12(2), 769–773 (2012).
[Crossref] [PubMed]

Phys. Rep. (1)

M. S. Dresselhaus, G. Dresselhaus, R. Saito, and A. Jorio, “Raman spectroscopy of carbon nanotubes,” Phys. Rep. 409(2), 47–99 (2005).
[Crossref]

Phys. Rev. A (1)

I. A. Walmsley, M. Mitsunaga, and C. L. Tang, “Theory of quantum beats in optical transmission-correlation and pump-probe experiments for a general Raman configuration,” Phys. Rev. A 38(9), 4681–4689 (1988).
[Crossref] [PubMed]

Phys. Rev. B (2)

H. M. Lawler, D. Areshkin, J. W. Mintmire, and C. T. White, “Radial-breathing mode frequencies for single-walled carbon nanotubes of arbitrary chirality: First-principles calculations,” Phys. Rev. B 72(23), 233403 (2005).
[Crossref]

D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, “Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots,” Phys. Rev. B 77(23), 235321 (2008).
[Crossref]

Phys. Rev. Lett. (1)

H. Telg, J. Maultzsch, S. Reich, F. Hennrich, and C. Thomsen, “Chirality distribution and transition energies of carbon nanotubes,” Phys. Rev. Lett. 93(17), 177401 (2004).
[Crossref] [PubMed]

Proc. IEEE (1)

J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proc. IEEE 57(8), 1408–1418 (1969).
[Crossref]

Science (1)

S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298(5602), 2361–2366 (2002).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 FFT power spectra of the time-domain signal that consists of three frequency components at 195, 200, and 210 cm−1 (three dashed lines) having different phases. The parameters that generate these spectra are given in Table 1. Phases of the 195 and 210 cm−1 components are varied from 0 to 1.5π, while that of the 200 cm−1 is fixed to zero.

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Fig. 2
Fig. 2 (a) A synthesized time domain signal that consists of one exponential and three damped sinusoids with the parameters given in Table 1. Gaussian random noise is added as well. (b) χ R 2 from the LPSVD analysis are plotted vs. reduced order.

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Fig. 3
Fig. 3 (a) The input spectrum showing the three damped sinusoids given in Table 1. The spectrum of the time trace shown in Fig. 2(a) calculated by (b) LPSVD with reduced order 7 and (c) FFT. The exponential component was subtracted prior to the FFT.

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Fig. 4
Fig. 4 (a) TA of HipCo SWCNT obtained by the pump and probes pulses centered at 1200 and 1180 nm, respectively. (b) Oscillation part of the TA signal obtained by subtracting the smoothed data.

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Fig. 5
Fig. 5 LPSVD and FFT analyses for the oscillation part of the TA signal of HipCo SWCNT. (a) χ R 2 vs. reduced order obtained from the LPSVD. (b) and (c) are the spectra obtained by LPSVD and FFT, respectively. (d) FFT power spectrum of the time trace constructed from the parameters shown in Table 2. (e) Same as (d) except that the phases in Table 2 are all set to zero.

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Tables (2)

Tables Icon

Table 1 Parameters of the Model Function that Consists of an Exponential Decay and Three Damped Sinusoids*

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Table 2 LPSVD Analysis for the CP Signal of a Micelle-suspended HipCo SWCNT Solution*

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Equations (2)

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

I(t)= ∑ i=1 3 a i exp(−t/ τ i )cos( ω i t+ ϕ i ) + a e exp(−t/ τ e ).
ν RBM =A/d+B,

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