Abstract

2D electronic spectroscopy is a widely exploited tool to study excited state dynamics. A high density of information is enclosed in 2D spectra. A crucial challenge is to objectively disentangle all the features of the third order optical signal. We propose a global analysis method based on the variable projection algorithm, which is able to reproduce simultaneously coherence and population dynamics of rephasing and non-rephasing contributions. Test measures at room temperature on a standard dye are used to validate the procedure and to discuss the advantages of the proposed methodology with respect to the currently employed analysis procedures.

© 2016 Optical Society of America

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References

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2016 (3)

J. Dostál, J. Pšenčík, and D. Zigmantas, “In situ mapping of the energy flow through the entire photosynthetic apparatus,” Nat. Chem. 8, 705–710 (2016).
[Crossref]

J. O. Tollerud, S. T. Cundiff, and J. A. Davis, “Revealing and characterizing dark excitons through coherent multidimensional spectroscopy,” Phys. Rev. Lett. 117(9), 097401 (2016).
[Crossref]

R. Singh, G. Moody, M. E. Siemens, H. Li, and S. T. Cundiff, “Quantifying spectral diffusion by the direct measurement of the correlation function for excitons in semiconductor quantum wells,” J. Opt. Soc. Am. B 33(7), C137–C143 (2016).
[Crossref]

2015 (5)

A. Volpato and E. Collini, “Time-frequency methods for coherent spectroscopy,” Opt. Express 23(15), 20040–20050 (2015).
[Crossref]

Y. L. Sheu, H. T. Wu, and L. Y. Hsu, “Exploring laser-driven quantum phenomena from a time-frequency analysis perspective: a comprehensive study,” Opt. Express 23(23), 30459–30482 (2015).
[Crossref]

F. V. A. Camargo, H. L. Anderson, S. R. Meech, and I. A. Heisler, “Time-resolved twisting dynamics in a porphyrin dimer characterized by two-dimensional electronic spectroscopy,” J. Phys. Chem. B 119, 14660–14667 (2015).
[Crossref]

A. Chenu and G. D. Scholes, “Coherence in energy transfer and photosynthesis,” Annu. Rev. Phys. Chem. 66, 69–96 (2015).
[Crossref]

T. R. Senty, S. K. Cushing, C. Wang, C. Matranga, and A. D. Bristow, “Inverting transient absorption data to determine transfer rates in quantum dotâǍŞTiO2 heterostructures,” J. Phys. Chem. C 119(11), 6337–6343 (2015).
[Crossref]

2014 (1)

A. Halpin, P. J. M. Johnson, and R. J. D. Miller, “Comment on “Engineering coherence among excited states in synthetic heterodimer systems”,” Science 344(6188), 1099 (2014).
[Crossref]

2013 (7)

D. Hayes, G. B. Griffin, and G. S. Engel, “Engineering coherence among excited states in synthetic heterodimer systems,” Science 340(6139), 1431–1434 (2013).
[Crossref]

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139, 224103 (2013).
[Crossref]

H. Li, A. D. Bristow, M. E. Siemens, G. Moody, and S. T. Cundiff, “Unraveling quantum pathways using optical 3D Fourier-transform spectroscopy,” Nat. Commun. 4, 1390 (2013).
[Crossref]

E. E. Ostroumov, R. M. Mulvaney, J. M. Anna, R. J. Cogdell, and G. D. Scholes, “Energy transfer pathways in light-harvesting complexes of purple bacteria as revealed by global kinetic analysis of two-dimensional transient spectra,” J. Phys. Chem. B 117(38), 11349–11362 (2013).
[Crossref]

E. E. Ostroumov, R. M. Mulvaney, R. J. Cogdell, and G. D. Scholes, “Broadband 2D electronic spectroscopy reveals a carotenoid dark state in purple bacteria,” Science 340(6128), 52–56 (2013).
[Crossref]

D. P. O’Leary and B. W. Rust, “Variable projection for nonlinear least squares problems,” Comput. Optim. and Appl. 54(3), 579–593 (2013).
[Crossref]

E. Collini, “Spectroscopic signatures of quantum-coherent energy transfer,” Chem. Soc. Rev. 42(12), 4932–4947 (2013).
[Crossref]

2012 (5)

C. Ruckebusch, M. Sliwa, P. Pernot, P. A. de Juan, and R. Tauler, “Comprehensive data analysis of femtosecond transient absorption spectra: a review,” J. Photochem. Photobiol. C 13(1), 1–27 (2012).
[Crossref]

V. Butkus, D. Zigmantas, L. Valkunas, and D. Abramavicius, “Vibrational vs. electronic coherences in 2D spectrum of molecular systems,” Chem. Phys. Lett. 545, 40–43 (2012).
[Crossref]

J. Almeida, J. Prior, and M. B. Plenio, “Computation of two-dimensional spectra assisted by compressed sampling,” J. Phys. Chem. Lett. 3(18), 2692–2696 (2012).
[Crossref]

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref]

K. A. Fransted, J. R. Caram, D. Hayes, and G. S. Engel, “Two-dimensional electronic spectroscopy of bacteriochlorophyll a in solution: elucidating the coherence dynamics of the Fenna-Matthews-Olson complex using its chromophore as a control,” J. Chem. Phys. 137, 125101 (2012).
[Crossref]

2011 (3)

G. Panitchayangkoon, D. V. Voronine, D. Abramavicius, J. R. Caram, N. H. C. Lewis, S. Mukamel, and G. S. Engel, “Direct evidence of quantum transport in photosynthetic light-harvesting complexes,” PNAS 108(52), 20908–20912 (2011).
[Crossref]

J. R. Caram and G. S. Engel, “Extracting dynamics of excitonic coherences in congested spectra of photosynthetic light harvesting antenna complexes,” Faraday Disc. 153, 93–104 (2011).
[Crossref]

R. Augulis and D. Zigmantas, “Two-dimensional electronic spectroscopy with double modulation lock-in detection: enhancement of sensitivity and noise resistance,” Opt. Express 19(14), 13126–13133 (2011).
[Crossref]

2009 (3)

A. Nemeth, J. Sperling, J. Hauer, H. F. Kauffmann, and F. Milota, “Compact phase-stable design for single- and double-quantum two-dimensional electronic spectroscopy,” Opt. Lett. 34(21), 3301–3303 (2009).
[Crossref]

D. B. Turner, K. W. Stone, K. Gundogdu, and K. A. Nelson, “Three-dimensional electronic spectroscopy of excitons in GaAs quantum wells,” J. Chem. Phys. 131, 144510 (2009).
[Crossref]

K. M. Mullen and I. H. M. Van Stokkum, “The variable projection algorithm in time-resolved spectroscopy, microscopy and mass spectrometry applications,” Numer. Algorithms 51(3), 319–340 (2009).
[Crossref]

2008 (1)

J. Savolainen, D. van der Linden, N. Dijkhuizen, and J. L. Herek, “Characterizing the functional dynamics of zinc phthalocyanine from femtoseconds to nanoseconds,” J. Photochem. Photobiol. A 196(1), 99–105 (2008).
[Crossref]

2007 (2)

G. S. Engel, T. R. Calhoun, E. L. Read, T. K. Ahn, T. Mančal, Y. C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref]

K. M. Mullen, M. Vengris, and I. H. M. Van Stokkum, “Algorithms for separable nonlinear least squares with application to modelling time-resolved spectra,” J. Global Optim. 38(2), 201–213 (2007).
[Crossref]

2004 (2)

T. Brixner, T. Mančal, I. V. Stiopkin, and G. R. Fleming, “Phase-stabilized two-dimensional electronic spectroscopy,” J. Chem. Phys. 121(9), 4221–4236 (2004).
[Crossref]

I. H. M. Van Stokkum, D. S. Larsen, and R. Van Grondelle, “Global and target analysis of time-resolved spectra,” Biochim. Biophys. Acta Bioenerg. 1657(2-3), 82–104 (2004).
[Crossref]

2003 (2)

D. M. Jonas, “Two-dimensional femtosecond spectroscopy,” Annu. Rev. Phys. Chem. 54, 425–463 (2003).
[Crossref]

G. Golub and V. Pereyra, “Separable nonlinear least squares: the variable projection method and its applications,” Inverse Problems 19(2), R1–R26 (2003).
[Crossref]

1994 (2)

D. Kundu, “A modified prony algorithm for sum of damped or undamped exponential signals,” Sankhya 56(B-3), 524–544 (1994).

R. W. Hendler and R. I. Shrager, “Deconvolutions based on singular value decomposition and the pseudoinverse: a guide for beginners,” J. Biochem. Bioph. Methods 28(1), 1–33 (1994).
[Crossref]

1992 (1)

E. R. Henry and J. Hofrichter, “Singular value decomposition: application to analysis of experimental data,” Methods Enzymol. 210, 129–192 (1992).
[Crossref]

1986 (1)

J. Tang and J. R. Norris, “LPZ spectral analysis using linear prediction and the z-transform,” J. Chem. Phys. 84, 5210–5211 (1986).
[Crossref]

1984 (1)

H. Ohtani, T. Kobayashi, T. Ohno, S. Kato, T. Tanno, and A. Yamada, “Nanosecond spectroscopy on the mechanism of the reduction of methylviologen 4431 sensitized by metallophthalocyanine,” J. Phys. Chem. 88, 4431–4435 (1984).
[Crossref]

1975 (1)

M. R. Osborne, “Some special nonlinear least squares problems,” SIAM J. Numer. Anal. 12(4), 571–592 (1975).
[Crossref]

1973 (1)

G. H. Golub and V. Pereyra, “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate,” SIAM J. Numer. Anal. 10(2), 413–432 (1973).
[Crossref]

Abramavicius, D.

V. Butkus, D. Zigmantas, L. Valkunas, and D. Abramavicius, “Vibrational vs. electronic coherences in 2D spectrum of molecular systems,” Chem. Phys. Lett. 545, 40–43 (2012).
[Crossref]

G. Panitchayangkoon, D. V. Voronine, D. Abramavicius, J. R. Caram, N. H. C. Lewis, S. Mukamel, and G. S. Engel, “Direct evidence of quantum transport in photosynthetic light-harvesting complexes,” PNAS 108(52), 20908–20912 (2011).
[Crossref]

L. Valkunas, D. Abramavicius, and T. Mančal, Molecular Excitation Dynamics and Relaxation: Quantum Theory and Spectroscopy(John Wiley & Sons, Inc., 2013).
[Crossref]

Ahn, T. K.

G. S. Engel, T. R. Calhoun, E. L. Read, T. K. Ahn, T. Mančal, Y. C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref]

Almeida, J.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139, 224103 (2013).
[Crossref]

J. Almeida, J. Prior, and M. B. Plenio, “Computation of two-dimensional spectra assisted by compressed sampling,” J. Phys. Chem. Lett. 3(18), 2692–2696 (2012).
[Crossref]

Anderson, H. L.

F. V. A. Camargo, H. L. Anderson, S. R. Meech, and I. A. Heisler, “Time-resolved twisting dynamics in a porphyrin dimer characterized by two-dimensional electronic spectroscopy,” J. Phys. Chem. B 119, 14660–14667 (2015).
[Crossref]

Anna, J. M.

E. E. Ostroumov, R. M. Mulvaney, J. M. Anna, R. J. Cogdell, and G. D. Scholes, “Energy transfer pathways in light-harvesting complexes of purple bacteria as revealed by global kinetic analysis of two-dimensional transient spectra,” J. Phys. Chem. B 117(38), 11349–11362 (2013).
[Crossref]

Augulis, R.

Belsley, M. S.

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref]

Blankenship, R. E.

G. S. Engel, T. R. Calhoun, E. L. Read, T. K. Ahn, T. Mančal, Y. C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref]

Bristow, A. D.

T. R. Senty, S. K. Cushing, C. Wang, C. Matranga, and A. D. Bristow, “Inverting transient absorption data to determine transfer rates in quantum dotâǍŞTiO2 heterostructures,” J. Phys. Chem. C 119(11), 6337–6343 (2015).
[Crossref]

H. Li, A. D. Bristow, M. E. Siemens, G. Moody, and S. T. Cundiff, “Unraveling quantum pathways using optical 3D Fourier-transform spectroscopy,” Nat. Commun. 4, 1390 (2013).
[Crossref]

Brixner, T.

T. Brixner, T. Mančal, I. V. Stiopkin, and G. R. Fleming, “Phase-stabilized two-dimensional electronic spectroscopy,” J. Chem. Phys. 121(9), 4221–4236 (2004).
[Crossref]

Butkus, V.

V. Butkus, D. Zigmantas, L. Valkunas, and D. Abramavicius, “Vibrational vs. electronic coherences in 2D spectrum of molecular systems,” Chem. Phys. Lett. 545, 40–43 (2012).
[Crossref]

Calhoun, T. R.

G. S. Engel, T. R. Calhoun, E. L. Read, T. K. Ahn, T. Mančal, Y. C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref]

Camargo, F. V. A.

F. V. A. Camargo, H. L. Anderson, S. R. Meech, and I. A. Heisler, “Time-resolved twisting dynamics in a porphyrin dimer characterized by two-dimensional electronic spectroscopy,” J. Phys. Chem. B 119, 14660–14667 (2015).
[Crossref]

Caram, J. R.

K. A. Fransted, J. R. Caram, D. Hayes, and G. S. Engel, “Two-dimensional electronic spectroscopy of bacteriochlorophyll a in solution: elucidating the coherence dynamics of the Fenna-Matthews-Olson complex using its chromophore as a control,” J. Chem. Phys. 137, 125101 (2012).
[Crossref]

J. R. Caram and G. S. Engel, “Extracting dynamics of excitonic coherences in congested spectra of photosynthetic light harvesting antenna complexes,” Faraday Disc. 153, 93–104 (2011).
[Crossref]

G. Panitchayangkoon, D. V. Voronine, D. Abramavicius, J. R. Caram, N. H. C. Lewis, S. Mukamel, and G. S. Engel, “Direct evidence of quantum transport in photosynthetic light-harvesting complexes,” PNAS 108(52), 20908–20912 (2011).
[Crossref]

Castro, E.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139, 224103 (2013).
[Crossref]

Cheng, Y. C.

G. S. Engel, T. R. Calhoun, E. L. Read, T. K. Ahn, T. Mančal, Y. C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref]

Chenu, A.

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A. Chenu and G. D. Scholes, “Coherence in energy transfer and photosynthesis,” Annu. Rev. Phys. Chem. 66, 69–96 (2015).
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Shrager, R. I.

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R. Singh, G. Moody, M. E. Siemens, H. Li, and S. T. Cundiff, “Quantifying spectral diffusion by the direct measurement of the correlation function for excitons in semiconductor quantum wells,” J. Opt. Soc. Am. B 33(7), C137–C143 (2016).
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C. Ruckebusch, M. Sliwa, P. Pernot, P. A. de Juan, and R. Tauler, “Comprehensive data analysis of femtosecond transient absorption spectra: a review,” J. Photochem. Photobiol. C 13(1), 1–27 (2012).
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J. O. Tollerud, S. T. Cundiff, and J. A. Davis, “Revealing and characterizing dark excitons through coherent multidimensional spectroscopy,” Phys. Rev. Lett. 117(9), 097401 (2016).
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D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
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J. Dostál, J. Pšenčík, and D. Zigmantas, “In situ mapping of the energy flow through the entire photosynthetic apparatus,” Nat. Chem. 8, 705–710 (2016).
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V. Butkus, D. Zigmantas, L. Valkunas, and D. Abramavicius, “Vibrational vs. electronic coherences in 2D spectrum of molecular systems,” Chem. Phys. Lett. 545, 40–43 (2012).
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I. H. M. Van Stokkum, D. S. Larsen, and R. Van Grondelle, “Global and target analysis of time-resolved spectra,” Biochim. Biophys. Acta Bioenerg. 1657(2-3), 82–104 (2004).
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Chem. Phys. Lett. (1)

V. Butkus, D. Zigmantas, L. Valkunas, and D. Abramavicius, “Vibrational vs. electronic coherences in 2D spectrum of molecular systems,” Chem. Phys. Lett. 545, 40–43 (2012).
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K. A. Fransted, J. R. Caram, D. Hayes, and G. S. Engel, “Two-dimensional electronic spectroscopy of bacteriochlorophyll a in solution: elucidating the coherence dynamics of the Fenna-Matthews-Olson complex using its chromophore as a control,” J. Chem. Phys. 137, 125101 (2012).
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K. M. Mullen, M. Vengris, and I. H. M. Van Stokkum, “Algorithms for separable nonlinear least squares with application to modelling time-resolved spectra,” J. Global Optim. 38(2), 201–213 (2007).
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J. Savolainen, D. van der Linden, N. Dijkhuizen, and J. L. Herek, “Characterizing the functional dynamics of zinc phthalocyanine from femtoseconds to nanoseconds,” J. Photochem. Photobiol. A 196(1), 99–105 (2008).
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C. Ruckebusch, M. Sliwa, P. Pernot, P. A. de Juan, and R. Tauler, “Comprehensive data analysis of femtosecond transient absorption spectra: a review,” J. Photochem. Photobiol. C 13(1), 1–27 (2012).
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E. E. Ostroumov, R. M. Mulvaney, J. M. Anna, R. J. Cogdell, and G. D. Scholes, “Energy transfer pathways in light-harvesting complexes of purple bacteria as revealed by global kinetic analysis of two-dimensional transient spectra,” J. Phys. Chem. B 117(38), 11349–11362 (2013).
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J. Almeida, J. Prior, and M. B. Plenio, “Computation of two-dimensional spectra assisted by compressed sampling,” J. Phys. Chem. Lett. 3(18), 2692–2696 (2012).
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H. Li, A. D. Bristow, M. E. Siemens, G. Moody, and S. T. Cundiff, “Unraveling quantum pathways using optical 3D Fourier-transform spectroscopy,” Nat. Commun. 4, 1390 (2013).
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Opt. Lett. (1)

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D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
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J. O. Tollerud, S. T. Cundiff, and J. A. Davis, “Revealing and characterizing dark excitons through coherent multidimensional spectroscopy,” Phys. Rev. Lett. 117(9), 097401 (2016).
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G. Panitchayangkoon, D. V. Voronine, D. Abramavicius, J. R. Caram, N. H. C. Lewis, S. Mukamel, and G. S. Engel, “Direct evidence of quantum transport in photosynthetic light-harvesting complexes,” PNAS 108(52), 20908–20912 (2011).
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Figures (7)

Fig. 1
Fig. 1 Examples of energy level schemes and Feynman diagrams representing (a) non-oscillating and (b) oscillating contributions to the signal. Right panels sketch the dynamics of the corresponding signals as a function of population time.
Fig. 2
Fig. 2 Schematic illustration of the fitting method. Rephasing and non-rephasing data (XR and XN) are subsampled and reshaped into the matrix Y, to which the global fitting procedure is applied. Decay constants, frequencies and matrix A are then recovered. Rephasing and non-rephasing amplitude maps are obtained from matrix A for each complex exponential decay component. Two types of maps can be identified: decay-associated spectra (DAS) and coherence-associated spectra (CAS).
Fig. 3
Fig. 3 (a) Normalized absorption spectrum of ZnPc in THF (black line) and laser spectrum (yellow area). (b) Raman spectrum of ZnPc powders with 633 nm excitation wavelength. (c) Energy levels diagram for ZnPc.
Fig. 4
Fig. 4 Rephasing (upper) and non-rephasing (lower) maps at t = 600 fs. Six traces extracted at representative points in rephasing (red lines) and non-rephasing (green lines) maps are shown (panels a–f).
Fig. 5
Fig. 5 Real part of DAS of the two non-oscillating components for the rephasing (a,b) and non-rephasing (c,d) signals. (a) and (c) are related to the component n = 1 with a long decay time. (b) and (d) are associated to the component n = 2 with time constant 0.38 ps.
Fig. 6
Fig. 6 Complete set of information obtained with the fitting procedure for a single oscillating component. The modulus and the phase of the CAS are shown for positive and negative beating frequencies and for rephasing and non-rephasing signals. As an example, the results for the 702 cm−1 component (n = 5) are shown.
Fig. 7
Fig. 7 Sum of modulus of CAS associated to positive and negative frequency for n = 3–7 components of rephasing (red) and non-rephasing (green) signal. Gray dots identify the coordinates where the oscillating signatures are expected to contribute, according to the DHO model. For an easier comparison, maps (a,f) are scaled by a factor 3.

Tables (1)

Tables Icon

Table 1 Output parameters of the fitting procedure applied to rephasing and non-rephasing 2D data collected on ZnPc solutions. Confidence intervals obtained from standard errors of the fit are less than 1 cm−1 for frequencies and less than 60 fs for time constants. The estimation of the errors was performed using a procedure based on the analysis of the Jacobian of the residuals as reported in [28].

Equations (5)

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

M k h = n = 1 N e t k b n A n h .
min z P Y M ( z ) 2 .
min A H × K Y M ( A , b ) 2
min b N ( I E ( b ) E ( b ) + ) Y 2 ,
Y = [ Y R , Y N ] ,

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