Abstract

We show that it is possible to phase multidimensional infrared spectra generated by a boxcars geometry four-wave mixing spectrometer directly from the signal generated by the molecular vibration of interest, without the need for auxiliary phasing measurements. For isolated vibrations, the phase profile of the 2D response smoothly varies between fixed phase limits, allowing for a general target for phasing independent of the degree of anharmonicity exhibited between the ground and excited state. As a proof of principle, the 2D response of the ∼2155 cm−1 thiocyanate stretch vibration of MeSCN, a system exhibiting anharmonicity such that the 0–1 and 1–2 transitions are spectrally isolated, is successfuly phased directly from the experimental spectra. The methodology is also applied to correctly phase extremely weak signals of the unnatural amino acid azidohomoalanine following background subtraction.

© 2017 Optical Society of America

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References

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  1. P. Hamm and M. Zanni, Concepts and Methods of 2D Infrared Spectroscopy (Cambridge University, 2011).
    [Crossref]
  2. M. Khalil, N. Demirdöven, and A. Tokmakoff, “Obtaining Absorptive Line Shapes in Two-Dimensional Infrared Vibrational Correlation Spectra,” Phys. Rev. Lett. 90, 047401 (2003).
    [Crossref] [PubMed]
  3. S. M. Gallagher Faeder and D. M. Jonas, “Two-Dimensional Electronic Correlation and Relaxation Spectra: Theory and Model Calculations,” J. Phys. Chem. A 103, 10489–10505 (1999).
    [Crossref]
  4. V. I. Prokhorenko, A. Halpin, and R. J. D. Miller, “Coherently-controlled two-dimensional photon echo electronic spectroscopy,” Opt. Express 17, 9764–9779 (2009).
    [Crossref] [PubMed]
  5. F. Milota, C. N. Lincoln, and J. Hauer, “Precise phasing of 2D-electronic spectra in a fully non-collinear phase-matching geometry,” Opt. Express 21, 15904–15911 (2013).
    [Crossref] [PubMed]
  6. A. D. Brisow, D. Karaiskaj, X. Dai, and S. T. Cundiff, “All-optical retrieval of the global phase for two-dimensional Fourier-transform spectroscopy,” Opt. Express 16, 18017–18027 (2008).
    [Crossref]
  7. E. H. G. Backus, S. Garrett-Roe, and P. Hamm, “Phasing problem of heterodyne-detected two-dimensional infrared spectroscopy,” Opt. Lett. 33, 2665–2667 (2008).
    [Crossref] [PubMed]
  8. D. B. Turner, K. E. Wilk, P. M. G. Curmi, and G. D. Scholes, “Comparison of Electronic and Vibrational Coherence Measured by Two-Dimensional Electronic Spectroscopy,” J. Phys. Chem. Lett. 2, 1904–1911 (2011).
    [Crossref]
  9. J. Helbing and P. Hamm, “Compact implementation of Fourier transform two-dimensional IR spectroscopy without phase ambiguity,” J. Opt. Soc. Am. B 28, 171–178 (2011).
    [Crossref]
  10. Y. Zhang, T.-M. Yan, and Y. H. Jiang, “Precise phase determination with the built-in spectral interferometry in two-dimensional electronic spectroscopy,” Opt. Lett. 41, 4134–4137 (2016).
    [Crossref] [PubMed]
  11. W. Rock, Y.-L. Li, P. Pagano, and C. M. Cheatum, “2D IR spectroscopy using Four-Wave Mixing, Pulse Shaping, and IR Upconversion: A Quantitative Comparison,” J. Phys. Chem. A 117, 6073–6083 (2013).
    [Crossref] [PubMed]
  12. P. Hamm, M. Lim, and R. H. Hochstrasser, “Structure of the Amide I Band of Peptides Measured by Femtosecond Nonlinear-Infrared Spectroscopy,” J. Phys. Chem. B 102, 6123–6138 (1998).
    [Crossref]
  13. V. Volkov, R. Schanz, and P. Hamm, “Active phase stabilization in Fourier-transform two-dimensional infrared spectroscopy,” Opt. Lett. 30, 2010–2012 (2005).
    [Crossref] [PubMed]
  14. R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
    [Crossref] [PubMed]
  15. P. Hamm, R. A. Kaindl, and J. Stenger, “Noise suppression in femtosecond mid-infrared light sources,” Opt. Lett. 25, 1798–1800 (2000).
    [Crossref]
  16. R. Bloem, S. Garrett-Roe, H. Strzalka, P. Hamm, and P. Donaldson, “Enhancing signal detection and completely eliminating scattering using quasi-phase-cycling in 2D IR experiments,” Opt. Express 18, 27067–27078 (2010).
    [Crossref]
  17. C. Dorrer, N. Belabas, J.-P. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1795–1802 (2000).
    [Crossref]
  18. S. T. Roberts, J. J. Loparo, and A. Tokmakoff, “Characterization of spectral diffusion from two-dimensional line shapes,” J. Chem. Phys. 125, 084502 (2006).
    [Crossref] [PubMed]
  19. A. Nemeth, F. Milota, T. Mančal, V. Lukeš, J. Hauer, H. F. Kauffmann, and J. Sperling, “Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments,” J. Chem. Phys. 132, 184514 (2010).
    [Crossref]
  20. H. Taskent-Sezgin, J. Chung, P. S. Banerjee, S. Nagarajan, R. B. Dyer, I. Carrico, and D. P. Raleigh, “Azidohomoalanine: A Conformationally Sensitive IR Probe of Protein Folding, Protein Structure, and Electrostatics,” Angew. Chem. Int. Ed. 49, 7473–7475 (2010).
    [Crossref]
  21. J. K. Chung, M. C. Thielges, and M. D. Fayer, “Conformational Dynamics and Stability of HP35 Studied with 2D IR Vibrational Echoes,” J. Am. Chem. Soc. 134, 12118–12124 (2012).
    [Crossref] [PubMed]
  22. M. M. Waegele, R. M. Culik, and F. Gai, “Site-Specific Spectroscopic Reporters of the Local Electric Field, Hydrations, Structure, and Dynamics of Biomolecules,” J. Phys. Chem. Lett. 2, 2598–2609 (2011).
    [Crossref] [PubMed]
  23. J.-J. Max and C. Chapados, “Isotope effects in liquid water by infrared spectroscopy. III. H2O and D2O spectra from 6000 to 0 cm−1,” J. Chem. Phys. 131, 184505 (2009).
    [Crossref]
  24. K. L. Koziol, P. J. M. Johnson, S. Stucki-Buchli, S. A. Waldauer, and P. Hamm, “Fast infrared spectroscopy of protein dynamics: advancing sensitivity and selectivity,” Curr. Opin. Struct. Biol. 34, 1–6 (2015).
    [Crossref] [PubMed]
  25. L. De Marco, W. Carpenter, H. Liu, R. Biswas, J. M. Bowman, and A. Tokmakoff, “Differences in the Vibrational Dynamics of H2O and D2O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water,” J. Phys. Chem. Lett. 7, 1769–1774 (2016).
    [Crossref] [PubMed]
  26. K. Ramasesha, L. De Marco, A. Mandal, and A. Tokmakoff, “Water vibrations have strongly mixed intra- and intermolecular character,” Nat. Chem. 5, 935–940 (2013).
    [Crossref] [PubMed]
  27. S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA 104, 14197–14202 (2007).
    [Crossref] [PubMed]
  28. L. P. DeFlores, R. A. Nicodemus, and A. Tokmakoff, “Two-dimensional Fourier transform spectroscopy in the pump-probe geometry,” Opt. Lett. 32, 2966–2968 (2007).
    [Crossref] [PubMed]
  29. S.-H. Shim and M. T. Zanni, “How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys. 11, 748–761 (2009).
    [Crossref] [PubMed]

2016 (2)

L. De Marco, W. Carpenter, H. Liu, R. Biswas, J. M. Bowman, and A. Tokmakoff, “Differences in the Vibrational Dynamics of H2O and D2O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water,” J. Phys. Chem. Lett. 7, 1769–1774 (2016).
[Crossref] [PubMed]

Y. Zhang, T.-M. Yan, and Y. H. Jiang, “Precise phase determination with the built-in spectral interferometry in two-dimensional electronic spectroscopy,” Opt. Lett. 41, 4134–4137 (2016).
[Crossref] [PubMed]

2015 (1)

K. L. Koziol, P. J. M. Johnson, S. Stucki-Buchli, S. A. Waldauer, and P. Hamm, “Fast infrared spectroscopy of protein dynamics: advancing sensitivity and selectivity,” Curr. Opin. Struct. Biol. 34, 1–6 (2015).
[Crossref] [PubMed]

2013 (3)

F. Milota, C. N. Lincoln, and J. Hauer, “Precise phasing of 2D-electronic spectra in a fully non-collinear phase-matching geometry,” Opt. Express 21, 15904–15911 (2013).
[Crossref] [PubMed]

K. Ramasesha, L. De Marco, A. Mandal, and A. Tokmakoff, “Water vibrations have strongly mixed intra- and intermolecular character,” Nat. Chem. 5, 935–940 (2013).
[Crossref] [PubMed]

W. Rock, Y.-L. Li, P. Pagano, and C. M. Cheatum, “2D IR spectroscopy using Four-Wave Mixing, Pulse Shaping, and IR Upconversion: A Quantitative Comparison,” J. Phys. Chem. A 117, 6073–6083 (2013).
[Crossref] [PubMed]

2012 (2)

R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
[Crossref] [PubMed]

J. K. Chung, M. C. Thielges, and M. D. Fayer, “Conformational Dynamics and Stability of HP35 Studied with 2D IR Vibrational Echoes,” J. Am. Chem. Soc. 134, 12118–12124 (2012).
[Crossref] [PubMed]

2011 (3)

M. M. Waegele, R. M. Culik, and F. Gai, “Site-Specific Spectroscopic Reporters of the Local Electric Field, Hydrations, Structure, and Dynamics of Biomolecules,” J. Phys. Chem. Lett. 2, 2598–2609 (2011).
[Crossref] [PubMed]

D. B. Turner, K. E. Wilk, P. M. G. Curmi, and G. D. Scholes, “Comparison of Electronic and Vibrational Coherence Measured by Two-Dimensional Electronic Spectroscopy,” J. Phys. Chem. Lett. 2, 1904–1911 (2011).
[Crossref]

J. Helbing and P. Hamm, “Compact implementation of Fourier transform two-dimensional IR spectroscopy without phase ambiguity,” J. Opt. Soc. Am. B 28, 171–178 (2011).
[Crossref]

2010 (3)

R. Bloem, S. Garrett-Roe, H. Strzalka, P. Hamm, and P. Donaldson, “Enhancing signal detection and completely eliminating scattering using quasi-phase-cycling in 2D IR experiments,” Opt. Express 18, 27067–27078 (2010).
[Crossref]

A. Nemeth, F. Milota, T. Mančal, V. Lukeš, J. Hauer, H. F. Kauffmann, and J. Sperling, “Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments,” J. Chem. Phys. 132, 184514 (2010).
[Crossref]

H. Taskent-Sezgin, J. Chung, P. S. Banerjee, S. Nagarajan, R. B. Dyer, I. Carrico, and D. P. Raleigh, “Azidohomoalanine: A Conformationally Sensitive IR Probe of Protein Folding, Protein Structure, and Electrostatics,” Angew. Chem. Int. Ed. 49, 7473–7475 (2010).
[Crossref]

2009 (3)

J.-J. Max and C. Chapados, “Isotope effects in liquid water by infrared spectroscopy. III. H2O and D2O spectra from 6000 to 0 cm−1,” J. Chem. Phys. 131, 184505 (2009).
[Crossref]

S.-H. Shim and M. T. Zanni, “How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys. 11, 748–761 (2009).
[Crossref] [PubMed]

V. I. Prokhorenko, A. Halpin, and R. J. D. Miller, “Coherently-controlled two-dimensional photon echo electronic spectroscopy,” Opt. Express 17, 9764–9779 (2009).
[Crossref] [PubMed]

2008 (2)

2007 (2)

L. P. DeFlores, R. A. Nicodemus, and A. Tokmakoff, “Two-dimensional Fourier transform spectroscopy in the pump-probe geometry,” Opt. Lett. 32, 2966–2968 (2007).
[Crossref] [PubMed]

S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA 104, 14197–14202 (2007).
[Crossref] [PubMed]

2006 (1)

S. T. Roberts, J. J. Loparo, and A. Tokmakoff, “Characterization of spectral diffusion from two-dimensional line shapes,” J. Chem. Phys. 125, 084502 (2006).
[Crossref] [PubMed]

2005 (1)

2003 (1)

M. Khalil, N. Demirdöven, and A. Tokmakoff, “Obtaining Absorptive Line Shapes in Two-Dimensional Infrared Vibrational Correlation Spectra,” Phys. Rev. Lett. 90, 047401 (2003).
[Crossref] [PubMed]

2000 (2)

1999 (1)

S. M. Gallagher Faeder and D. M. Jonas, “Two-Dimensional Electronic Correlation and Relaxation Spectra: Theory and Model Calculations,” J. Phys. Chem. A 103, 10489–10505 (1999).
[Crossref]

1998 (1)

P. Hamm, M. Lim, and R. H. Hochstrasser, “Structure of the Amide I Band of Peptides Measured by Femtosecond Nonlinear-Infrared Spectroscopy,” J. Phys. Chem. B 102, 6123–6138 (1998).
[Crossref]

Backus, E. H. G.

Banerjee, P. S.

H. Taskent-Sezgin, J. Chung, P. S. Banerjee, S. Nagarajan, R. B. Dyer, I. Carrico, and D. P. Raleigh, “Azidohomoalanine: A Conformationally Sensitive IR Probe of Protein Folding, Protein Structure, and Electrostatics,” Angew. Chem. Int. Ed. 49, 7473–7475 (2010).
[Crossref]

Belabas, N.

Biswas, R.

L. De Marco, W. Carpenter, H. Liu, R. Biswas, J. M. Bowman, and A. Tokmakoff, “Differences in the Vibrational Dynamics of H2O and D2O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water,” J. Phys. Chem. Lett. 7, 1769–1774 (2016).
[Crossref] [PubMed]

Bloem, R.

R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
[Crossref] [PubMed]

R. Bloem, S. Garrett-Roe, H. Strzalka, P. Hamm, and P. Donaldson, “Enhancing signal detection and completely eliminating scattering using quasi-phase-cycling in 2D IR experiments,” Opt. Express 18, 27067–27078 (2010).
[Crossref]

Bowman, J. M.

L. De Marco, W. Carpenter, H. Liu, R. Biswas, J. M. Bowman, and A. Tokmakoff, “Differences in the Vibrational Dynamics of H2O and D2O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water,” J. Phys. Chem. Lett. 7, 1769–1774 (2016).
[Crossref] [PubMed]

Brisow, A. D.

Buchli, B.

R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
[Crossref] [PubMed]

Carpenter, W.

L. De Marco, W. Carpenter, H. Liu, R. Biswas, J. M. Bowman, and A. Tokmakoff, “Differences in the Vibrational Dynamics of H2O and D2O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water,” J. Phys. Chem. Lett. 7, 1769–1774 (2016).
[Crossref] [PubMed]

Carrico, I.

H. Taskent-Sezgin, J. Chung, P. S. Banerjee, S. Nagarajan, R. B. Dyer, I. Carrico, and D. P. Raleigh, “Azidohomoalanine: A Conformationally Sensitive IR Probe of Protein Folding, Protein Structure, and Electrostatics,” Angew. Chem. Int. Ed. 49, 7473–7475 (2010).
[Crossref]

Chapados, C.

J.-J. Max and C. Chapados, “Isotope effects in liquid water by infrared spectroscopy. III. H2O and D2O spectra from 6000 to 0 cm−1,” J. Chem. Phys. 131, 184505 (2009).
[Crossref]

Cheatum, C. M.

W. Rock, Y.-L. Li, P. Pagano, and C. M. Cheatum, “2D IR spectroscopy using Four-Wave Mixing, Pulse Shaping, and IR Upconversion: A Quantitative Comparison,” J. Phys. Chem. A 117, 6073–6083 (2013).
[Crossref] [PubMed]

Chung, J.

H. Taskent-Sezgin, J. Chung, P. S. Banerjee, S. Nagarajan, R. B. Dyer, I. Carrico, and D. P. Raleigh, “Azidohomoalanine: A Conformationally Sensitive IR Probe of Protein Folding, Protein Structure, and Electrostatics,” Angew. Chem. Int. Ed. 49, 7473–7475 (2010).
[Crossref]

Chung, J. K.

J. K. Chung, M. C. Thielges, and M. D. Fayer, “Conformational Dynamics and Stability of HP35 Studied with 2D IR Vibrational Echoes,” J. Am. Chem. Soc. 134, 12118–12124 (2012).
[Crossref] [PubMed]

Culik, R. M.

M. M. Waegele, R. M. Culik, and F. Gai, “Site-Specific Spectroscopic Reporters of the Local Electric Field, Hydrations, Structure, and Dynamics of Biomolecules,” J. Phys. Chem. Lett. 2, 2598–2609 (2011).
[Crossref] [PubMed]

Cundiff, S. T.

Curmi, P. M. G.

D. B. Turner, K. E. Wilk, P. M. G. Curmi, and G. D. Scholes, “Comparison of Electronic and Vibrational Coherence Measured by Two-Dimensional Electronic Spectroscopy,” J. Phys. Chem. Lett. 2, 1904–1911 (2011).
[Crossref]

Dai, X.

De Marco, L.

L. De Marco, W. Carpenter, H. Liu, R. Biswas, J. M. Bowman, and A. Tokmakoff, “Differences in the Vibrational Dynamics of H2O and D2O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water,” J. Phys. Chem. Lett. 7, 1769–1774 (2016).
[Crossref] [PubMed]

K. Ramasesha, L. De Marco, A. Mandal, and A. Tokmakoff, “Water vibrations have strongly mixed intra- and intermolecular character,” Nat. Chem. 5, 935–940 (2013).
[Crossref] [PubMed]

DeFlores, L. P.

Demirdöven, N.

M. Khalil, N. Demirdöven, and A. Tokmakoff, “Obtaining Absorptive Line Shapes in Two-Dimensional Infrared Vibrational Correlation Spectra,” Phys. Rev. Lett. 90, 047401 (2003).
[Crossref] [PubMed]

Donaldson, P.

Dorrer, C.

Dyer, R. B.

H. Taskent-Sezgin, J. Chung, P. S. Banerjee, S. Nagarajan, R. B. Dyer, I. Carrico, and D. P. Raleigh, “Azidohomoalanine: A Conformationally Sensitive IR Probe of Protein Folding, Protein Structure, and Electrostatics,” Angew. Chem. Int. Ed. 49, 7473–7475 (2010).
[Crossref]

Fayer, M. D.

J. K. Chung, M. C. Thielges, and M. D. Fayer, “Conformational Dynamics and Stability of HP35 Studied with 2D IR Vibrational Echoes,” J. Am. Chem. Soc. 134, 12118–12124 (2012).
[Crossref] [PubMed]

Gai, F.

M. M. Waegele, R. M. Culik, and F. Gai, “Site-Specific Spectroscopic Reporters of the Local Electric Field, Hydrations, Structure, and Dynamics of Biomolecules,” J. Phys. Chem. Lett. 2, 2598–2609 (2011).
[Crossref] [PubMed]

Gallagher Faeder, S. M.

S. M. Gallagher Faeder and D. M. Jonas, “Two-Dimensional Electronic Correlation and Relaxation Spectra: Theory and Model Calculations,” J. Phys. Chem. A 103, 10489–10505 (1999).
[Crossref]

Garrett-Roe, S.

Halpin, A.

Hamm, P.

K. L. Koziol, P. J. M. Johnson, S. Stucki-Buchli, S. A. Waldauer, and P. Hamm, “Fast infrared spectroscopy of protein dynamics: advancing sensitivity and selectivity,” Curr. Opin. Struct. Biol. 34, 1–6 (2015).
[Crossref] [PubMed]

R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
[Crossref] [PubMed]

J. Helbing and P. Hamm, “Compact implementation of Fourier transform two-dimensional IR spectroscopy without phase ambiguity,” J. Opt. Soc. Am. B 28, 171–178 (2011).
[Crossref]

R. Bloem, S. Garrett-Roe, H. Strzalka, P. Hamm, and P. Donaldson, “Enhancing signal detection and completely eliminating scattering using quasi-phase-cycling in 2D IR experiments,” Opt. Express 18, 27067–27078 (2010).
[Crossref]

E. H. G. Backus, S. Garrett-Roe, and P. Hamm, “Phasing problem of heterodyne-detected two-dimensional infrared spectroscopy,” Opt. Lett. 33, 2665–2667 (2008).
[Crossref] [PubMed]

V. Volkov, R. Schanz, and P. Hamm, “Active phase stabilization in Fourier-transform two-dimensional infrared spectroscopy,” Opt. Lett. 30, 2010–2012 (2005).
[Crossref] [PubMed]

P. Hamm, R. A. Kaindl, and J. Stenger, “Noise suppression in femtosecond mid-infrared light sources,” Opt. Lett. 25, 1798–1800 (2000).
[Crossref]

P. Hamm, M. Lim, and R. H. Hochstrasser, “Structure of the Amide I Band of Peptides Measured by Femtosecond Nonlinear-Infrared Spectroscopy,” J. Phys. Chem. B 102, 6123–6138 (1998).
[Crossref]

P. Hamm and M. Zanni, Concepts and Methods of 2D Infrared Spectroscopy (Cambridge University, 2011).
[Crossref]

Hauer, J.

F. Milota, C. N. Lincoln, and J. Hauer, “Precise phasing of 2D-electronic spectra in a fully non-collinear phase-matching geometry,” Opt. Express 21, 15904–15911 (2013).
[Crossref] [PubMed]

A. Nemeth, F. Milota, T. Mančal, V. Lukeš, J. Hauer, H. F. Kauffmann, and J. Sperling, “Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments,” J. Chem. Phys. 132, 184514 (2010).
[Crossref]

Helbing, J.

Hochstrasser, R. H.

P. Hamm, M. Lim, and R. H. Hochstrasser, “Structure of the Amide I Band of Peptides Measured by Femtosecond Nonlinear-Infrared Spectroscopy,” J. Phys. Chem. B 102, 6123–6138 (1998).
[Crossref]

Jelesarov, I.

R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
[Crossref] [PubMed]

Jiang, Y. H.

Joffre, M.

Johnson, P. J. M.

K. L. Koziol, P. J. M. Johnson, S. Stucki-Buchli, S. A. Waldauer, and P. Hamm, “Fast infrared spectroscopy of protein dynamics: advancing sensitivity and selectivity,” Curr. Opin. Struct. Biol. 34, 1–6 (2015).
[Crossref] [PubMed]

Jonas, D. M.

S. M. Gallagher Faeder and D. M. Jonas, “Two-Dimensional Electronic Correlation and Relaxation Spectra: Theory and Model Calculations,” J. Phys. Chem. A 103, 10489–10505 (1999).
[Crossref]

Kaindl, R. A.

Karaiskaj, D.

Kauffmann, H. F.

A. Nemeth, F. Milota, T. Mančal, V. Lukeš, J. Hauer, H. F. Kauffmann, and J. Sperling, “Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments,” J. Chem. Phys. 132, 184514 (2010).
[Crossref]

Khalil, M.

M. Khalil, N. Demirdöven, and A. Tokmakoff, “Obtaining Absorptive Line Shapes in Two-Dimensional Infrared Vibrational Correlation Spectra,” Phys. Rev. Lett. 90, 047401 (2003).
[Crossref] [PubMed]

Koziol, K.

R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
[Crossref] [PubMed]

Koziol, K. L.

K. L. Koziol, P. J. M. Johnson, S. Stucki-Buchli, S. A. Waldauer, and P. Hamm, “Fast infrared spectroscopy of protein dynamics: advancing sensitivity and selectivity,” Curr. Opin. Struct. Biol. 34, 1–6 (2015).
[Crossref] [PubMed]

Li, Y.-L.

W. Rock, Y.-L. Li, P. Pagano, and C. M. Cheatum, “2D IR spectroscopy using Four-Wave Mixing, Pulse Shaping, and IR Upconversion: A Quantitative Comparison,” J. Phys. Chem. A 117, 6073–6083 (2013).
[Crossref] [PubMed]

Likforman, J.-P.

Lim, M.

P. Hamm, M. Lim, and R. H. Hochstrasser, “Structure of the Amide I Band of Peptides Measured by Femtosecond Nonlinear-Infrared Spectroscopy,” J. Phys. Chem. B 102, 6123–6138 (1998).
[Crossref]

Lincoln, C. N.

Ling, Y. L.

S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA 104, 14197–14202 (2007).
[Crossref] [PubMed]

Liu, H.

L. De Marco, W. Carpenter, H. Liu, R. Biswas, J. M. Bowman, and A. Tokmakoff, “Differences in the Vibrational Dynamics of H2O and D2O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water,” J. Phys. Chem. Lett. 7, 1769–1774 (2016).
[Crossref] [PubMed]

Loparo, J. J.

S. T. Roberts, J. J. Loparo, and A. Tokmakoff, “Characterization of spectral diffusion from two-dimensional line shapes,” J. Chem. Phys. 125, 084502 (2006).
[Crossref] [PubMed]

Lukeš, V.

A. Nemeth, F. Milota, T. Mančal, V. Lukeš, J. Hauer, H. F. Kauffmann, and J. Sperling, “Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments,” J. Chem. Phys. 132, 184514 (2010).
[Crossref]

Mancal, T.

A. Nemeth, F. Milota, T. Mančal, V. Lukeš, J. Hauer, H. F. Kauffmann, and J. Sperling, “Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments,” J. Chem. Phys. 132, 184514 (2010).
[Crossref]

Mandal, A.

K. Ramasesha, L. De Marco, A. Mandal, and A. Tokmakoff, “Water vibrations have strongly mixed intra- and intermolecular character,” Nat. Chem. 5, 935–940 (2013).
[Crossref] [PubMed]

Max, J.-J.

J.-J. Max and C. Chapados, “Isotope effects in liquid water by infrared spectroscopy. III. H2O and D2O spectra from 6000 to 0 cm−1,” J. Chem. Phys. 131, 184505 (2009).
[Crossref]

Miller, R. J. D.

Milota, F.

F. Milota, C. N. Lincoln, and J. Hauer, “Precise phasing of 2D-electronic spectra in a fully non-collinear phase-matching geometry,” Opt. Express 21, 15904–15911 (2013).
[Crossref] [PubMed]

A. Nemeth, F. Milota, T. Mančal, V. Lukeš, J. Hauer, H. F. Kauffmann, and J. Sperling, “Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments,” J. Chem. Phys. 132, 184514 (2010).
[Crossref]

Nagarajan, S.

H. Taskent-Sezgin, J. Chung, P. S. Banerjee, S. Nagarajan, R. B. Dyer, I. Carrico, and D. P. Raleigh, “Azidohomoalanine: A Conformationally Sensitive IR Probe of Protein Folding, Protein Structure, and Electrostatics,” Angew. Chem. Int. Ed. 49, 7473–7475 (2010).
[Crossref]

Nemeth, A.

A. Nemeth, F. Milota, T. Mančal, V. Lukeš, J. Hauer, H. F. Kauffmann, and J. Sperling, “Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments,” J. Chem. Phys. 132, 184514 (2010).
[Crossref]

Nicodemus, R. A.

Pagano, P.

W. Rock, Y.-L. Li, P. Pagano, and C. M. Cheatum, “2D IR spectroscopy using Four-Wave Mixing, Pulse Shaping, and IR Upconversion: A Quantitative Comparison,” J. Phys. Chem. A 117, 6073–6083 (2013).
[Crossref] [PubMed]

Prokhorenko, V. I.

Raleigh, D. P.

H. Taskent-Sezgin, J. Chung, P. S. Banerjee, S. Nagarajan, R. B. Dyer, I. Carrico, and D. P. Raleigh, “Azidohomoalanine: A Conformationally Sensitive IR Probe of Protein Folding, Protein Structure, and Electrostatics,” Angew. Chem. Int. Ed. 49, 7473–7475 (2010).
[Crossref]

Ramasesha, K.

K. Ramasesha, L. De Marco, A. Mandal, and A. Tokmakoff, “Water vibrations have strongly mixed intra- and intermolecular character,” Nat. Chem. 5, 935–940 (2013).
[Crossref] [PubMed]

Roberts, S. T.

S. T. Roberts, J. J. Loparo, and A. Tokmakoff, “Characterization of spectral diffusion from two-dimensional line shapes,” J. Chem. Phys. 125, 084502 (2006).
[Crossref] [PubMed]

Rock, W.

W. Rock, Y.-L. Li, P. Pagano, and C. M. Cheatum, “2D IR spectroscopy using Four-Wave Mixing, Pulse Shaping, and IR Upconversion: A Quantitative Comparison,” J. Phys. Chem. A 117, 6073–6083 (2013).
[Crossref] [PubMed]

Samatanga, B.

R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
[Crossref] [PubMed]

Schanz, R.

Scholes, G. D.

D. B. Turner, K. E. Wilk, P. M. G. Curmi, and G. D. Scholes, “Comparison of Electronic and Vibrational Coherence Measured by Two-Dimensional Electronic Spectroscopy,” J. Phys. Chem. Lett. 2, 1904–1911 (2011).
[Crossref]

Shim, S.-H.

S.-H. Shim and M. T. Zanni, “How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys. 11, 748–761 (2009).
[Crossref] [PubMed]

S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA 104, 14197–14202 (2007).
[Crossref] [PubMed]

Sperling, J.

A. Nemeth, F. Milota, T. Mančal, V. Lukeš, J. Hauer, H. F. Kauffmann, and J. Sperling, “Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments,” J. Chem. Phys. 132, 184514 (2010).
[Crossref]

Stenger, J.

Strasfeld, D. B.

S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA 104, 14197–14202 (2007).
[Crossref] [PubMed]

Strzalka, H.

Stucki-Buchli, S.

K. L. Koziol, P. J. M. Johnson, S. Stucki-Buchli, S. A. Waldauer, and P. Hamm, “Fast infrared spectroscopy of protein dynamics: advancing sensitivity and selectivity,” Curr. Opin. Struct. Biol. 34, 1–6 (2015).
[Crossref] [PubMed]

Taskent-Sezgin, H.

H. Taskent-Sezgin, J. Chung, P. S. Banerjee, S. Nagarajan, R. B. Dyer, I. Carrico, and D. P. Raleigh, “Azidohomoalanine: A Conformationally Sensitive IR Probe of Protein Folding, Protein Structure, and Electrostatics,” Angew. Chem. Int. Ed. 49, 7473–7475 (2010).
[Crossref]

Thielges, M. C.

J. K. Chung, M. C. Thielges, and M. D. Fayer, “Conformational Dynamics and Stability of HP35 Studied with 2D IR Vibrational Echoes,” J. Am. Chem. Soc. 134, 12118–12124 (2012).
[Crossref] [PubMed]

Tokmakoff, A.

L. De Marco, W. Carpenter, H. Liu, R. Biswas, J. M. Bowman, and A. Tokmakoff, “Differences in the Vibrational Dynamics of H2O and D2O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water,” J. Phys. Chem. Lett. 7, 1769–1774 (2016).
[Crossref] [PubMed]

K. Ramasesha, L. De Marco, A. Mandal, and A. Tokmakoff, “Water vibrations have strongly mixed intra- and intermolecular character,” Nat. Chem. 5, 935–940 (2013).
[Crossref] [PubMed]

L. P. DeFlores, R. A. Nicodemus, and A. Tokmakoff, “Two-dimensional Fourier transform spectroscopy in the pump-probe geometry,” Opt. Lett. 32, 2966–2968 (2007).
[Crossref] [PubMed]

S. T. Roberts, J. J. Loparo, and A. Tokmakoff, “Characterization of spectral diffusion from two-dimensional line shapes,” J. Chem. Phys. 125, 084502 (2006).
[Crossref] [PubMed]

M. Khalil, N. Demirdöven, and A. Tokmakoff, “Obtaining Absorptive Line Shapes in Two-Dimensional Infrared Vibrational Correlation Spectra,” Phys. Rev. Lett. 90, 047401 (2003).
[Crossref] [PubMed]

Turner, D. B.

D. B. Turner, K. E. Wilk, P. M. G. Curmi, and G. D. Scholes, “Comparison of Electronic and Vibrational Coherence Measured by Two-Dimensional Electronic Spectroscopy,” J. Phys. Chem. Lett. 2, 1904–1911 (2011).
[Crossref]

Volkov, V.

Waegele, M. M.

M. M. Waegele, R. M. Culik, and F. Gai, “Site-Specific Spectroscopic Reporters of the Local Electric Field, Hydrations, Structure, and Dynamics of Biomolecules,” J. Phys. Chem. Lett. 2, 2598–2609 (2011).
[Crossref] [PubMed]

Waldauer, S. A.

K. L. Koziol, P. J. M. Johnson, S. Stucki-Buchli, S. A. Waldauer, and P. Hamm, “Fast infrared spectroscopy of protein dynamics: advancing sensitivity and selectivity,” Curr. Opin. Struct. Biol. 34, 1–6 (2015).
[Crossref] [PubMed]

R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
[Crossref] [PubMed]

Walser, R.

R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
[Crossref] [PubMed]

Wilk, K. E.

D. B. Turner, K. E. Wilk, P. M. G. Curmi, and G. D. Scholes, “Comparison of Electronic and Vibrational Coherence Measured by Two-Dimensional Electronic Spectroscopy,” J. Phys. Chem. Lett. 2, 1904–1911 (2011).
[Crossref]

Yan, T.-M.

Zanni, M.

P. Hamm and M. Zanni, Concepts and Methods of 2D Infrared Spectroscopy (Cambridge University, 2011).
[Crossref]

Zanni, M. T.

S.-H. Shim and M. T. Zanni, “How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys. 11, 748–761 (2009).
[Crossref] [PubMed]

S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA 104, 14197–14202 (2007).
[Crossref] [PubMed]

Zhang, Y.

Angew. Chem. Int. Ed. (1)

H. Taskent-Sezgin, J. Chung, P. S. Banerjee, S. Nagarajan, R. B. Dyer, I. Carrico, and D. P. Raleigh, “Azidohomoalanine: A Conformationally Sensitive IR Probe of Protein Folding, Protein Structure, and Electrostatics,” Angew. Chem. Int. Ed. 49, 7473–7475 (2010).
[Crossref]

Curr. Opin. Struct. Biol. (1)

K. L. Koziol, P. J. M. Johnson, S. Stucki-Buchli, S. A. Waldauer, and P. Hamm, “Fast infrared spectroscopy of protein dynamics: advancing sensitivity and selectivity,” Curr. Opin. Struct. Biol. 34, 1–6 (2015).
[Crossref] [PubMed]

J. Am. Chem. Soc. (1)

J. K. Chung, M. C. Thielges, and M. D. Fayer, “Conformational Dynamics and Stability of HP35 Studied with 2D IR Vibrational Echoes,” J. Am. Chem. Soc. 134, 12118–12124 (2012).
[Crossref] [PubMed]

J. Chem. Phys. (3)

J.-J. Max and C. Chapados, “Isotope effects in liquid water by infrared spectroscopy. III. H2O and D2O spectra from 6000 to 0 cm−1,” J. Chem. Phys. 131, 184505 (2009).
[Crossref]

S. T. Roberts, J. J. Loparo, and A. Tokmakoff, “Characterization of spectral diffusion from two-dimensional line shapes,” J. Chem. Phys. 125, 084502 (2006).
[Crossref] [PubMed]

A. Nemeth, F. Milota, T. Mančal, V. Lukeš, J. Hauer, H. F. Kauffmann, and J. Sperling, “Vibrational wave packet induced oscillations in two-dimensional electronic spectra. I. Experiments,” J. Chem. Phys. 132, 184514 (2010).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. Chem. A (2)

S. M. Gallagher Faeder and D. M. Jonas, “Two-Dimensional Electronic Correlation and Relaxation Spectra: Theory and Model Calculations,” J. Phys. Chem. A 103, 10489–10505 (1999).
[Crossref]

W. Rock, Y.-L. Li, P. Pagano, and C. M. Cheatum, “2D IR spectroscopy using Four-Wave Mixing, Pulse Shaping, and IR Upconversion: A Quantitative Comparison,” J. Phys. Chem. A 117, 6073–6083 (2013).
[Crossref] [PubMed]

J. Phys. Chem. B (2)

P. Hamm, M. Lim, and R. H. Hochstrasser, “Structure of the Amide I Band of Peptides Measured by Femtosecond Nonlinear-Infrared Spectroscopy,” J. Phys. Chem. B 102, 6123–6138 (1998).
[Crossref]

R. Bloem, K. Koziol, S. A. Waldauer, B. Buchli, R. Walser, B. Samatanga, I. Jelesarov, and P. Hamm, “Ligand Binding Studied by 2D IR Spectroscopy Using the Azidohomoalanine Label,” J. Phys. Chem. B 116, 13705–13712 (2012).
[Crossref] [PubMed]

J. Phys. Chem. Lett. (3)

D. B. Turner, K. E. Wilk, P. M. G. Curmi, and G. D. Scholes, “Comparison of Electronic and Vibrational Coherence Measured by Two-Dimensional Electronic Spectroscopy,” J. Phys. Chem. Lett. 2, 1904–1911 (2011).
[Crossref]

M. M. Waegele, R. M. Culik, and F. Gai, “Site-Specific Spectroscopic Reporters of the Local Electric Field, Hydrations, Structure, and Dynamics of Biomolecules,” J. Phys. Chem. Lett. 2, 2598–2609 (2011).
[Crossref] [PubMed]

L. De Marco, W. Carpenter, H. Liu, R. Biswas, J. M. Bowman, and A. Tokmakoff, “Differences in the Vibrational Dynamics of H2O and D2O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water,” J. Phys. Chem. Lett. 7, 1769–1774 (2016).
[Crossref] [PubMed]

Nat. Chem. (1)

K. Ramasesha, L. De Marco, A. Mandal, and A. Tokmakoff, “Water vibrations have strongly mixed intra- and intermolecular character,” Nat. Chem. 5, 935–940 (2013).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (5)

Phys. Chem. Chem. Phys. (1)

S.-H. Shim and M. T. Zanni, “How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping,” Phys. Chem. Chem. Phys. 11, 748–761 (2009).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

M. Khalil, N. Demirdöven, and A. Tokmakoff, “Obtaining Absorptive Line Shapes in Two-Dimensional Infrared Vibrational Correlation Spectra,” Phys. Rev. Lett. 90, 047401 (2003).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA 104, 14197–14202 (2007).
[Crossref] [PubMed]

Other (1)

P. Hamm and M. Zanni, Concepts and Methods of 2D Infrared Spectroscopy (Cambridge University, 2011).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Simulated purely absorptive 2D IR spectra (left) and associated phase profiles (right) as a function of anharmonicity (ω01ω12) for (a) 250 cm−1, (b) 25 cm−1, (c) 2.5 cm−1, representing three common classes of spectral response: fully isolated transitions, vibrations which overlap only minimally between the ground and excited state response, and significantly overlapping transitions where even the central frequencies of each transition overlap with the wings of other transition. d) Single frequency phase profiles along ω1 = 2155 cm−1 are shown in a) black, b) grey, c) light grey, respectively. Dashed lines show phase values of −3π/2, −π/2, and π/2. Contours of the 2D IR spectra are shown at ±10% intervals of the signal maxima, while the phase profiles have contours drawn in steps of π/10 from −2π to 2π.
Fig. 2
Fig. 2 Direct phasing of heterodyne-detected 2D IR spectra of MeSCN in DMF. a) Power spectrum and b) the associated phase spectrum (right) of the t2 = 250 fs 2D response of the thiocyanate stretch vibration. From the power spectrum, ground and excited state transitions are observed separated along ω3 = −25 cm−1. Contour lines are drawn at 10% intervals of the maximum amplitude of the power spectrum, and at intervals of π/10 between ±2π for the phase spectrum. The discontinuities near the centre of the phase spectrum arise due to the near-zero amplitude of the experimental response along the nodal line between the ground and excited state transitions. c) The phase profiles through ω1 = 2155 cm−1 for both the experimental data (black points, bottom axis) and from the simulated 2D response with an anharmonicity of 25 cm−1 (grey line, top axis, taken from Fig. 1(b)), showing the excellent agreement between the theoretical and experimental phase profiles through the central frequency of the thiocyanate stretch vibration. A constant offset of Δϕ ≈ 0.45π is observed between the experimental and simulated spectra, and represents the global phase offset which must be corrected to generate the absorptive and dispersive 2D spectra.
Fig. 3
Fig. 3 Purely absorptive 2D IR spectra of MeSCN in DMF at select waiting times (indicated top left), directly phased as outlined in Fig. 2. Inhomogeneous broadening is observed at early waiting times, but on a 10 ps timescale the transition displays a homogeneous response as a result of spectral diffusion. Contours are drawn at ±10% intervals of the signal maximum of the t2 = 250 fs spectrum.
Fig. 4
Fig. 4 Alignment of time domain interferograms based on solvent response. The (a) power spectrum (contours drawn at 10% intervals of the maximum amplitude) and b) phase profile (contours drawn in steps of π/10) of 100 μM Aha in D2O solvent, where the response is dominated by a broad solvent background which spans the entire spectral domain of interest. The phase profile in particular shows an effectively flat phase in the spectral region of interest, and can thus be used to align subsequent measurements. This is realized through spectral integration of the time domain signals across the detection frequency range of the spectrometer to give the highest signal to noise for the determination of the phase, where c) the phase offset of ∼0.7π is visible in the spectrally-integrated response. The phase of ∼0.7π represents the per se unknown phase of the water background in addition to the imperfect control and knowledge of the relative phases of the excitation pulses. Rolling the time domain signals by the negative of this net phase offset in the Fourier domain allows for individual alignment of each set of time-domain interferograms seperately.
Fig. 5
Fig. 5 Phasing the isolated Aha response. a) The power spectrum of the Aha response following background subtraction in the time domain. The central excitation frequency of the power spectrum is observed to be at ∼2120 cm−1. b) The experimental phase profile at ω1 = 2120 cm−1, showing the characteristic progression between fixed phase limits of [−3π/2, π] across the detection frequency window associated with the power spectral response. A residual offset of ∼ 0.11π is observed between the experimental phase of the Aha response and the expected fixed phase limits from the simulated response. Correction of this phase offset leads to c) the purely absorptive spectrum of Aha without phase ambiguity, showing 0–1 and 1–2 transitions with an amplitude ratio of ∼2:1. Contours are drawn in steps of ±10% the signal maximum.

Equations (7)

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R R = μ 4 ( e i ( ( ω 01 Δ ) t 3 ω 01 t 1 ) e i ω 01 ( t 3 t 1 ) ) e g ( t 1 ) + g ( t 2 ) g ( t 3 ) g ( t 1 + t 2 ) g ( t 2 + t 3 ) + g ( t 1 + t 2 + t 3 ) R N R = μ 4 ( e i ( ( ω 01 Δ ) t 3 + ω 01 t 1 ) e i ω 01 ( t 3 + t 1 ) ) e g ( t 1 ) g ( t 2 ) g ( t 3 ) + g ( t 1 + t 2 ) + g ( t 2 + t 3 ) g ( t 1 + t 2 + t 3 )
g ( t ) = Δ ω 2 τ c 2 [ e t / τ c + t τ c 1 ] ,
S R ( ω 1 , t 2 , ω 3 ) = 0 0 R R e i ω 1 t 1 e i ω 3 t 3 d t 1 d t 3 S N R ( ω 1 , t 2 , ω 3 ) = 0 0 R N R e i ω 1 t 1 e i ω 3 t 3 d t 1 d t 3 ,
S A ( ω 1 , t 2 , ω 3 ) = [ S R ( ω 1 , t 2 , ω 3 ) + S N R ( ω 1 , t 2 , ω 3 ) ] .
S P ( ω 1 , t 2 , ω 3 ) = Arg [ S R ( ω 1 , t 2 , ω 3 ) + S N R ( ω 1 , t 2 , ω 3 ) ] .
S A ( ω 1 , t 2 , ω 3 ) = [ e i Δ ϕ ( S R ( ω 1 , t 2 , ω 3 ) + S N R ( ω 1 , t 2 , ω 3 ) ) ]
S P ( ω 1 , t 2 , ω 3 ) = Arg [ S R ( ω 1 , t 2 , ω 3 ) + S N R ( ω 1 , t 2 , ω 3 ) ] Δ ϕ .

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