Abstract

We examine the effect that pulse chirp has on the shape of two- dimensional electronic spectra through calculations and experiments. For the calculations we use a model two electronic level system with a solvent interaction represented by a simple Gaussian correlation function and compare the resulting spectra to experiments carried out on an organic dye molecule (Rhodamine 800). Both calculations and experiments show that distortions due to chirp are most significant when the pulses used in the experiment have different amounts of chirp, introducing peak shape asymmetry that could be interpreted as spectrally dependent relaxation. When all pulses have similar chirp the distortions are reduced but still affect the anti-diagonal symmetry of the peak shapes and introduce negative features that could be interpreted as excited state absorption.

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2009 (3)

2008 (1)

2007 (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. U.S.A. 104(36), 14197–14202 (2007).
[CrossRef] [PubMed]

2006 (3)

K. Lazonder, M. S. Pshenichnikov, and D. A. Wiersma, “Easy interpretation of optical two-dimensional correlation spectra,” Opt. Lett. 31(22), 3354–3356 (2006).
[CrossRef] [PubMed]

D. Zigmantas, E. L. Read, T. Mancal, T. Brixner, A. T. Gardiner, R. J. Cogdell, and G. R. Fleming, “Two-dimensional electronic spectroscopy of the B800-B820 light-harvesting complex,” Proc. Natl. Acad. Sci. U.S.A. 103(34), 12672–12677 (2006).
[CrossRef] [PubMed]

J. J. Loparo, S. T. Roberts, and A. Tokmakoff, “Multidimensional infrared spectroscopy of water. I. Vibrational dynamics in two-dimensional IR line shapes,” J. Chem. Phys. 125, 194522 (2006).
[CrossRef] [PubMed]

2005 (3)

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, “Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O,” Nature 434(7030), 199–202 (2005).
[CrossRef] [PubMed]

P. Baum and E. Riedle, “Design and calibration of zero-additional-phase SPIDER,” J. Opt. Soc. Am. B 22(9), 1875–1883 (2005).
[CrossRef]

2004 (2)

D. Abramavicius and S. Mukamel, “Disentangling multidimensional femtosecond spectra of excitons by pulse shaping with coherent control,” J. Chem. Phys . 120, 8373-8378 (2004).
[CrossRef] [PubMed]

J. B. Asbury, T. Steinel, K. Kwak, S. A. Corcelli, C. P. Lawrence, J. L. Skinner, and M. D. Fayer, “Dynamics of water probed with vibrational echo correlation spectroscopy,” J. Chem. Phys. 121(24), 12431–12446 (2004).
[CrossRef] [PubMed]

2003 (2)

D. A. Farrow, A. Yu, and D. M. Jonas, “Spectral relaxation in pump-probe transients,” J. Chem. Phys. 118(20), 9348–9356 (2003).
[CrossRef]

D. M. Jonas, “Two-dimensional femtosecond spectroscopy,” Annu. Rev. Phys. Chem. 54(1), 425–463 (2003).
[CrossRef] [PubMed]

2002 (1)

J. D. Hybl, A. Yu, D. A. Farrow, and D. M. Jonas, “Polar solvation dynamics in the femtosecond evolution of two-dimensional Fourier transform spectra,” J. Phys. Chem. A 106(34), 7651–7654 (2002).
[CrossRef]

2001 (1)

K. Ohta, D. S. Larsen, M. Yang, and G. R. Fleming, “Influence of intramolecular vibrations in third-order, time-domain resonant spectroscopies. II. Numerical calculations,” J. Chem. Phys. 114(18), 8020–8039 (2001).
[CrossRef]

1999 (1)

S. M. G. Faeder and D. M. Jonas, “Two-dimensional electronic correlation and relaxation spectra: Theory and model calculations,” J. Phys. Chem. A 103(49), 10489–10505 (1999).
[CrossRef]

1998 (1)

J. D. Hybl, A. W. Albrecht, S. M. G. Faeder, and D. M. Jonas, “Two-dimensional electronic spectroscopy,” Chem. Phys. Lett. 297(3-4), 307–313 (1998).
[CrossRef]

1997 (1)

Abramavicius, D.

D. Abramavicius and S. Mukamel, “Disentangling multidimensional femtosecond spectra of excitons by pulse shaping with coherent control,” J. Chem. Phys . 120, 8373-8378 (2004).
[CrossRef] [PubMed]

Albrecht, A. W.

J. D. Hybl, A. W. Albrecht, S. M. G. Faeder, and D. M. Jonas, “Two-dimensional electronic spectroscopy,” Chem. Phys. Lett. 297(3-4), 307–313 (1998).
[CrossRef]

Asbury, J. B.

J. B. Asbury, T. Steinel, K. Kwak, S. A. Corcelli, C. P. Lawrence, J. L. Skinner, and M. D. Fayer, “Dynamics of water probed with vibrational echo correlation spectroscopy,” J. Chem. Phys. 121(24), 12431–12446 (2004).
[CrossRef] [PubMed]

Baum, P.

Blankenship, R. E.

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

Brixner, T.

D. Zigmantas, E. L. Read, T. Mancal, T. Brixner, A. T. Gardiner, R. J. Cogdell, and G. R. Fleming, “Two-dimensional electronic spectroscopy of the B800-B820 light-harvesting complex,” Proc. Natl. Acad. Sci. U.S.A. 103(34), 12672–12677 (2006).
[CrossRef] [PubMed]

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

Bruner, B. D.

M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, “Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O,” Nature 434(7030), 199–202 (2005).
[CrossRef] [PubMed]

Cho, M.

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

Chugh, B.

M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, “Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O,” Nature 434(7030), 199–202 (2005).
[CrossRef] [PubMed]

Cogdell, R. J.

D. Zigmantas, E. L. Read, T. Mancal, T. Brixner, A. T. Gardiner, R. J. Cogdell, and G. R. Fleming, “Two-dimensional electronic spectroscopy of the B800-B820 light-harvesting complex,” Proc. Natl. Acad. Sci. U.S.A. 103(34), 12672–12677 (2006).
[CrossRef] [PubMed]

Corcelli, S. A.

J. B. Asbury, T. Steinel, K. Kwak, S. A. Corcelli, C. P. Lawrence, J. L. Skinner, and M. D. Fayer, “Dynamics of water probed with vibrational echo correlation spectroscopy,” J. Chem. Phys. 121(24), 12431–12446 (2004).
[CrossRef] [PubMed]

Cowan, M. L.

M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, “Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O,” Nature 434(7030), 199–202 (2005).
[CrossRef] [PubMed]

Dwyer, J. R.

M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, “Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O,” Nature 434(7030), 199–202 (2005).
[CrossRef] [PubMed]

Elsaesser, T.

M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, “Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O,” Nature 434(7030), 199–202 (2005).
[CrossRef] [PubMed]

Faeder, S. M. G.

S. M. G. Faeder and D. M. Jonas, “Two-dimensional electronic correlation and relaxation spectra: Theory and model calculations,” J. Phys. Chem. A 103(49), 10489–10505 (1999).
[CrossRef]

J. D. Hybl, A. W. Albrecht, S. M. G. Faeder, and D. M. Jonas, “Two-dimensional electronic spectroscopy,” Chem. Phys. Lett. 297(3-4), 307–313 (1998).
[CrossRef]

Farrow, D. A.

D. A. Farrow, A. Yu, and D. M. Jonas, “Spectral relaxation in pump-probe transients,” J. Chem. Phys. 118(20), 9348–9356 (2003).
[CrossRef]

J. D. Hybl, A. Yu, D. A. Farrow, and D. M. Jonas, “Polar solvation dynamics in the femtosecond evolution of two-dimensional Fourier transform spectra,” J. Phys. Chem. A 106(34), 7651–7654 (2002).
[CrossRef]

Fayer, M. D.

J. B. Asbury, T. Steinel, K. Kwak, S. A. Corcelli, C. P. Lawrence, J. L. Skinner, and M. D. Fayer, “Dynamics of water probed with vibrational echo correlation spectroscopy,” J. Chem. Phys. 121(24), 12431–12446 (2004).
[CrossRef] [PubMed]

Fleming, G. R.

D. Zigmantas, E. L. Read, T. Mancal, T. Brixner, A. T. Gardiner, R. J. Cogdell, and G. R. Fleming, “Two-dimensional electronic spectroscopy of the B800-B820 light-harvesting complex,” Proc. Natl. Acad. Sci. U.S.A. 103(34), 12672–12677 (2006).
[CrossRef] [PubMed]

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

K. Ohta, D. S. Larsen, M. Yang, and G. R. Fleming, “Influence of intramolecular vibrations in third-order, time-domain resonant spectroscopies. II. Numerical calculations,” J. Chem. Phys. 114(18), 8020–8039 (2001).
[CrossRef]

Gardiner, A. T.

D. Zigmantas, E. L. Read, T. Mancal, T. Brixner, A. T. Gardiner, R. J. Cogdell, and G. R. Fleming, “Two-dimensional electronic spectroscopy of the B800-B820 light-harvesting complex,” Proc. Natl. Acad. Sci. U.S.A. 103(34), 12672–12677 (2006).
[CrossRef] [PubMed]

Halpin, A.

Huse, N.

M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, “Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O,” Nature 434(7030), 199–202 (2005).
[CrossRef] [PubMed]

Hybl, J. D.

J. D. Hybl, A. Yu, D. A. Farrow, and D. M. Jonas, “Polar solvation dynamics in the femtosecond evolution of two-dimensional Fourier transform spectra,” J. Phys. Chem. A 106(34), 7651–7654 (2002).
[CrossRef]

J. D. Hybl, A. W. Albrecht, S. M. G. Faeder, and D. M. Jonas, “Two-dimensional electronic spectroscopy,” Chem. Phys. Lett. 297(3-4), 307–313 (1998).
[CrossRef]

Jonas, D. M.

D. A. Farrow, A. Yu, and D. M. Jonas, “Spectral relaxation in pump-probe transients,” J. Chem. Phys. 118(20), 9348–9356 (2003).
[CrossRef]

D. M. Jonas, “Two-dimensional femtosecond spectroscopy,” Annu. Rev. Phys. Chem. 54(1), 425–463 (2003).
[CrossRef] [PubMed]

J. D. Hybl, A. Yu, D. A. Farrow, and D. M. Jonas, “Polar solvation dynamics in the femtosecond evolution of two-dimensional Fourier transform spectra,” J. Phys. Chem. A 106(34), 7651–7654 (2002).
[CrossRef]

S. M. G. Faeder and D. M. Jonas, “Two-dimensional electronic correlation and relaxation spectra: Theory and model calculations,” J. Phys. Chem. A 103(49), 10489–10505 (1999).
[CrossRef]

J. D. Hybl, A. W. Albrecht, S. M. G. Faeder, and D. M. Jonas, “Two-dimensional electronic spectroscopy,” Chem. Phys. Lett. 297(3-4), 307–313 (1998).
[CrossRef]

Kwak, K.

J. B. Asbury, T. Steinel, K. Kwak, S. A. Corcelli, C. P. Lawrence, J. L. Skinner, and M. D. Fayer, “Dynamics of water probed with vibrational echo correlation spectroscopy,” J. Chem. Phys. 121(24), 12431–12446 (2004).
[CrossRef] [PubMed]

Larsen, D. S.

K. Ohta, D. S. Larsen, M. Yang, and G. R. Fleming, “Influence of intramolecular vibrations in third-order, time-domain resonant spectroscopies. II. Numerical calculations,” J. Chem. Phys. 114(18), 8020–8039 (2001).
[CrossRef]

Lawrence, C. P.

J. B. Asbury, T. Steinel, K. Kwak, S. A. Corcelli, C. P. Lawrence, J. L. Skinner, and M. D. Fayer, “Dynamics of water probed with vibrational echo correlation spectroscopy,” J. Chem. Phys. 121(24), 12431–12446 (2004).
[CrossRef] [PubMed]

Lazonder, K.

Lewis, K. L. M.

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. U.S.A. 104(36), 14197–14202 (2007).
[CrossRef] [PubMed]

Loparo, J. J.

J. J. Loparo, S. T. Roberts, and A. Tokmakoff, “Multidimensional infrared spectroscopy of water. I. Vibrational dynamics in two-dimensional IR line shapes,” J. Chem. Phys. 125, 194522 (2006).
[CrossRef] [PubMed]

Mancal, T.

D. Zigmantas, E. L. Read, T. Mancal, T. Brixner, A. T. Gardiner, R. J. Cogdell, and G. R. Fleming, “Two-dimensional electronic spectroscopy of the B800-B820 light-harvesting complex,” Proc. Natl. Acad. Sci. U.S.A. 103(34), 12672–12677 (2006).
[CrossRef] [PubMed]

Miller, R. J. D.

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]

M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, “Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O,” Nature 434(7030), 199–202 (2005).
[CrossRef] [PubMed]

Mukamel, S.

D. Abramavicius and S. Mukamel, “Disentangling multidimensional femtosecond spectra of excitons by pulse shaping with coherent control,” J. Chem. Phys . 120, 8373-8378 (2004).
[CrossRef] [PubMed]

Myers, J. A.

Nibbering, E. T. J.

M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, “Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O,” Nature 434(7030), 199–202 (2005).
[CrossRef] [PubMed]

Ogilvie, J. P.

Ohta, K.

K. Ohta, D. S. Larsen, M. Yang, and G. R. Fleming, “Influence of intramolecular vibrations in third-order, time-domain resonant spectroscopies. II. Numerical calculations,” J. Chem. Phys. 114(18), 8020–8039 (2001).
[CrossRef]

Piel, J.

Prokhorenko, V. I.

Pshenichnikov, M. S.

Read, E. L.

D. Zigmantas, E. L. Read, T. Mancal, T. Brixner, A. T. Gardiner, R. J. Cogdell, and G. R. Fleming, “Two-dimensional electronic spectroscopy of the B800-B820 light-harvesting complex,” Proc. Natl. Acad. Sci. U.S.A. 103(34), 12672–12677 (2006).
[CrossRef] [PubMed]

Riedle, E.

Roberts, S. T.

J. J. Loparo, S. T. Roberts, and A. Tokmakoff, “Multidimensional infrared spectroscopy of water. I. Vibrational dynamics in two-dimensional IR line shapes,” J. Chem. Phys. 125, 194522 (2006).
[CrossRef] [PubMed]

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(5), 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. U.S.A. 104(36), 14197–14202 (2007).
[CrossRef] [PubMed]

Skinner, J. L.

J. B. Asbury, T. Steinel, K. Kwak, S. A. Corcelli, C. P. Lawrence, J. L. Skinner, and M. D. Fayer, “Dynamics of water probed with vibrational echo correlation spectroscopy,” J. Chem. Phys. 121(24), 12431–12446 (2004).
[CrossRef] [PubMed]

Steinel, T.

J. B. Asbury, T. Steinel, K. Kwak, S. A. Corcelli, C. P. Lawrence, J. L. Skinner, and M. D. Fayer, “Dynamics of water probed with vibrational echo correlation spectroscopy,” J. Chem. Phys. 121(24), 12431–12446 (2004).
[CrossRef] [PubMed]

Stenger, J.

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

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. U.S.A. 104(36), 14197–14202 (2007).
[CrossRef] [PubMed]

Tekavec, P. F.

Tokmakoff, A.

J. J. Loparo, S. T. Roberts, and A. Tokmakoff, “Multidimensional infrared spectroscopy of water. I. Vibrational dynamics in two-dimensional IR line shapes,” J. Chem. Phys. 125, 194522 (2006).
[CrossRef] [PubMed]

Vaswani, H. M.

T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005).
[CrossRef] [PubMed]

Wiersma, D. A.

Wilhelm, T.

Yang, M.

K. Ohta, D. S. Larsen, M. Yang, and G. R. Fleming, “Influence of intramolecular vibrations in third-order, time-domain resonant spectroscopies. II. Numerical calculations,” J. Chem. Phys. 114(18), 8020–8039 (2001).
[CrossRef]

Yu, A.

D. A. Farrow, A. Yu, and D. M. Jonas, “Spectral relaxation in pump-probe transients,” J. Chem. Phys. 118(20), 9348–9356 (2003).
[CrossRef]

J. D. Hybl, A. Yu, D. A. Farrow, and D. M. Jonas, “Polar solvation dynamics in the femtosecond evolution of two-dimensional Fourier transform spectra,” J. Phys. Chem. A 106(34), 7651–7654 (2002).
[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(5), 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. U.S.A. 104(36), 14197–14202 (2007).
[CrossRef] [PubMed]

Zigmantas, D.

D. Zigmantas, E. L. Read, T. Mancal, T. Brixner, A. T. Gardiner, R. J. Cogdell, and G. R. Fleming, “Two-dimensional electronic spectroscopy of the B800-B820 light-harvesting complex,” Proc. Natl. Acad. Sci. U.S.A. 103(34), 12672–12677 (2006).
[CrossRef] [PubMed]

Annu. Rev. Phys. Chem. (1)

D. M. Jonas, “Two-dimensional femtosecond spectroscopy,” Annu. Rev. Phys. Chem. 54(1), 425–463 (2003).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

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J. Opt. Soc. Am. B (1)

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S. M. G. Faeder and D. M. Jonas, “Two-dimensional electronic correlation and relaxation spectra: Theory and model calculations,” J. Phys. Chem. A 103(49), 10489–10505 (1999).
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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(5), 748–761 (2009).
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Proc. Natl. Acad. Sci. U.S.A. (2)

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. U.S.A. 104(36), 14197–14202 (2007).
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Other (1)

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Figures (11)

Fig. 1
Fig. 1

Timing diagram for 2D Fourier transform optical spectroscopy.

Fig. 2
Fig. 2

Simulated spectra with transform-limited probe pulses and chirped pump pulses (top row: ϕ′′ = −1000 fs2, middle row: transform-limited, bottom row: ϕ′′ = + 1000 fs2) at different T delays (T = 0, 30, 60, 90, 120 fs from left to right). Contours are evenly spaced at 5% of the maximum. The color scale is chosen such that the background color is zero, while colors that are deeper blue or red are negative and positive respectively. The T = 0 transform-limited spectrum shows the locations at which the anti-diagonal widths are reported in Fig. 3.

Fig. 3
Fig. 3

Anti-diagonal peak width as a function of T for transform-limited pulses (left), positively-chirped pump pulses (ϕ′′ = + 1000 fs2) (middle) and negatively-chirped pump pulses (ϕ′′ = −1000 fs2) (right). The black line corresponds to the width at the center of the spectrum, while the red and blue lines correspond to widths on the red and blue sides of the spectrum at positions indicated in Fig. 2.

Fig. 4
Fig. 4

Simulated spectra with transform-limited probe pulses and pump pulses with different amounts of chirp (ϕ′′ = −1000 fs2, −500 fs2, 0 fs2, + 500 fs2, + 1000 fs2, left to right) at T = 0 fs. Contours are evenly spaced at 5% of the maximum. The color scale is chosen such that the background color is zero, while colors that are deeper blue or red are negative and positive respectively.

Fig. 5
Fig. 5

Simulated spectra with transform-limited pump pulses and chirped probe pulses (top row: ϕ′′ = + 1000 fs2, bottom row: ϕ′′ = −1000 fs2) at different T delays (T = 0, 30, 60, 90, 120 fs from left to right). Contours are evenly spaced at 5% of the maximum. The color scale is chosen such that the background color is zero, while colors that are deeper blue or red are negative and positive respectively.

Fig. 6
Fig. 6

Simulated spectra with both pump and probe pulses chirped (top row: ϕ′′ = + 1000 fs2, bottom row: ϕ′′ = −1000 fs2) at different T delays (T = 0, 30, 60, 90, 120 fs from left to right). Contours are evenly spaced at 5% of the maximum. The color scale is chosen such that the background color is zero, while colors that are deeper blue or red are negative and positive respectively.

Fig. 7
Fig. 7

Experimental spectra with transform-limited probe pulses and chirped pump pulses (top row: ϕ′′ = −1000 fs2, middle row: transform limited, bottom row: ϕ′′ = + 1000 fs2) at different T delays (T = 0, 30, 60, 90, 120 fs from left to right). Contours are plotted at intervals of 5% of the maximum for levels above 15%. The color scale is chosen such that the background color is zero, while colors that are deeper blue or red are negative and positive respectively.

Fig. 8
Fig. 8

Experimental data with transform-limited pump and probe pulses chirped by 1 inch of fused silica (ϕ′′ = 2400 fs2) for different waiting times (T=0, 30, 60, 90, 120 fs from left to right). Contours are plotted at intervals of 5% of the maximum for levels above 15%.

Fig. 9
Fig. 9

Experimental data with both pump and probe pulses chirped equally by 1 inch of fused silica (ϕ′′ = 2400 fs2) for different waiting times (T=0, 30, 60, 90, 120 fs from left to right). Contours are plotted at intervals of 5% of the maximum for levels above 15%.

Fig. 10
Fig. 10

a): Schematic describing the origin of the distortions that occur in 2D spectra when the pump pulses are positively chirped and the probe pulse is transform-limited: the relaxation time for the red (Tred) and blue (Tblue) components are unequal, leading to broader anti-diagonal widths at low frequency (since Tblue < Tred). b): When the pump pulses are transform-limited and the probe is positively chirped the opposite case arises (Tblue > Tred), leading to broader anti-diagonal widths at high frequency. When negative chirps are used the opposite trends to those depicted here are seen.

Fig. 11
Fig. 11

Simulated spectra with for fast spectral relaxation (τg = 50 fs) at different T delays (T = 0, 15, 30, 45, 100 fs from left to right). Both pump and probe pulses are chirped (ϕ′′ = + 1000 fs2). Contours are evenly spaced at 5% of the maximum. The color scale is chosen such that the background color is zero, while colors that are deeper blue or red are negative and positive respectively.

Equations (6)

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E j ( t ) = A ( t t j ) e i ω j ( t t j ) + i ϕ j ( t ) + c . c
ϕ ( ω ) = ϕ ( ω 0 ) + ϕ ( ω ω 0 ) + 1 2 ϕ ( ω ω 0 ) 2 + ...
P ( 3 ) ( t , T , τ ) = 0 0 0 S ( 3 ) ( τ 1 , τ 2 , τ 3 ) E 1 * ( t t 1 τ 1 ) E 2 ( t t 2 τ 2 ) E 3 ( t t 3 τ 3 ) d τ 1 d τ 2 d τ 3 + c . c
S 2 D ( ω t , T , ω τ ) Re ( i ω t P ( 3 ) ( ω t , T , ω τ ) E 3 * ( ω t ) )
M ( t ) = exp ( t 2 τ g 2 )
g ( t ) = i λ 0 t M ( t 1 ) d t 1 + Δ 2 0 t 0 t 1 M ( t 2 ) d t 2 d t 1

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