Abstract

We demonstrate a “drop-in” modification of the pulse-shaped pump-probe geometry two-dimensional Fourier transform spectrometer that significantly improves its performance by making the measurement background-free. The modification uses a hybrid diffractive optic/pulse-shaping approach that combines the advantages of background-free detection with the precise timing and phase-cycling capabilities enabled by pulse-shaping. In addition, we present a simple new method for accurate phasing of optically heterodyned two-dimensional spectra. We demonstrate the high quality of data obtainable with this approach by reporting two-dimensional Fourier transform electronic spectra of chlorophyll a in glycerol/water at 77 K.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  36. S. H. Shim, 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]
  37. D. Keusters, H. S. Tan, W. S. Warren, “Role of pulse phase and direction in two-dimensional optical spectroscopy,” J. Phys. Chem. A 103(49), 10369–10380 (1999).
    [CrossRef]
  38. E. L. Read, G. S. Engel, T. R. Calhoun, T. Mancal, T. K. Ahn, R. E. Blankenship, G. R. Fleming, “Cross-peak-specific two-dimensional electronic spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 104(36), 14203–14208 (2007).
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    [CrossRef]
  41. J. P. Ogilvie, M. Plazanet, G. Dadusc, R. J. D. Miller, “Dynamics of ligand escape in myoglobin: Q-band transient absorption and four-wave mixing studies,” J. Phys. Chem. B 106(40), 10460–10467 (2002).
    [CrossRef]
  42. V. P. Singh, A. F. Fidler, B. S. Rolczynski, G. S. Engel, “Independent phasing of rephasing and non-rephasing 2D electronic spectra,” J. Chem. Phys. 139(8), 084201 (2013).
    [CrossRef] [PubMed]

2013 (5)

P. Tyagi, J. I. Saari, B. Walsh, A. Kabir, V. Crozatier, N. Forget, P. Kambhampati, “Two-color two-dimensional electronic spectroscopy using dual acousto-optic pulse shapers for complete amplitude, phase, and polarization control of femtosecond laser pulses,” J. Phys. Chem. A 117(29), 6264–6269 (2013).
[CrossRef] [PubMed]

W. Rock, Y. L. Li, P. Pagano, C. M. Cheatum, “2D IR spectroscopy using four-wave mixing, pulse shaping, and IR upconversion: a quantitative comparison,” J. Phys. Chem. A 117(29), 6073–6083 (2013).
[CrossRef] [PubMed]

V. P. Singh, A. F. Fidler, B. S. Rolczynski, G. S. Engel, “Independent phasing of rephasing and non-rephasing 2D electronic spectra,” J. Chem. Phys. 139(8), 084201 (2013).
[CrossRef] [PubMed]

F. Milota, C. N. Lincoln, J. Hauer, “Precise phasing of 2D-electronic spectra in a fully non-collinear phase-matching geometry,” Opt. Express 21(13), 15904–15911 (2013).
[CrossRef] [PubMed]

D. E. Wilcox, F. D. Fuller, J. P. Ogilvie, “Fast second-harmonic generation frequency-resolved optical gating using only a pulse shaper,” Opt. Lett. 38(16), 2980–2983 (2013).
[CrossRef] [PubMed]

2012 (3)

Z. Y. Zhang, K. L. Wells, E. W. J. Hyland, H. S. Tan, “Phase-cycling schemes for pump-probe beam geometry two-dimensional electronic spectroscopy,” Chem. Phys. Lett. 550, 156–161 (2012).
[CrossRef]

J. M. Anna, E. E. Ostroumov, K. Maghlaoui, J. Barber, G. D. Scholes, “Two-dimensional electronic spectroscopy reveals ultrafast downhill energy transfer in photosystem I trimers of the cyanobacterium Thermosynechococcus elongatus,” J. Phys. Chem. Lett. 3(24), 3677–3684 (2012).
[CrossRef]

K. L. M. Lewis, J. P. Ogilvie, “Probing photosynthetic energy and charge transfer with two-dimensional electronic spectroscopy,” J. Phys. Chem. Lett. 3(4), 503–510 (2012).
[CrossRef]

2011 (1)

2010 (3)

P. F. Tekavec, J. A. Myers, K. L. M. Lewis, F. D. Fuller, J. P. Ogilvie, “Effects of chirp on two-dimensional Fourier transform electronic spectra,” Opt. Express 18(11), 11015–11024 (2010).
[CrossRef] [PubMed]

N. Christensson, F. Milota, A. Nemeth, I. Pugliesi, E. Riedle, J. Sperling, T. Pullerits, H. F. Kauffmann, J. Hauer, “Electronic double-quantum coherences and their impact on ultrafast spectroscopy: the example of β-carotene,” J. Phys. Chem. Lett. 1(23), 3366–3370 (2010).
[CrossRef] [PubMed]

E. Harel, A. F. Fidler, G. S. Engel, “Real-time mapping of electronic structure with single-shot two-dimensional electronic spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(38), 16444–16447 (2010).
[CrossRef] [PubMed]

2009 (5)

S. H. Shim, 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]

V. I. Prokhorenko, A. Halpin, R. J. D. Miller, “Coherently-controlled two-dimensional photon echo electronic spectroscopy,” Opt. Express 17(12), 9764–9779 (2009).
[CrossRef] [PubMed]

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

K. W. Stone, D. B. Turner, K. Gundogdu, S. T. Cundiff, K. A. Nelson, “Exciton-exciton correlations revealed by two-quantum, two-dimensional Fourier transform optical spectroscopy,” Acc. Chem. Res. 42(9), 1452–1461 (2009).
[CrossRef] [PubMed]

K. W. Stone, K. Gundogdu, D. B. Turner, X. Q. Li, S. T. Cundiff, K. A. Nelson, “Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells,” Science 324(5931), 1169–1173 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (5)

E. M. Grumstrup, S. H. Shim, M. A. Montgomery, N. H. Damrauer, M. T. Zanni, “Facile collection of two-dimensional electronic spectra using femtosecond pulse-shaping technology,” Opt. Express 15(25), 16681–16689 (2007).
[CrossRef] [PubMed]

E. L. Read, G. S. Engel, T. R. Calhoun, T. Mancal, T. K. Ahn, R. E. Blankenship, G. R. Fleming, “Cross-peak-specific two-dimensional electronic spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 104(36), 14203–14208 (2007).
[CrossRef] [PubMed]

S. H. Shim, D. B. Strasfeld, Y. L. Ling, 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]

J. C. Vaughan, T. Hornung, K. W. Stone, K. A. Nelson, “Coherently controlled ultrafast four-wave mixing spectroscopy,” J. Phys. Chem. A 111(23), 4873–4883 (2007).
[CrossRef] [PubMed]

P. F. Tekavec, G. A. Lott, A. H. Marcus, “Fluorescence-detected two-dimensional electronic coherence spectroscopy by acousto-optic phase modulation,” J. Chem. Phys. 127(21), 214307 (2007).
[CrossRef] [PubMed]

2005 (1)

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

2004 (2)

M. L. Cowan, J. P. Ogilvie, R. J. D. Miller, “Two-dimensional spectroscopy using diffractive optics based phased-locked photon echoes,” Chem. Phys. Lett. 386(1-3), 184–189 (2004).
[CrossRef]

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

2003 (2)

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

P. F. Tian, D. Keusters, Y. Suzaki, W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science 300(5625), 1553–1555 (2003).
[CrossRef] [PubMed]

2002 (2)

J. D. Hybl, A. Yu, D. A. Farrow, 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. P. Ogilvie, M. Plazanet, G. Dadusc, R. J. D. Miller, “Dynamics of ligand escape in myoglobin: Q-band transient absorption and four-wave mixing studies,” J. Phys. Chem. B 106(40), 10460–10467 (2002).
[CrossRef]

2000 (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[CrossRef]

1999 (2)

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

D. Keusters, H. S. Tan, W. S. Warren, “Role of pulse phase and direction in two-dimensional optical spectroscopy,” J. Phys. Chem. A 103(49), 10369–10380 (1999).
[CrossRef]

1998 (2)

G. D. Goodno, G. Dadusc, R. J. D. Miller, “Ultrafast heterodyne-detected transient-grating spectroscopy using diffractive optics,” J. Opt. Soc. Am. B 15(6), 1791–1794 (1998).
[CrossRef]

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

1997 (2)

1995 (1)

1994 (1)

1979 (1)

M. D. Levenson, G. L. Eesley, “Polarization selective optical heterodyne-detection for dramatically improved sensitivity in laser spectroscopy,” Appl. Phys. 19(1), 1–17 (1979).
[CrossRef]

Ahn, T. K.

E. L. Read, G. S. Engel, T. R. Calhoun, T. Mancal, T. K. Ahn, R. E. Blankenship, G. R. Fleming, “Cross-peak-specific two-dimensional electronic spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 104(36), 14203–14208 (2007).
[CrossRef] [PubMed]

Albrecht, A. W.

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

Anna, J. M.

J. M. Anna, E. E. Ostroumov, K. Maghlaoui, J. Barber, G. D. Scholes, “Two-dimensional electronic spectroscopy reveals ultrafast downhill energy transfer in photosystem I trimers of the cyanobacterium Thermosynechococcus elongatus,” J. Phys. Chem. Lett. 3(24), 3677–3684 (2012).
[CrossRef]

Augulis, R.

Barber, J.

J. M. Anna, E. E. Ostroumov, K. Maghlaoui, J. Barber, G. D. Scholes, “Two-dimensional electronic spectroscopy reveals ultrafast downhill energy transfer in photosystem I trimers of the cyanobacterium Thermosynechococcus elongatus,” J. Phys. Chem. Lett. 3(24), 3677–3684 (2012).
[CrossRef]

Blankenship, R. E.

E. L. Read, G. S. Engel, T. R. Calhoun, T. Mancal, T. K. Ahn, R. E. Blankenship, G. R. Fleming, “Cross-peak-specific two-dimensional electronic spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 104(36), 14203–14208 (2007).
[CrossRef] [PubMed]

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

Brixner, T.

U. Selig, F. Langhojer, F. Dimler, T. Löhrig, C. Schwarz, B. Gieseking, T. Brixner, “Inherently phase-stable coherent two-dimensional spectroscopy using only conventional optics,” Opt. Lett. 33(23), 2851–2853 (2008).
[CrossRef] [PubMed]

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

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

Calhoun, T. R.

E. L. Read, G. S. Engel, T. R. Calhoun, T. Mancal, T. K. Ahn, R. E. Blankenship, G. R. Fleming, “Cross-peak-specific two-dimensional electronic spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 104(36), 14203–14208 (2007).
[CrossRef] [PubMed]

Cheatum, C. M.

W. Rock, Y. L. Li, P. Pagano, C. M. Cheatum, “2D IR spectroscopy using four-wave mixing, pulse shaping, and IR upconversion: a quantitative comparison,” J. Phys. Chem. A 117(29), 6073–6083 (2013).
[CrossRef] [PubMed]

Cheriaux, G.

Cho, M.

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

Christensson, N.

N. Christensson, F. Milota, A. Nemeth, I. Pugliesi, E. Riedle, J. Sperling, T. Pullerits, H. F. Kauffmann, J. Hauer, “Electronic double-quantum coherences and their impact on ultrafast spectroscopy: the example of β-carotene,” J. Phys. Chem. Lett. 1(23), 3366–3370 (2010).
[CrossRef] [PubMed]

Cowan, M. L.

M. L. Cowan, J. P. Ogilvie, R. J. D. Miller, “Two-dimensional spectroscopy using diffractive optics based phased-locked photon echoes,” Chem. Phys. Lett. 386(1-3), 184–189 (2004).
[CrossRef]

Crozatier, V.

P. Tyagi, J. I. Saari, B. Walsh, A. Kabir, V. Crozatier, N. Forget, P. Kambhampati, “Two-color two-dimensional electronic spectroscopy using dual acousto-optic pulse shapers for complete amplitude, phase, and polarization control of femtosecond laser pulses,” J. Phys. Chem. A 117(29), 6264–6269 (2013).
[CrossRef] [PubMed]

Cundiff, S. T.

K. W. Stone, K. Gundogdu, D. B. Turner, X. Q. Li, S. T. Cundiff, K. A. Nelson, “Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells,” Science 324(5931), 1169–1173 (2009).
[CrossRef] [PubMed]

K. W. Stone, D. B. Turner, K. Gundogdu, S. T. Cundiff, K. A. Nelson, “Exciton-exciton correlations revealed by two-quantum, two-dimensional Fourier transform optical spectroscopy,” Acc. Chem. Res. 42(9), 1452–1461 (2009).
[CrossRef] [PubMed]

Dadusc, G.

J. P. Ogilvie, M. Plazanet, G. Dadusc, R. J. D. Miller, “Dynamics of ligand escape in myoglobin: Q-band transient absorption and four-wave mixing studies,” J. Phys. Chem. B 106(40), 10460–10467 (2002).
[CrossRef]

G. D. Goodno, G. Dadusc, R. J. D. Miller, “Ultrafast heterodyne-detected transient-grating spectroscopy using diffractive optics,” J. Opt. Soc. Am. B 15(6), 1791–1794 (1998).
[CrossRef]

Damrauer, N. H.

Dimler, F.

Eesley, G. L.

M. D. Levenson, G. L. Eesley, “Polarization selective optical heterodyne-detection for dramatically improved sensitivity in laser spectroscopy,” Appl. Phys. 19(1), 1–17 (1979).
[CrossRef]

Engel, G. S.

V. P. Singh, A. F. Fidler, B. S. Rolczynski, G. S. Engel, “Independent phasing of rephasing and non-rephasing 2D electronic spectra,” J. Chem. Phys. 139(8), 084201 (2013).
[CrossRef] [PubMed]

E. Harel, A. F. Fidler, G. S. Engel, “Real-time mapping of electronic structure with single-shot two-dimensional electronic spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(38), 16444–16447 (2010).
[CrossRef] [PubMed]

E. L. Read, G. S. Engel, T. R. Calhoun, T. Mancal, T. K. Ahn, R. E. Blankenship, G. R. Fleming, “Cross-peak-specific two-dimensional electronic spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 104(36), 14203–14208 (2007).
[CrossRef] [PubMed]

Faeder, S. M. G.

S. M. G. Faeder, 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, D. M. Jonas, “Two-dimensional electronic spectroscopy,” Chem. Phys. Lett. 297(3-4), 307–313 (1998).
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Zigmantas, D.

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K. W. Stone, D. B. Turner, K. Gundogdu, S. T. Cundiff, K. A. Nelson, “Exciton-exciton correlations revealed by two-quantum, two-dimensional Fourier transform optical spectroscopy,” Acc. Chem. Res. 42(9), 1452–1461 (2009).
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Annu. Rev. Phys. Chem. (1)

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Appl. Phys. (1)

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Chem. Phys. Lett. (3)

Z. Y. Zhang, K. L. Wells, E. W. J. Hyland, H. S. Tan, “Phase-cycling schemes for pump-probe beam geometry two-dimensional electronic spectroscopy,” Chem. Phys. Lett. 550, 156–161 (2012).
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J. Chem. Phys. (3)

T. Brixner, T. Mancal, I. V. Stiopkin, G. R. Fleming, “Phase-stabilized two-dimensional electronic spectroscopy,” J. Chem. Phys. 121(9), 4221–4236 (2004).
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V. P. Singh, A. F. Fidler, B. S. Rolczynski, G. S. Engel, “Independent phasing of rephasing and non-rephasing 2D electronic spectra,” J. Chem. Phys. 139(8), 084201 (2013).
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J. Opt. Soc. Am. B (3)

J. Phys. Chem. A (6)

W. Rock, Y. L. Li, P. Pagano, C. M. Cheatum, “2D IR spectroscopy using four-wave mixing, pulse shaping, and IR upconversion: a quantitative comparison,” J. Phys. Chem. A 117(29), 6073–6083 (2013).
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J. Phys. Chem. B (1)

J. P. Ogilvie, M. Plazanet, G. Dadusc, R. J. D. Miller, “Dynamics of ligand escape in myoglobin: Q-band transient absorption and four-wave mixing studies,” J. Phys. Chem. B 106(40), 10460–10467 (2002).
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J. Phys. Chem. Lett. (3)

K. L. M. Lewis, J. P. Ogilvie, “Probing photosynthetic energy and charge transfer with two-dimensional electronic spectroscopy,” J. Phys. Chem. Lett. 3(4), 503–510 (2012).
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N. Christensson, F. Milota, A. Nemeth, I. Pugliesi, E. Riedle, J. Sperling, T. Pullerits, H. F. Kauffmann, J. Hauer, “Electronic double-quantum coherences and their impact on ultrafast spectroscopy: the example of β-carotene,” J. Phys. Chem. Lett. 1(23), 3366–3370 (2010).
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J. M. Anna, E. E. Ostroumov, K. Maghlaoui, J. Barber, G. D. Scholes, “Two-dimensional electronic spectroscopy reveals ultrafast downhill energy transfer in photosystem I trimers of the cyanobacterium Thermosynechococcus elongatus,” J. Phys. Chem. Lett. 3(24), 3677–3684 (2012).
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Nature (1)

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Opt. Express (6)

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Phys. Chem. Chem. Phys. (1)

S. H. Shim, 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. (3)

E. Harel, A. F. Fidler, G. S. Engel, “Real-time mapping of electronic structure with single-shot two-dimensional electronic spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 107(38), 16444–16447 (2010).
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E. L. Read, G. S. Engel, T. R. Calhoun, T. Mancal, T. K. Ahn, R. E. Blankenship, G. R. Fleming, “Cross-peak-specific two-dimensional electronic spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 104(36), 14203–14208 (2007).
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S. H. Shim, D. B. Strasfeld, Y. L. Ling, 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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Rev. Sci. Instrum. (1)

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Science (2)

P. F. Tian, D. Keusters, Y. Suzaki, W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science 300(5625), 1553–1555 (2003).
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Figures (4)

Fig. 1
Fig. 1

Experimental Setup. (A) The diagram (not to scale) in lens notation of our interferometer. The round cornered dotted box indicates the “drop-in” addition to a traditional pulse-shaped pump-probe geometry 2DES setup. In our realization of the design, spherical mirrors are used with focal lengths f = 500 mm for the focusing mirror and f = 250 mm for the imaging mirror. (B) Four pulse timing diagrams are shown illustrating the origin of the signals emitted in the local oscillator direction. These diagrams communicate several things. The arrival time of the pulses is shown by their vertical displacement from the center of the diagram. The phase of the pump pulse is indicated by a color coordinated box and letter (x or y). The k-vector of the beam is indicated by the corner of the box on which it lies. Below the diagram is an equation giving the phase-cycling dependence of the signal.

Fig. 2
Fig. 2

Relative phase of the signal measured at t1 = 0 delay, calculated by spectral interferometry [39]. (A) We demonstrate that the standard deviation of the signal phase is nearly independent of frequency. (B) The phase stability measurement as a function of time for the central frequency. In this plot measurements were averaged for a minute to produce the points shown in green.

Fig. 3
Fig. 3

Demonstration of various 3rd order signals on Chlorophyll a in 50/50 (v/v) ethanol/glycerol at 77° K. The contour plots are drawn on a linear scale, with 1 contour above and below 0 omitted to suppress the noise floor. (A) The real rephasing spectrum with contours 100 contours over the range. (B) The real non-rephasing spectrum with 50 contours over the range. (C) A comparison of measurement to measurement signal variation between pump-probe and the phased transient-grating at the peak of the signal. There are three consecutive laser shots per measurement shown for the transient-grating signal (1 for each phase-cycle) and two consecutive laser shots (pump on and pump off) per measurement shown for the pump probe signal. The black line around which the signals vary represents the mean signal value in shared, but arbitrary units. The observed per measurement signal to noise ratio (S/N) (mean value divided by the standard deviation) is 32.2 for transient-grating and 1.3 for pump probe. Thus, factoring in the number of laser shots per measurement, we see a 19.5 fold S/N improvement at the peak of the signal.

Fig. 4
Fig. 4

Comparison of different phasing protocols. (A) Phased absorptive 2DES spectrum obtained from an exhaustive grid search with the quadratic phase model, and (B) the projection of the phased absorptive 2D spectrum to the spectrally resolved pump-probe. (C) Analytic phasing approach described in the text, showing the retrieved absorptive spectrum 2D spectrum, and (D) the projection of the phased absorptive 2D spectrum to the spectrally-resolved pump-probe signal. (E) The corrective phase applied under both models (solid line is the analytic model, dots for quadratic). (F) A slice of the objective function at the optimal quadratic phase (21 rad/fs2), which demonstrates the rugged nature of the objective function. The global optimum, corresponding to the phasing presented in sub-figures (A)-(E), can be seen at (0.9, 21).

Equations (3)

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[ S R S NR S TG ]=[ e i( y 1 x 1 ) e i( x 1 y 1 ) 1 e i( y 2 x 2 ) e i( x 2 y 2 ) 1 e i( y 3 x 3 ) e i( x 3 y 3 ) 1 ][ S 1 S 2 S 3 ]
[ { ( x 1 , y 1 ),( x 2 , y 2 ),( x 3 , y 3 ) }={ ( 0,0 ),( 0, 2π 3 ),( 0, 4π 3 ) } ]
min | | TG( ω ) |cos[ φ TG ( ω )+θ( ω ) ]αPP( ω ) | 2 2

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