Abstract

In many potential applications of two-dimensional (2D) electronic spectroscopy the excitation energies per pulse are strictly limited, while the samples are strongly scattering. We demonstrate a technique, based on double-modulation of incident laser beams with mechanical choppers, which can be implemented in almost any non-collinear four wave mixing scheme including 2D spectroscopy setup. The technique virtually eliminates artifacts or “ghost” signals in 2D spectra, which arise due to scattering and accumulation of long-lived species. To illustrate the advantages of the technique, we show a comparison of porphyrin J-aggregate 2D spectra obtained with different methods following by discussion.

© 2011 OSA

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  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]
  2. N. S. Ginsberg, Y. C. Cheng, and G. R. Fleming, “Two-dimensional electronic spectroscopy of molecular aggregates,” Acc. Chem. Res. 42(9), 1352–1363 (2009).
    [CrossRef] [PubMed]
  3. P. F. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, “Femtosecond phase-coherent two-dimensional spectroscopy,” Science 300(5625), 1553–1555 (2003).
    [CrossRef] [PubMed]
  4. E. M. Grumstrup, S.-H. Shim, M. A. Montgomery, N. H. Damrauer, and M. T. Zanni, “Facile collection of two-dimensional electronic spectra using femtosecond pulse-shaping technology,” Opt. Express 15(25), 16681–16689 (2007).
    [CrossRef] [PubMed]
  5. S. M. Gallagher 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]
  6. M. L. Cowan, J. P. Ogilvie, and R. J. D. Miller, “Two-dimensional spectroscopy using diffractive optics based phase-locked photon echoes,” Chem. Phys. Lett. 386(1-3), 184–189 (2004).
    [CrossRef]
  7. 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] [PubMed]
  8. J. C. Vaughan, T. Hornung, K. W. Stone, and K. A. Nelson, “Coherently controlled ultrafast four-wave mixing spectroscopy,” J. Phys. Chem. A 111(23), 4873–4883 (2007).
    [CrossRef] [PubMed]
  9. T. Brixner, I. V. Stiopkin, and G. R. Fleming, “Tunable two-dimensional femtosecond spectroscopy,” Opt. Lett. 29(8), 884–886 (2004).
    [CrossRef] [PubMed]
  10. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995).
    [CrossRef]
  11. V. I. Prokhorenko, A. Halpin, and R. J. D. Miller, “Coherently-controlled two-dimensional photon echo electronic spectroscopy,” Opt. Express 17(12), 9764–9779 (2009).
    [CrossRef] [PubMed]
  12. R. Rotomskis, R. Augulis, V. Snitka, R. Valiokas, and B. Liedberg, “Hierarchical structure of TPPS4 J-aggregates on substrate revealed by atomic force microscopy,” J. Phys. Chem. B 108(9), 2833–2838 (2004).
    [CrossRef]
  13. 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(14), 144510 (2009).
    [CrossRef] [PubMed]
  14. J. Kim, S. Mukamel, and G. D. Scholes, “Two-dimensional electronic double-quantum coherence spectroscopy,” Acc. Chem. Res. 42(9), 1375–1384 (2009).
    [CrossRef] [PubMed]
  15. A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
    [CrossRef] [PubMed]

2010 (1)

A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
[CrossRef] [PubMed]

2009 (4)

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

N. S. Ginsberg, Y. C. Cheng, and G. R. Fleming, “Two-dimensional electronic spectroscopy of molecular aggregates,” Acc. Chem. Res. 42(9), 1352–1363 (2009).
[CrossRef] [PubMed]

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(14), 144510 (2009).
[CrossRef] [PubMed]

J. Kim, S. Mukamel, and G. D. Scholes, “Two-dimensional electronic double-quantum coherence spectroscopy,” Acc. Chem. Res. 42(9), 1375–1384 (2009).
[CrossRef] [PubMed]

2007 (2)

2004 (4)

T. Brixner, I. V. Stiopkin, and G. R. Fleming, “Tunable two-dimensional femtosecond spectroscopy,” Opt. Lett. 29(8), 884–886 (2004).
[CrossRef] [PubMed]

R. Rotomskis, R. Augulis, V. Snitka, R. Valiokas, and B. Liedberg, “Hierarchical structure of TPPS4 J-aggregates on substrate revealed by atomic force microscopy,” J. Phys. Chem. B 108(9), 2833–2838 (2004).
[CrossRef]

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

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] [PubMed]

2003 (1)

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

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(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]

1995 (1)

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]

Augulis, R.

R. Rotomskis, R. Augulis, V. Snitka, R. Valiokas, and B. Liedberg, “Hierarchical structure of TPPS4 J-aggregates on substrate revealed by atomic force microscopy,” J. Phys. Chem. B 108(9), 2833–2838 (2004).
[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] [PubMed]

T. Brixner, I. V. Stiopkin, and G. R. Fleming, “Tunable two-dimensional femtosecond spectroscopy,” Opt. Lett. 29(8), 884–886 (2004).
[CrossRef] [PubMed]

Cheng, Y. C.

N. S. Ginsberg, Y. C. Cheng, and G. R. Fleming, “Two-dimensional electronic spectroscopy of molecular aggregates,” Acc. Chem. Res. 42(9), 1352–1363 (2009).
[CrossRef] [PubMed]

Chériaux, G.

Christensson, N.

A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
[CrossRef] [PubMed]

Cowan, M. L.

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

Damrauer, N. H.

Faeder, S. M. G.

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]

Fleming, G. R.

N. S. Ginsberg, Y. C. Cheng, and G. R. Fleming, “Two-dimensional electronic spectroscopy of molecular aggregates,” Acc. Chem. Res. 42(9), 1352–1363 (2009).
[CrossRef] [PubMed]

T. Brixner, I. V. Stiopkin, and G. R. Fleming, “Tunable two-dimensional femtosecond spectroscopy,” Opt. Lett. 29(8), 884–886 (2004).
[CrossRef] [PubMed]

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] [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(49), 10489–10505 (1999).
[CrossRef]

Ginsberg, N. S.

N. S. Ginsberg, Y. C. Cheng, and G. R. Fleming, “Two-dimensional electronic spectroscopy of molecular aggregates,” Acc. Chem. Res. 42(9), 1352–1363 (2009).
[CrossRef] [PubMed]

Grumstrup, E. M.

Gundogdu, K.

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(14), 144510 (2009).
[CrossRef] [PubMed]

Halpin, A.

Hauer, J.

A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
[CrossRef] [PubMed]

Hornung, T.

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

Hybl, J. D.

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]

Joffre, M.

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(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]

Kauffmann, H. F.

A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
[CrossRef] [PubMed]

Keusters, D.

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

Kim, J.

J. Kim, S. Mukamel, and G. D. Scholes, “Two-dimensional electronic double-quantum coherence spectroscopy,” Acc. Chem. Res. 42(9), 1375–1384 (2009).
[CrossRef] [PubMed]

Lepetit, L.

Liedberg, B.

R. Rotomskis, R. Augulis, V. Snitka, R. Valiokas, and B. Liedberg, “Hierarchical structure of TPPS4 J-aggregates on substrate revealed by atomic force microscopy,” J. Phys. Chem. B 108(9), 2833–2838 (2004).
[CrossRef]

Mancal, T.

A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
[CrossRef] [PubMed]

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] [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(12), 9764–9779 (2009).
[CrossRef] [PubMed]

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

Milota, F.

A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
[CrossRef] [PubMed]

Montgomery, M. A.

Mukamel, S.

J. Kim, S. Mukamel, and G. D. Scholes, “Two-dimensional electronic double-quantum coherence spectroscopy,” Acc. Chem. Res. 42(9), 1375–1384 (2009).
[CrossRef] [PubMed]

Nelson, K. A.

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(14), 144510 (2009).
[CrossRef] [PubMed]

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

Nemeth, A.

A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
[CrossRef] [PubMed]

Ogilvie, J. P.

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

Prokhorenko, V. I.

Pullerits, T.

A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
[CrossRef] [PubMed]

Rotomskis, R.

R. Rotomskis, R. Augulis, V. Snitka, R. Valiokas, and B. Liedberg, “Hierarchical structure of TPPS4 J-aggregates on substrate revealed by atomic force microscopy,” J. Phys. Chem. B 108(9), 2833–2838 (2004).
[CrossRef]

Scholes, G. D.

J. Kim, S. Mukamel, and G. D. Scholes, “Two-dimensional electronic double-quantum coherence spectroscopy,” Acc. Chem. Res. 42(9), 1375–1384 (2009).
[CrossRef] [PubMed]

Shim, S.-H.

Snitka, V.

R. Rotomskis, R. Augulis, V. Snitka, R. Valiokas, and B. Liedberg, “Hierarchical structure of TPPS4 J-aggregates on substrate revealed by atomic force microscopy,” J. Phys. Chem. B 108(9), 2833–2838 (2004).
[CrossRef]

Sperling, J.

A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
[CrossRef] [PubMed]

Stiopkin, I. V.

T. Brixner, I. V. Stiopkin, and G. R. Fleming, “Tunable two-dimensional femtosecond spectroscopy,” Opt. Lett. 29(8), 884–886 (2004).
[CrossRef] [PubMed]

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] [PubMed]

Stone, K. W.

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(14), 144510 (2009).
[CrossRef] [PubMed]

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

Suzaki, Y.

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

Tian, P. F.

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

Turner, D. B.

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(14), 144510 (2009).
[CrossRef] [PubMed]

Valiokas, R.

R. Rotomskis, R. Augulis, V. Snitka, R. Valiokas, and B. Liedberg, “Hierarchical structure of TPPS4 J-aggregates on substrate revealed by atomic force microscopy,” J. Phys. Chem. B 108(9), 2833–2838 (2004).
[CrossRef]

Vaughan, J. C.

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

Warren, W. S.

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

Zanni, M. T.

Acc. Chem. Res. (2)

N. S. Ginsberg, Y. C. Cheng, and G. R. Fleming, “Two-dimensional electronic spectroscopy of molecular aggregates,” Acc. Chem. Res. 42(9), 1352–1363 (2009).
[CrossRef] [PubMed]

J. Kim, S. Mukamel, and G. D. Scholes, “Two-dimensional electronic double-quantum coherence spectroscopy,” Acc. Chem. Res. 42(9), 1375–1384 (2009).
[CrossRef] [PubMed]

Chem. Phys. Lett. (2)

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]

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

J. Chem. Phys. (3)

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] [PubMed]

A. Nemeth, F. Milota, T. Mančal, T. Pullerits, J. Sperling, J. Hauer, H. F. Kauffmann, and N. Christensson, “Double-quantum two-dimensional electronic spectroscopy of a three-level system: experiments and simulations,” J. Chem. Phys. 133(9), 094505 (2010).
[CrossRef] [PubMed]

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(14), 144510 (2009).
[CrossRef] [PubMed]

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

J. Phys. Chem. A (2)

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

S. M. Gallagher 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. Phys. Chem. B (1)

R. Rotomskis, R. Augulis, V. Snitka, R. Valiokas, and B. Liedberg, “Hierarchical structure of TPPS4 J-aggregates on substrate revealed by atomic force microscopy,” J. Phys. Chem. B 108(9), 2833–2838 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Science (1)

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

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Figures (3)

Fig. 1
Fig. 1

Schematics of the experimental setup (distances are not to scale). Two parallel beams of femtosecond laser pulses (1&2 and 3&4) are focused by a spherical mirror SM1 onto a transmission diffractive grating G. Only the first positive and negative diffractive orders are generated with high efficiency, the rest is blocked by a mask (not shown). The resulting four beams are directed to a spherical mirror SM2 and focused into the sample S. Beam 4 (LO) is attenuated by the neutral density filter F (OD = 3). The time delays of beams 1, 2, and 3 are finely adjusted by movable fused silica wedge pairs W1, W2, and W3, respectively. W1 and W2 are scanned during the measurement, while W3 is kept constant. Beams 1 and 2 are modulated by choppers C1 and C2, respectively. The emitted third order signal field and LO propagate in the same direction through the iris I, while beams 1, 2, and 3 are blocked. M1 and M2 are planar folding mirrors. Inset shows the timing diagram of the pulse sequence used.

Fig. 2
Fig. 2

Data acquisition and processing sequence (schematics). For clarity, all the data except of chart (f) is displayed for a single modulation case. (a) A strip of pixels of the CCD sensor (3-5 rows) is illuminated by interfering signal and LO beams. (b) Hardware binning is applied: groups of n CCD rows are shifted into the register and read-out resulting in single lines in the acquired data set (c). A spike rejection and a high-pass filters are applied to the columns of the acquired data set: (d) – a single column before filtering, (e) – the same column after filtering. (f) The view of the filtered data in the frequency domain (a double modulation case, see text for details). (g) An interferogram extracted by calculating the Fourier coefficients at the signal modulation frequency: f mod for the single modulation case, |f mod1-f mod2| and/or f mod1 + f mod2 for the double modulation case.

Fig. 3
Fig. 3

The illustration of scatter induced distortions of 2D spectrum of a scattering sample (TPPS4 J-aggregates) at t 2 = 20 fs, (a) 2D spectrum obtained directly from untreated data. (b) Spectrum extracted solely from scattering data measured with beam 3 blocked. (c) 2D spectrum obtained by subtracting the scattering signal (b) from the untreated data (a). (d) 2D spectrum obtained by the double modulation lock-in method. The measurement durations for obtaining spectra (c) and (d) are approximately the same.

Equations (1)

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I j = Re ( k N j , k e 2 π i f mod f read k + i φ ) .

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