Abstract

We introduce an advanced and flexible spectral focusing coherent anti-Stokes Raman scattering (CARS) microspectroscopy scheme based on the independent control of pump, Stokes, and probe frequencies offered by a pulse shaper. Adjusting the instantaneous bandwidth of 10 fs pulses in the focus of a microscope to different Raman linewidths assures high spectral resolution and signal intensities from the CH-bond to the fingerprint region. Experimental results are confirmed by simulations based on the CARS signal generation process. By delaying the probe, increased signal intensity and minimized nonresonant background are achieved while enabling time-dependent measurements. Contrast based on the difference of decoherence times is established and used to distinguish initially overlapping CH resonances of sunflower oil. Because of the transform-limited nature of the tailored probe, enhanced instantaneous nonlinear signals enable simultaneous multimodal imaging and molecule-specific CARS contrast as demonstrated on human skin tissue.

© 2016 Optical Society of America

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    [Crossref]
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  38. A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Full characterization of the third-order nonlinear susceptibility using a single-beam coherent anti-Stokes Raman scattering setup,” Opt. Lett. 37, 4239–4241 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  50. I. Pope, W. Langbein, P. Watson, and P. Borri, “Simultaneous hyperspectral differential-CARS, TPF and SHG microscopy with a single 5  fs Ti:Sa laser,” Opt. Express 21, 7096–7106 (2013).
    [Crossref]
  51. A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Elimination of two-photon excited fluorescence using a single-beam coherent anti-Stokes Raman scattering setup,” J. Raman Spectrosc. 44, 1379–1384 (2013).
    [Crossref]

2015 (3)

C. H. Camp and M. T. Cicerone, “Chemically sensitive bioimaging with coherent Raman scattering,” Nat. Photonics 9, 295–305 (2015).
[Crossref]

A. Wipfler, T. Buckup, and M. Motzkus, “Fast single-beam-CARS imaging scheme based on in silico optimization of excitation phases,” J. Raman Spectrosc. 46, 679–682 (2015).
[Crossref]

L. Brückner, T. Buckup, and M. Motzkus, “Enhancement of coherent anti-Stokes Raman signal via tailored probing in spectral focusing,” Opt. Lett. 40, 5204–5207 (2015).
[Crossref]

2014 (4)

J. Rehbinder, L. Brückner, A. Wipfler, T. Buckup, and M. Motzkus, “Multimodal nonlinear optical microscopy with shaped 10  fs pulses,” Opt. Express 22, 28790–28797 (2014).
[Crossref]

C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
[Crossref]

I. Pope, L. Payne, G. Zoriniants, E. Thomas, O. Williams, P. Watson, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman scattering microscopy of single nanodiamonds,” Nat. Nanotechnol. 9, 940–946 (2014).
[Crossref]

Y. Zhang, Y. R. Zhen, O. Neumann, J. K. Day, P. Nordlander, and N. J. Halas, “Coherent anti-Stokes Raman scattering with single-molecule sensitivity using a plasmonic Fano resonance,” Nat. Commun. 5, 4424 (2014).

2013 (3)

A. S. Duarte, J. Rehbinder, R. R. B. Correia, T. Buckup, and M. Motzkus, “Mapping impurity of single-walled carbon nanotubes in bulk samples with multiplex coherent anti-Stokes Raman microscopy,” Nano Lett. 13, 697–702 (2013).
[Crossref]

I. Pope, W. Langbein, P. Watson, and P. Borri, “Simultaneous hyperspectral differential-CARS, TPF and SHG microscopy with a single 5  fs Ti:Sa laser,” Opt. Express 21, 7096–7106 (2013).
[Crossref]

A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Elimination of two-photon excited fluorescence using a single-beam coherent anti-Stokes Raman scattering setup,” J. Raman Spectrosc. 44, 1379–1384 (2013).
[Crossref]

2012 (3)

A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Full characterization of the third-order nonlinear susceptibility using a single-beam coherent anti-Stokes Raman scattering setup,” Opt. Lett. 37, 4239–4241 (2012).
[Crossref]

C. Krafft, B. Dietzek, M. Schmitt, and J. Popp, “Raman and coherent anti-Stokes Raman scattering microspectroscopy for biomedical applications,” J. Biomed. Opt. 17, 040801 (2012).
[Crossref]

A. Wipfler, T. Buckup, and M. Motzkus, “Multiplexing single-beam coherent anti-Stokes Raman spectroscopy with heterodyne detection,” Appl. Phys. Lett. 100, 071102 (2012).
[Crossref]

2011 (2)

A. C. W. van Rhijn, M. Jurna, A. Jafarpour, J. L. Herek, and H. L. Offerhaus, “Phase-shaping strategies for coherent anti-Stokes Raman scattering,” J. Raman Spectrosc. 42, 1859–1863 (2011).
[Crossref]

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. W. Xu, S. Roy, J. R. Gord, and M. Dantus, “Binary phase shaping for selective single-beam CARS spectroscopy and imaging of gas-phase molecules,” J. Raman Spectrosc. 42, 393–398 (2011).
[Crossref]

2009 (4)

Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).
[Crossref]

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys. 130, 034302 (2009).
[Crossref]

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40, 809–816 (2009).
[Crossref]

A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, Y. W. Jia, J. P. Pezacki, and A. Stolow, “Optimally chirped multimodal CARS microscopy based on a single Ti:sapphire oscillator,” Opt. Express 17, 2984–2996 (2009).
[Crossref]

2008 (4)

I. Rocha-Mendoza, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman microspectroscopy using spectral focusing with glass dispersion,” Appl. Phys. Lett. 93, 201103 (2008).
[Crossref]

B. J. Sussman, R. Lausten, and A. Stolow, “Focusing of light following a 4-f pulse shaper: considerations for quantum control,” Phys. Rev. A 77, 043416 (2008).
[Crossref]

B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10, 681–691 (2008).
[Crossref]

Y. J. Lee and M. T. Cicerone, “Vibrational dephasing time imaging by time-resolved broadband coherent anti-Stokes Raman scattering microscopy,” Appl. Phys. Lett. 92, 041108 (2008).
[Crossref]

2007 (1)

B. von Vacano, L. Meyer, and M. Motzkus, “Rapid polymer blend imaging with quantitative broadband multiplex CARS microscopy,” J. Raman Spectrosc. 38, 916–926 (2007).
[Crossref]

2006 (3)

2005 (4)

H. Kano and H. Hamaguchi, “Vibrationally resonant imaging of a single living cell by supercontinuum-based multiplex coherent anti-Stokes Raman scattering microspectroscopy,” Opt. Express 13, 1322–1327 (2005).
[Crossref]

S. H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72, 041803 (2005).
[Crossref]

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Cote, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[Crossref]

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[Crossref]

2004 (1)

T. Hellerer, A. M. K. Enejder, and A. Zumbusch, “Spectral focusing: high spectral resolution spectroscopy with broad-bandwidth laser pulses,” Appl. Phys. Lett. 85, 25–27 (2004).
[Crossref]

2003 (4)

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90, 213902 (2003).
[Crossref]

E. Gershgoren, R. A. Bartels, J. T. Fourkas, R. Tobey, M. M. Murnane, and H. C. Kapteyn, “Simplified setup for high-resolution spectroscopy that uses ultrashort pulses,” Opt. Lett. 28, 361–363 (2003).
[Crossref]

A. N. Naumov and A. M. Zheltikov, “Frequency-time and time-space mappings with broadband and supercontinuum chirped pulses in coherent wave mixing and pump-probe techniques,” Appl. Phys. B 77, 369–376 (2003).
[Crossref]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherent anti-Stokes Raman spectroscopy in the fingerprint spectral region,” J. Chem. Phys. 118, 9208–9215 (2003).
[Crossref]

2002 (3)

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505–1507 (2002).
[Crossref]

J. X. Chen, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493–8498 (2002).
[Crossref]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418, 512–514 (2002).
[Crossref]

2001 (2)

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B 105, 1277–1280 (2001).
[Crossref]

J. X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26, 1341–1343 (2001).
[Crossref]

2000 (1)

A. M. Zheltikov, “Coherent anti-Stokes Raman scattering: from proof-of-the-principle experiments to femtosecond CARS and higher order wave-mixing generalizations,” J. Raman Spectrosc. 31, 653–667 (2000).
[Crossref]

1999 (1)

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[Crossref]

1996 (1)

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[Crossref]

1992 (1)

E. T. J. Nibbering, D. A. Wiersma, and K. Duppen, “Ultrafast nonlinear spectroscopy with chirped optical pulses,” Phys. Rev. Lett. 68, 514–517 (1992).
[Crossref]

1990 (2)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[Crossref]

H. Sadeghijorabchi, P. J. Hendra, R. H. Wilson, and P. S. Belton, “Determination of the total unsaturation in oils and margarines by Fourier-transform Raman-spectroscopy,” J. Am. Oil Chem. Soc. 67, 483–486 (1990).
[Crossref]

1980 (1)

1979 (1)

J. L. Oudar, R. W. Smith, and Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman-spectroscopy,” Appl. Phys. Lett. 34, 758–760 (1979).
[Crossref]

Bartels, R. A.

Belton, P. S.

H. Sadeghijorabchi, P. J. Hendra, R. H. Wilson, and P. S. Belton, “Determination of the total unsaturation in oils and margarines by Fourier-transform Raman-spectroscopy,” J. Am. Oil Chem. Soc. 67, 483–486 (1990).
[Crossref]

Book, L. D.

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505–1507 (2002).
[Crossref]

J. X. Chen, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493–8498 (2002).
[Crossref]

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B 105, 1277–1280 (2001).
[Crossref]

J. X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26, 1341–1343 (2001).
[Crossref]

Borri, P.

I. Pope, L. Payne, G. Zoriniants, E. Thomas, O. Williams, P. Watson, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman scattering microscopy of single nanodiamonds,” Nat. Nanotechnol. 9, 940–946 (2014).
[Crossref]

I. Pope, W. Langbein, P. Watson, and P. Borri, “Simultaneous hyperspectral differential-CARS, TPF and SHG microscopy with a single 5  fs Ti:Sa laser,” Opt. Express 21, 7096–7106 (2013).
[Crossref]

I. Rocha-Mendoza, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman microspectroscopy using spectral focusing with glass dispersion,” Appl. Phys. Lett. 93, 201103 (2008).
[Crossref]

Brückner, L.

Buckup, T.

L. Brückner, T. Buckup, and M. Motzkus, “Enhancement of coherent anti-Stokes Raman signal via tailored probing in spectral focusing,” Opt. Lett. 40, 5204–5207 (2015).
[Crossref]

A. Wipfler, T. Buckup, and M. Motzkus, “Fast single-beam-CARS imaging scheme based on in silico optimization of excitation phases,” J. Raman Spectrosc. 46, 679–682 (2015).
[Crossref]

J. Rehbinder, L. Brückner, A. Wipfler, T. Buckup, and M. Motzkus, “Multimodal nonlinear optical microscopy with shaped 10  fs pulses,” Opt. Express 22, 28790–28797 (2014).
[Crossref]

A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Elimination of two-photon excited fluorescence using a single-beam coherent anti-Stokes Raman scattering setup,” J. Raman Spectrosc. 44, 1379–1384 (2013).
[Crossref]

A. S. Duarte, J. Rehbinder, R. R. B. Correia, T. Buckup, and M. Motzkus, “Mapping impurity of single-walled carbon nanotubes in bulk samples with multiplex coherent anti-Stokes Raman microscopy,” Nano Lett. 13, 697–702 (2013).
[Crossref]

A. Wipfler, T. Buckup, and M. Motzkus, “Multiplexing single-beam coherent anti-Stokes Raman spectroscopy with heterodyne detection,” Appl. Phys. Lett. 100, 071102 (2012).
[Crossref]

A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Full characterization of the third-order nonlinear susceptibility using a single-beam coherent anti-Stokes Raman scattering setup,” Opt. Lett. 37, 4239–4241 (2012).
[Crossref]

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40, 809–816 (2009).
[Crossref]

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C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
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C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
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A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Elimination of two-photon excited fluorescence using a single-beam coherent anti-Stokes Raman scattering setup,” J. Raman Spectrosc. 44, 1379–1384 (2013).
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E. T. J. Nibbering, D. A. Wiersma, and K. Duppen, “Ultrafast nonlinear spectroscopy with chirped optical pulses,” Phys. Rev. Lett. 68, 514–517 (1992).
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A. C. W. van Rhijn, M. Jurna, A. Jafarpour, J. L. Herek, and H. L. Offerhaus, “Phase-shaping strategies for coherent anti-Stokes Raman scattering,” J. Raman Spectrosc. 42, 1859–1863 (2011).
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D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90, 213902 (2003).
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Pestov, D.

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Pope, I.

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C. Krafft, B. Dietzek, M. Schmitt, and J. Popp, “Raman and coherent anti-Stokes Raman scattering microspectroscopy for biomedical applications,” J. Biomed. Opt. 17, 040801 (2012).
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E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31, 241–243 (2006).
[Crossref]

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Cote, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[Crossref]

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C. L. Evans, E. O. Potma, M. Puoris’haag, D. Cote, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[Crossref]

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J. Rehbinder, L. Brückner, A. Wipfler, T. Buckup, and M. Motzkus, “Multimodal nonlinear optical microscopy with shaped 10  fs pulses,” Opt. Express 22, 28790–28797 (2014).
[Crossref]

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[Crossref]

A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Elimination of two-photon excited fluorescence using a single-beam coherent anti-Stokes Raman scattering setup,” J. Raman Spectrosc. 44, 1379–1384 (2013).
[Crossref]

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[Crossref]

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C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
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Rocha-Mendoza, I.

I. Rocha-Mendoza, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman microspectroscopy using spectral focusing with glass dispersion,” Appl. Phys. Lett. 93, 201103 (2008).
[Crossref]

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P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. W. Xu, S. Roy, J. R. Gord, and M. Dantus, “Binary phase shaping for selective single-beam CARS spectroscopy and imaging of gas-phase molecules,” J. Raman Spectrosc. 42, 393–398 (2011).
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Schmitt, M.

C. Krafft, B. Dietzek, M. Schmitt, and J. Popp, “Raman and coherent anti-Stokes Raman scattering microspectroscopy for biomedical applications,” J. Biomed. Opt. 17, 040801 (2012).
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J. L. Oudar, R. W. Smith, and Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman-spectroscopy,” Appl. Phys. Lett. 34, 758–760 (1979).
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N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherent anti-Stokes Raman spectroscopy in the fingerprint spectral region,” J. Chem. Phys. 118, 9208–9215 (2003).
[Crossref]

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90, 213902 (2003).
[Crossref]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418, 512–514 (2002).
[Crossref]

Smith, R. W.

J. L. Oudar, R. W. Smith, and Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman-spectroscopy,” Appl. Phys. Lett. 34, 758–760 (1979).
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W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
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B. J. Sussman, R. Lausten, and A. Stolow, “Focusing of light following a 4-f pulse shaper: considerations for quantum control,” Phys. Rev. A 77, 043416 (2008).
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I. Pope, L. Payne, G. Zoriniants, E. Thomas, O. Williams, P. Watson, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman scattering microscopy of single nanodiamonds,” Nat. Nanotechnol. 9, 940–946 (2014).
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A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505–1507 (2002).
[Crossref]

J. X. Chen, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493–8498 (2002).
[Crossref]

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B 105, 1277–1280 (2001).
[Crossref]

von Vacano, B.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40, 809–816 (2009).
[Crossref]

B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10, 681–691 (2008).
[Crossref]

B. von Vacano, L. Meyer, and M. Motzkus, “Rapid polymer blend imaging with quantitative broadband multiplex CARS microscopy,” J. Raman Spectrosc. 38, 916–926 (2007).
[Crossref]

B. von Vacano, W. Wohlleben, and M. Motzkus, “Single-beam CARS spectroscopy applied to low-wavenumber vibrational modes,” J. Raman Spectrosc. 37, 404–410 (2006).
[Crossref]

B. von Vacano, T. Buckup, and M. Motzkus, “Highly sensitive single-beam heterodyne coherent anti-Stokes Raman scattering,” Opt. Lett. 31, 2495–2497 (2006).
[Crossref]

Walker, A. R. H.

C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
[Crossref]

Watson, P.

I. Pope, L. Payne, G. Zoriniants, E. Thomas, O. Williams, P. Watson, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman scattering microscopy of single nanodiamonds,” Nat. Nanotechnol. 9, 940–946 (2014).
[Crossref]

I. Pope, W. Langbein, P. Watson, and P. Borri, “Simultaneous hyperspectral differential-CARS, TPF and SHG microscopy with a single 5  fs Ti:Sa laser,” Opt. Express 21, 7096–7106 (2013).
[Crossref]

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[Crossref]

Wefers, M. M.

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[Crossref]

Wiersma, D. A.

E. T. J. Nibbering, D. A. Wiersma, and K. Duppen, “Ultrafast nonlinear spectroscopy with chirped optical pulses,” Phys. Rev. Lett. 68, 514–517 (1992).
[Crossref]

Williams, O.

I. Pope, L. Payne, G. Zoriniants, E. Thomas, O. Williams, P. Watson, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman scattering microscopy of single nanodiamonds,” Nat. Nanotechnol. 9, 940–946 (2014).
[Crossref]

Wilson, R. H.

H. Sadeghijorabchi, P. J. Hendra, R. H. Wilson, and P. S. Belton, “Determination of the total unsaturation in oils and margarines by Fourier-transform Raman-spectroscopy,” J. Am. Oil Chem. Soc. 67, 483–486 (1990).
[Crossref]

Wipfler, A.

A. Wipfler, T. Buckup, and M. Motzkus, “Fast single-beam-CARS imaging scheme based on in silico optimization of excitation phases,” J. Raman Spectrosc. 46, 679–682 (2015).
[Crossref]

J. Rehbinder, L. Brückner, A. Wipfler, T. Buckup, and M. Motzkus, “Multimodal nonlinear optical microscopy with shaped 10  fs pulses,” Opt. Express 22, 28790–28797 (2014).
[Crossref]

A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Elimination of two-photon excited fluorescence using a single-beam coherent anti-Stokes Raman scattering setup,” J. Raman Spectrosc. 44, 1379–1384 (2013).
[Crossref]

A. Wipfler, T. Buckup, and M. Motzkus, “Multiplexing single-beam coherent anti-Stokes Raman spectroscopy with heterodyne detection,” Appl. Phys. Lett. 100, 071102 (2012).
[Crossref]

A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Full characterization of the third-order nonlinear susceptibility using a single-beam coherent anti-Stokes Raman scattering setup,” Opt. Lett. 37, 4239–4241 (2012).
[Crossref]

Wohlleben, W.

B. von Vacano, W. Wohlleben, and M. Motzkus, “Single-beam CARS spectroscopy applied to low-wavenumber vibrational modes,” J. Raman Spectrosc. 37, 404–410 (2006).
[Crossref]

Wrzesinski, P. J.

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. W. Xu, S. Roy, J. R. Gord, and M. Dantus, “Binary phase shaping for selective single-beam CARS spectroscopy and imaging of gas-phase molecules,” J. Raman Spectrosc. 42, 393–398 (2011).
[Crossref]

Xie, X. S.

E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31, 241–243 (2006).
[Crossref]

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Cote, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[Crossref]

J. X. Chen, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493–8498 (2002).
[Crossref]

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505–1507 (2002).
[Crossref]

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B 105, 1277–1280 (2001).
[Crossref]

J. X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26, 1341–1343 (2001).
[Crossref]

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[Crossref]

Xu, B. W.

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. W. Xu, S. Roy, J. R. Gord, and M. Dantus, “Binary phase shaping for selective single-beam CARS spectroscopy and imaging of gas-phase molecules,” J. Raman Spectrosc. 42, 393–398 (2011).
[Crossref]

Zhang, Y.

Y. Zhang, Y. R. Zhen, O. Neumann, J. K. Day, P. Nordlander, and N. J. Halas, “Coherent anti-Stokes Raman scattering with single-molecule sensitivity using a plasmonic Fano resonance,” Nat. Commun. 5, 4424 (2014).

Zheltikov, A. M.

A. N. Naumov and A. M. Zheltikov, “Frequency-time and time-space mappings with broadband and supercontinuum chirped pulses in coherent wave mixing and pump-probe techniques,” Appl. Phys. B 77, 369–376 (2003).
[Crossref]

A. M. Zheltikov, “Coherent anti-Stokes Raman scattering: from proof-of-the-principle experiments to femtosecond CARS and higher order wave-mixing generalizations,” J. Raman Spectrosc. 31, 653–667 (2000).
[Crossref]

Zhen, Y. R.

Y. Zhang, Y. R. Zhen, O. Neumann, J. K. Day, P. Nordlander, and N. J. Halas, “Coherent anti-Stokes Raman scattering with single-molecule sensitivity using a plasmonic Fano resonance,” Nat. Commun. 5, 4424 (2014).

Zoriniants, G.

I. Pope, L. Payne, G. Zoriniants, E. Thomas, O. Williams, P. Watson, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman scattering microscopy of single nanodiamonds,” Nat. Nanotechnol. 9, 940–946 (2014).
[Crossref]

Zumbusch, A.

T. Hellerer, A. M. K. Enejder, and A. Zumbusch, “Spectral focusing: high spectral resolution spectroscopy with broad-bandwidth laser pulses,” Appl. Phys. Lett. 85, 25–27 (2004).
[Crossref]

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[Crossref]

Annu. Rev. Phys. Chem. (1)

Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem. 60, 277–292 (2009).
[Crossref]

Appl. Phys. B (1)

A. N. Naumov and A. M. Zheltikov, “Frequency-time and time-space mappings with broadband and supercontinuum chirped pulses in coherent wave mixing and pump-probe techniques,” Appl. Phys. B 77, 369–376 (2003).
[Crossref]

Appl. Phys. Lett. (6)

A. Wipfler, T. Buckup, and M. Motzkus, “Multiplexing single-beam coherent anti-Stokes Raman spectroscopy with heterodyne detection,” Appl. Phys. Lett. 100, 071102 (2012).
[Crossref]

T. Hellerer, A. M. K. Enejder, and A. Zumbusch, “Spectral focusing: high spectral resolution spectroscopy with broad-bandwidth laser pulses,” Appl. Phys. Lett. 85, 25–27 (2004).
[Crossref]

I. Rocha-Mendoza, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman microspectroscopy using spectral focusing with glass dispersion,” Appl. Phys. Lett. 93, 201103 (2008).
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J. L. Oudar, R. W. Smith, and Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman-spectroscopy,” Appl. Phys. Lett. 34, 758–760 (1979).
[Crossref]

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505–1507 (2002).
[Crossref]

Y. J. Lee and M. T. Cicerone, “Vibrational dephasing time imaging by time-resolved broadband coherent anti-Stokes Raman scattering microscopy,” Appl. Phys. Lett. 92, 041108 (2008).
[Crossref]

IEEE J. Quantum Electron. (1)

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[Crossref]

J. Am. Oil Chem. Soc. (1)

H. Sadeghijorabchi, P. J. Hendra, R. H. Wilson, and P. S. Belton, “Determination of the total unsaturation in oils and margarines by Fourier-transform Raman-spectroscopy,” J. Am. Oil Chem. Soc. 67, 483–486 (1990).
[Crossref]

J. Biomed. Opt. (1)

C. Krafft, B. Dietzek, M. Schmitt, and J. Popp, “Raman and coherent anti-Stokes Raman scattering microspectroscopy for biomedical applications,” J. Biomed. Opt. 17, 040801 (2012).
[Crossref]

J. Chem. Phys. (2)

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys. 130, 034302 (2009).
[Crossref]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherent anti-Stokes Raman spectroscopy in the fingerprint spectral region,” J. Chem. Phys. 118, 9208–9215 (2003).
[Crossref]

J. Phys. Chem. B (2)

J. X. Chen, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493–8498 (2002).
[Crossref]

J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B 105, 1277–1280 (2001).
[Crossref]

J. Raman Spectrosc. (8)

B. von Vacano, W. Wohlleben, and M. Motzkus, “Single-beam CARS spectroscopy applied to low-wavenumber vibrational modes,” J. Raman Spectrosc. 37, 404–410 (2006).
[Crossref]

A. M. Zheltikov, “Coherent anti-Stokes Raman scattering: from proof-of-the-principle experiments to femtosecond CARS and higher order wave-mixing generalizations,” J. Raman Spectrosc. 31, 653–667 (2000).
[Crossref]

A. C. W. van Rhijn, M. Jurna, A. Jafarpour, J. L. Herek, and H. L. Offerhaus, “Phase-shaping strategies for coherent anti-Stokes Raman scattering,” J. Raman Spectrosc. 42, 1859–1863 (2011).
[Crossref]

B. von Vacano, L. Meyer, and M. Motzkus, “Rapid polymer blend imaging with quantitative broadband multiplex CARS microscopy,” J. Raman Spectrosc. 38, 916–926 (2007).
[Crossref]

A. Wipfler, T. Buckup, and M. Motzkus, “Fast single-beam-CARS imaging scheme based on in silico optimization of excitation phases,” J. Raman Spectrosc. 46, 679–682 (2015).
[Crossref]

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. W. Xu, S. Roy, J. R. Gord, and M. Dantus, “Binary phase shaping for selective single-beam CARS spectroscopy and imaging of gas-phase molecules,” J. Raman Spectrosc. 42, 393–398 (2011).
[Crossref]

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40, 809–816 (2009).
[Crossref]

A. Wipfler, J. Rehbinder, T. Buckup, and M. Motzkus, “Elimination of two-photon excited fluorescence using a single-beam coherent anti-Stokes Raman scattering setup,” J. Raman Spectrosc. 44, 1379–1384 (2013).
[Crossref]

Nano Lett. (1)

A. S. Duarte, J. Rehbinder, R. R. B. Correia, T. Buckup, and M. Motzkus, “Mapping impurity of single-walled carbon nanotubes in bulk samples with multiplex coherent anti-Stokes Raman microscopy,” Nano Lett. 13, 697–702 (2013).
[Crossref]

Nat. Commun. (1)

Y. Zhang, Y. R. Zhen, O. Neumann, J. K. Day, P. Nordlander, and N. J. Halas, “Coherent anti-Stokes Raman scattering with single-molecule sensitivity using a plasmonic Fano resonance,” Nat. Commun. 5, 4424 (2014).

Nat. Methods (1)

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[Crossref]

Nat. Nanotechnol. (1)

I. Pope, L. Payne, G. Zoriniants, E. Thomas, O. Williams, P. Watson, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman scattering microscopy of single nanodiamonds,” Nat. Nanotechnol. 9, 940–946 (2014).
[Crossref]

Nat. Photonics (2)

C. H. Camp and M. T. Cicerone, “Chemically sensitive bioimaging with coherent Raman scattering,” Nat. Photonics 9, 295–305 (2015).
[Crossref]

C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
[Crossref]

Nature (1)

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418, 512–514 (2002).
[Crossref]

Opt. Express (4)

Opt. Lett. (7)

Phys. Chem. Chem. Phys. (1)

B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10, 681–691 (2008).
[Crossref]

Phys. Rev. A (2)

S. H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72, 041803 (2005).
[Crossref]

B. J. Sussman, R. Lausten, and A. Stolow, “Focusing of light following a 4-f pulse shaper: considerations for quantum control,” Phys. Rev. A 77, 043416 (2008).
[Crossref]

Phys. Rev. Lett. (3)

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[Crossref]

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90, 213902 (2003).
[Crossref]

E. T. J. Nibbering, D. A. Wiersma, and K. Duppen, “Ultrafast nonlinear spectroscopy with chirped optical pulses,” Phys. Rev. Lett. 68, 514–517 (1992).
[Crossref]

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

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Cote, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[Crossref]

Science (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[Crossref]

Other (2)

C. Rulliere, Femtosecond Laser Pulses: Principles and Experiments, 2nd ed. (Springer, 2005), p. 357.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, 1988).

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Figures (10)

Fig. 1.
Fig. 1. General overview of the flexibility and the main modalities of tailored spectral focusing. (a) Equally chirped pump and Stokes frequencies lead to a constant instantaneous frequency difference (IFD) that drives a certain Raman mode at a frequency Ω . The spectral resolution can be controlled by the chirp of pump and Stokes and is represented by the bandwidth of the excitation Δ Ω IFD . (b) The IFD and therefore the addressed Raman mode can be chosen by changing the time delay of pump and Stokes. Pump/Stokes frequencies outside the overlapping region do not take part in the excitation process (gray box) and can be cut off with the pulse shaper by amplitude shaping. Continually scanning the time delay allows for recording CARS spectra. (c) By identifying frequencies acting solely as probe, independent control thereof enables line scans with temporal resolution as well as increased signal levels. (d) Because of the narrow excitation, signal generated by the probe (green), which lies in the region between pump and Stokes, or by the pump acting as probe (blue) can be spectrally separated. Thereby, a large part of the background is suppressed. Merging the information of (a)–(d) into a single picture provides a compact and comprehensive description of tailored spectral focusing (e.g., Figs. 4 and 9).
Fig. 2.
Fig. 2. Experimental single-beam CARS setup. ChM, chirped mirrors; G, gratings; CM, cylindrical mirrors; SLM, spatial light modulator; Pol., polarizer; MO, microscope objectives; IF, interference filter; FM, flip mirror; F, filters; CARS, SHG, and TPEF, photomultipliers with bandpass filters for multimodal imaging.
Fig. 3.
Fig. 3. (a) The third-order susceptibility contains a nonresonant electronic contribution (offset) and the vibrational resonances of the molecule. It is calculated from Eq. (3) with linewidths Γ of 15    cm 1 at 1000    cm 1 , 2000    cm 1 , and 2500    cm 1 . (b) The excitation probability for spectral focusing (red) is nonzero only at the chosen resonance Ω , while the transform-limited pulse (black) is nonspecific throughout the spectrum. The molecular response in (c) shows that only one specific molecular resonance is excited in spectral focusing. In the case of a transform-limited pulse, not only are all resonances excited simultaneously but so are all virtual levels within the width of the spectrum. This leads to an overwhelming nonresonant background.
Fig. 4.
Fig. 4. (a) and (b) show the blue-shifted spectral focusing CH stretching signal of acetonitrile as measured in the experiment. (c) depicts the laser spectrum with the applied phase functions for pump, Stokes, and probe regions as indicated at the right side of the figure. The distance of the parabolas determines the IFD, indicated as Ω. The time distribution of the frequencies is presented in (d). From the induced coherence, the shifted signal in (b) is constantly generated by the pump acting as a probe (blue) and the time-delayed probe frequencies (red). The integrated detector signal measured is shown by the corresponding signals in (a). The steep linear probe phase is cut off to better show the parabolic phase of pump and Stokes needed for spectral focusing.
Fig. 5.
Fig. 5. (a) The spectral focusing signal generated by the time-delayed probe is linearly dependent on the probe intensity measured in the focus and confirms that it is detached from the excitation process. (b) Because of space–time coupling, the probe intensity in the focus depends on the slope of the linear phase and therefore on the time delay. The probe delay is defined as the delay of the probe in relation to the end of the excitation.
Fig. 6.
Fig. 6. (a) Probe delay scan for different amounts of chirp measuring the CH stretching vibration of acetonitrile at 2942    cm 1 . The data is corrected for space–time coupling and normalized to the data at 1000    fs 2 . (b) Spectra of sunflower oil measured at different probe delays at a constant chirp of 5000    fs 2 . For better comparison, the spectra are normalized to the CH stretching vibration at 2850    cm 1 . At later time delays, the asymmetric olefinic =CH signal at 3015    cm 1 can be easily differentiated from the neighboring modes.
Fig. 7.
Fig. 7. Influence of the chirp rate on the measured linewidth. (a) Phase, time-frequency plot, and resulting instantaneous bandwidth for low ( Δ ω 1 , red) and significantly higher chirp ( Δ ω 2 , green). (b) Excitation process following from the phases in (a). The combination of the instantaneous bandwidths of pump and Stokes can lead to excitation within a range Δ Ω IFD [see Fig. 1(a)] around a selectable center frequency. In case No. 2 the IFD coincides with the resonance while in Nos. 1 and 3 the IFD is detuned away from the resonance by Δ Ω . (c) Spectral resolution increases with the chirp rate and approaches the natural linewidth depicted as a gray area.
Fig. 8.
Fig. 8. Comparison of the measured (red) and simulated (black) linewidths obtained for the CH stretching vibration of acetonitrile at 2942    cm 1 in dependence of the amount of chirp applied. The measured spectra for 3000    fs 2 and 9000    fs 2 are depicted in light and deep red, respectively. The inset shows the obtained FWHM of the lines in dependence of the chirp. The probe was delayed in all cases to 300 fs after the end of the excitation.
Fig. 9.
Fig. 9. (a) and (b) show the blue-shifted spectral focusing signal in the fingerprint region of toluene as measured in the experiment. (c) depicts the spectrum with the applied phase functions for pump, Stokes, and probe regions as indicated at the right side of the figure. Note that their order has changed compared to Fig. 4. The time distribution of the frequencies is depicted in (d). The signal generated by the pump acting as probe (blue) cannot pass the filter at 700 nm ( 14,285    cm 1 ). As shown in (a), the detector records only the signal generated by the time-delayed probe frequencies (red). (e) Influence of the amount of chirp on the measured linewidth of the band at 1004    cm 1 . Applied chirps from top to bottom are 2000    fs 2 , 3000    fs 2 , 5000    fs 2 , 7000    fs 2 , 9000    fs 2 , 12,000    fs 2 , and 15,000    fs 2 . The delay of the probe was set to 200 fs after the end of the excitation.
Fig. 10.
Fig. 10. Multimodal imaging of 200    μm × 200    μm human skin tissue with (a) a transform-limited pulse and (b), (d)–(f) spectral focusing. (c) illustrates the high contrast achieved with spectral focusing (black line) compared to TL pulses (gray background) along the blue lines in (a) and (b). The images show (a) and (b) CARS, (d) SHG, and (e) TPEF signal. (f) A multimodal RGB image is constructed by combining the simultaneously collected CARS (red), SHG (blue), and TPEF (green) data obtained with a spectral focusing phase function. The chirp was set to 3000    fs 2 , and the probe was delayed 100 fs after the end of the excitation (Fig. 4). Signals were collected using photomultipliers and bandpass filters (CARS: 640 ± 10    nm , SHG: 400 ± 10    nm , TPEF 500 ± 20    nm ).

Equations (4)

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E CARS ( ω ) = 0 d Ω E Pr ( ω Ω ) χ ( 3 ) ( Ω ) A ( Ω ) R ( Ω ) ,
A ( Ω ) = 0 d ω | E P u ( ω ) E S t * ( ω Ω ) | e i Δ ϕ ,
χ ( 3 ) ( Ω ) = χ NR + A Raman Ω Ω res i Γ ,
E CARS ( ω ) = 4 π 2 F ( F 1 { χ ( 3 ) ( Ω ) } × F [ | F 1 { E ( ω ) } | 2 ] F 1 { E ( ω ) } ) .

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