Abstract

We present a single-beam coherent Raman microscopy method based on pump–probe, time-resolved stimulated Raman scattering (SRS) measurements with shaped probe pulses. In the single-beam method, we divide a broadband laser spectrum into three frequency bands for the pump, phase-modulated (PM) probe, and local oscillator (LO) probe pulses. Multiple low-wavenumber Raman modes are efficiently excited by an impulsive pump pulse, and a specific Raman mode can be selectively probed using temporal beam coupling between the PM and LO probe pulses via the Raman-induced refractive index modulation. To achieve both high sensitivity and a high spectral resolution, we allocate a large spectral bandwidth (164  cm1) to two probe bands and use a new selective detection scheme based on the spectral focusing technique. By giving a strong group delay dispersion to the probes (45000  fs2), we can obtain an improved spectral resolution of down to 25  cm1. In a proof-of-concept experiment, the intrinsic molecular-vibration contrast of sevoflurane, an inhaled anesthetic drug, is successfully visualized. This result suggests that single-beam SRS imaging with pulse shaping is a potentially powerful tool for detecting the Raman signals of small-molecule drugs in living cells and tissues.

© 2017 Optical Society of America

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References

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2016 (1)

2015 (3)

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]

J.-X. Cheng and X. S. Xie, “Vibrational spectroscopic imaging of living systems: An emerging platform for biology and medicine,” Science 350, aaa8870 (2015).
[Crossref]

M. Kawagishi, Y. Obara, T. Suzuki, M. Hayashi, K. Misawa, and S. Terada, “Direct label-free measurement of the distribution of small molecular weight compound inside thick biological tissue using coherent Raman microspectroscopy,” Sci. Rep. 5, 13868 (2015).
[Crossref]

2014 (3)

N. A. Belsey, N. L. Garrett, L. R. Contreras-Rojas, A. J. Pickup-Gerlaugh, G. J. Price, J. Moger, and R. H. Guy, “Evaluation of drug delivery to intact and porated skin by coherent Raman scattering and fluorescence microscopies,” J. Control. Release 174, 37–42 (2014).
[Crossref]

L. Wei, F. Hu, Y. Shen, Z. Chen, Y. Yu, C. Lin, M. C. Wang, and W. Min, “Live-cell imaging with alkyne-tagged small biomolecules by stimulated Raman scattering,” Nat. Methods 11, 410–412 (2014).
[Crossref]

D. Zhang, P. Wang, M. N. Slipchenko, and J.-X. Cheng, “Fast vibrational imaging of single cells and tissues by stimulated Raman scattering microscopy,” Acc. Chem. Res. 47, 2282–2290 (2014).
[Crossref]

2013 (1)

D. Fu, G. Holtom, C. Freudiger, X. Zhang, and X. S. Xie, “Hyperspectral imaging with stimulated Raman scattering by chirped femtosecond lasers,” J. Phys. Chem. B 117, 4634–4640 (2013).
[Crossref]

2012 (1)

C. W. Freudiger, R. Pfannl, D. A. Orringer, B. G. Saar, M. Ji, Q. Zeng, L. Ottoboni, W. Ying, C. Waeber, J. R. Sims, P. L. De Jager, O. Sagher, M. A. Philbert, X. Xu, S. Kesari, X. S. Xie, and G. S. Young, “Multicolored stain-free histopathology with coherent Raman imaging,” Lab. Invest. 92, 1492–1502 (2012).
[Crossref]

2011 (4)

B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharmaceutics 8, 969–975 (2011).
[Crossref]

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent nonlinear optical imaging: Beyond fluorescence microscopy,” Annu. Rev. Phys. Chem. 62, 507–530 (2011).
[Crossref]

T. Suzuki and K. Misawa, “Efficient heterodyne CARS measurement by combining spectral phase modulation with temporal delay technique,” Opt. Express 19, 11463–11470 (2011).
[Crossref]

T. Wu, J. Tang, B. Hajj, and M. Cui, “Phase resolved interferometric spectral modulation (PRISM) for ultrafast pulse measurement and compression,” Opt. Express 19, 12961–12968 (2011).
[Crossref]

2010 (4)

O. Katz, J. M. Levitt, E. Grinvald, and Y. Silberberg, “Single-beam coherent Raman spectroscopy and microscopy via spectral notch shaping,” Opt. Express 18, 22693–22701 (2010).
[Crossref]

P. D. Chowdary, Z. Jiang, E. J. Chaney, W. A. Benalcazar, D. L. Marks, M. Gruebele, and S. A. Boppart, “Molecular histopathology by spectrally reconstructed nonlinear interferometric vibrational imaging,” Cancer Res. 70, 9562–9569 (2010).
[Crossref]

S. Mukamel and S. Rahav, “Ultrafast nonlinear optical signals viewed from the molecule’s perspective: Kramers–Heisenberg transition-amplitudes versus susceptibilities,” Adv. At. Mol. Opt. Phys. 59, 233–263 (2010).

S. Rahav and S. Mukamel, “Stimulated coherent anti-Stokes Raman spectroscopy (CARS) resonances originate from double-slit interference of two-photon Stokes pathways,” Proc. Natl. Acad. Sci. 107, 4825–4829 (2010).
[Crossref]

2009 (3)

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

P. Nandakumar, A. Kovalev, and A. Volkmer, “Vibrational imaging based on stimulated Raman scattering microscopy,” New J. Phys. 11, 033026 (2009).
[Crossref]

Y. Ozeki, F. Dake, S. Kajiyama, K. Fukui, and K. Itoh, “Analysis and experimental assessment of the sensitivity of stimulated Raman scattering microscopy,” Opt. Express 17, 3651–3658 (2009).
[Crossref]

2008 (3)

H. Li, D. A. Harris, B. Xu, P. J. Wrzesinski, V. V. Lozovoy, and M. Dantus, “Coherent mode-selective Raman excitation towards standoff detection,” Opt. Express 16, 5499–5504 (2008).
[Crossref]

C. L. Evans and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: Chemically selective imaging for biology and medicine,” Annu. Rev. Anal. Chem. 1, 883–909 (2008).
[Crossref]

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857–1861 (2008).
[Crossref]

2006 (2)

2005 (2)

H. Kano and H. Hamaguchi, “Ultrabroadband (> 2500  cm-1) multiplex coherent anti-Stokes Raman scattering microspectroscopy using a supercontinuum generated from a photonic crystal fiber,” Appl. Phys. Lett. 86, 121113 (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]

2004 (3)

B. R. Stockwell, “Exploring biology with small organic molecules,” Nature 432, 846–854 (2004).
[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]

T. W. Kee and M. T. Cicerone, “Simple approach to one-laser, broadband coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 29, 2701–2703 (2004).
[Crossref]

2003 (1)

X. Nan, J.-X. Cheng, and X. S. Xie, “Vibrational imaging of lipid droplets in live fibroblast cell with coherent anti-Stokes Raman scattering microscopy,” J. Lipid Res. 44, 2202–2208 (2003).
[Crossref]

2002 (3)

D. Oron, N. Dudovich, and Y. Silberberg, “Single-pulse phase-contrast nonlinear Raman spectroscopy,” Phys. Rev. Lett. 89, 273001 (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]

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

2001 (1)

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, ultrashort laser pulses,” Appl. Phys. B 73, 273–277 (2001).
[Crossref]

1999 (2)

M. Yoshizawa and M. Kurosawa, “Femtosecond time-resolved Raman spectroscopy using stimulated Raman scattering,” Phys. Rev. A 61, 013808 (1999).
[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]

1998 (1)

1994 (1)

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. 64, 137–139 (1994).
[Crossref]

1991 (1)

D. Naumann, D. Helm, and H. Labischinski, “Microbiological characterizations by FT-IR spectroscopy,” Nature 351, 81–82 (1991).
[Crossref]

1990 (1)

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman microspectroscopy,” Nature 347, 301–303 (1990).
[Crossref]

1960 (1)

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745–808 (1960).
[Crossref]

Albersheim, W. J.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745–808 (1960).
[Crossref]

Arndt-Jovin, D. J.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman microspectroscopy,” Nature 347, 301–303 (1990).
[Crossref]

Auston, D. H.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. 64, 137–139 (1994).
[Crossref]

Belsey, N. A.

N. A. Belsey, N. L. Garrett, L. R. Contreras-Rojas, A. J. Pickup-Gerlaugh, G. J. Price, J. Moger, and R. H. Guy, “Evaluation of drug delivery to intact and porated skin by coherent Raman scattering and fluorescence microscopies,” J. Control. Release 174, 37–42 (2014).
[Crossref]

Benalcazar, W. A.

P. D. Chowdary, Z. Jiang, E. J. Chaney, W. A. Benalcazar, D. L. Marks, M. Gruebele, and S. A. Boppart, “Molecular histopathology by spectrally reconstructed nonlinear interferometric vibrational imaging,” Cancer Res. 70, 9562–9569 (2010).
[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]

Boppart, S. A.

P. D. Chowdary, Z. Jiang, E. J. Chaney, W. A. Benalcazar, D. L. Marks, M. Gruebele, and S. A. Boppart, “Molecular histopathology by spectrally reconstructed nonlinear interferometric vibrational imaging,” Cancer Res. 70, 9562–9569 (2010).
[Crossref]

Brückner, L.

Buckup, T.

Carrasco, S.

Caster, A. G.

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]

Chaney, E. J.

P. D. Chowdary, Z. Jiang, E. J. Chaney, W. A. Benalcazar, D. L. Marks, M. Gruebele, and S. A. Boppart, “Molecular histopathology by spectrally reconstructed nonlinear interferometric vibrational imaging,” Cancer Res. 70, 9562–9569 (2010).
[Crossref]

Chen, Z.

L. Wei, F. Hu, Y. Shen, Z. Chen, Y. Yu, C. Lin, M. C. Wang, and W. Min, “Live-cell imaging with alkyne-tagged small biomolecules by stimulated Raman scattering,” Nat. Methods 11, 410–412 (2014).
[Crossref]

Cheng, J.-X.

J.-X. Cheng and X. S. Xie, “Vibrational spectroscopic imaging of living systems: An emerging platform for biology and medicine,” Science 350, aaa8870 (2015).
[Crossref]

D. Zhang, P. Wang, M. N. Slipchenko, and J.-X. Cheng, “Fast vibrational imaging of single cells and tissues by stimulated Raman scattering microscopy,” Acc. Chem. Res. 47, 2282–2290 (2014).
[Crossref]

X. Nan, J.-X. Cheng, and X. S. Xie, “Vibrational imaging of lipid droplets in live fibroblast cell with coherent anti-Stokes Raman scattering microscopy,” J. Lipid Res. 44, 2202–2208 (2003).
[Crossref]

Chowdary, P. D.

P. D. Chowdary, Z. Jiang, E. J. Chaney, W. A. Benalcazar, D. L. Marks, M. Gruebele, and S. A. Boppart, “Molecular histopathology by spectrally reconstructed nonlinear interferometric vibrational imaging,” Cancer Res. 70, 9562–9569 (2010).
[Crossref]

Cicerone, M. T.

Contreras-Rojas, L. R.

N. A. Belsey, N. L. Garrett, L. R. Contreras-Rojas, A. J. Pickup-Gerlaugh, G. J. Price, J. Moger, and R. H. Guy, “Evaluation of drug delivery to intact and porated skin by coherent Raman scattering and fluorescence microscopies,” J. Control. Release 174, 37–42 (2014).
[Crossref]

B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharmaceutics 8, 969–975 (2011).
[Crossref]

Cui, M.

Dake, F.

Dantus, M.

Darlington, S.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745–808 (1960).
[Crossref]

De Jager, P. L.

C. W. Freudiger, R. Pfannl, D. A. Orringer, B. G. Saar, M. Ji, Q. Zeng, L. Ottoboni, W. Ying, C. Waeber, J. R. Sims, P. L. De Jager, O. Sagher, M. A. Philbert, X. Xu, S. Kesari, X. S. Xie, and G. S. Young, “Multicolored stain-free histopathology with coherent Raman imaging,” Lab. Invest. 92, 1492–1502 (2012).
[Crossref]

de Mul, F. F. M.

G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman microspectroscopy,” Nature 347, 301–303 (1990).
[Crossref]

Dela Cruz, J. M.

Dudovich, N.

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

D. Oron, N. Dudovich, and Y. Silberberg, “Single-pulse phase-contrast nonlinear Raman spectroscopy,” Phys. Rev. Lett. 89, 273001 (2002).
[Crossref]

Enejder, A. M. K.

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]

Evans, C. L.

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C. W. Freudiger, R. Pfannl, D. A. Orringer, B. G. Saar, M. Ji, Q. Zeng, L. Ottoboni, W. Ying, C. Waeber, J. R. Sims, P. L. De Jager, O. Sagher, M. A. Philbert, X. Xu, S. Kesari, X. S. Xie, and G. S. Young, “Multicolored stain-free histopathology with coherent Raman imaging,” Lab. Invest. 92, 1492–1502 (2012).
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C. W. Freudiger, R. Pfannl, D. A. Orringer, B. G. Saar, M. Ji, Q. Zeng, L. Ottoboni, W. Ying, C. Waeber, J. R. Sims, P. L. De Jager, O. Sagher, M. A. Philbert, X. Xu, S. Kesari, X. S. Xie, and G. S. Young, “Multicolored stain-free histopathology with coherent Raman imaging,” Lab. Invest. 92, 1492–1502 (2012).
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L. Wei, F. Hu, Y. Shen, Z. Chen, Y. Yu, C. Lin, M. C. Wang, and W. Min, “Live-cell imaging with alkyne-tagged small biomolecules by stimulated Raman scattering,” Nat. Methods 11, 410–412 (2014).
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C. W. Freudiger, R. Pfannl, D. A. Orringer, B. G. Saar, M. Ji, Q. Zeng, L. Ottoboni, W. Ying, C. Waeber, J. R. Sims, P. L. De Jager, O. Sagher, M. A. Philbert, X. Xu, S. Kesari, X. S. Xie, and G. S. Young, “Multicolored stain-free histopathology with coherent Raman imaging,” Lab. Invest. 92, 1492–1502 (2012).
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W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent nonlinear optical imaging: Beyond fluorescence microscopy,” Annu. Rev. Phys. Chem. 62, 507–530 (2011).
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X. Nan, J.-X. Cheng, and X. S. Xie, “Vibrational imaging of lipid droplets in live fibroblast cell with coherent anti-Stokes Raman scattering microscopy,” J. Lipid Res. 44, 2202–2208 (2003).
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B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharmaceutics 8, 969–975 (2011).
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Nat. Methods (1)

L. Wei, F. Hu, Y. Shen, Z. Chen, Y. Yu, C. Lin, M. C. Wang, and W. Min, “Live-cell imaging with alkyne-tagged small biomolecules by stimulated Raman scattering,” Nat. Methods 11, 410–412 (2014).
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D. Oron, N. Dudovich, and Y. Silberberg, “Single-pulse phase-contrast nonlinear Raman spectroscopy,” Phys. Rev. Lett. 89, 273001 (2002).
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Science (2)

J.-X. Cheng and X. S. Xie, “Vibrational spectroscopic imaging of living systems: An emerging platform for biology and medicine,” Science 350, aaa8870 (2015).
[Crossref]

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857–1861 (2008).
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J.-X. Cheng and X. S. Xie, eds., Coherent Raman Scattering Microscopy (Taylor and Francis, 2011).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

A. Yariv and P. Yeh, Photonics, Optical Electronics in Modern Communications, 6th ed. (Oxford University, 2006).

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Figures (9)

Fig. 1.
Fig. 1.

Schematics of the SRS processes: (a)–(c) amplitude-modulated SRS (AM-SRS) and (d)–(f) phase-modulated SRS (PM-SRS). (a), (d) Frequency allocation and output intensity modulation, (b), (e) pulse train and radio-frequency modulation diagram, and (c), (f) temporal pulse intensity and effective refractive index change in the ultrafast regime. The non-resonant background contribution is not illustrated here for brevity.

Fig. 2.
Fig. 2.

Spectrally focused detection scheme: (a) group delay diagram of a perfectly frequency-matched detection where Δ Ω R = 0 , (b) spectral interference corresponding to case (a) providing maximal SRS output, (c) group delay diagram of a detuned case where Δ Ω R 0 , and (d) spectral interference corresponding to case (c), where the net SRS signal integrated over the LO band is cancelled out.

Fig. 3.
Fig. 3.

Single-beam PM-SRS microscope (CM: chirp mirrors, VHG: volume holographic grating, SLM: spatial light modulator, OI: optical isolator, PBS: polarizing beam splitter, BPF: bandpass filter, EOM: electro-optic phase modulator, λ / 4 : quarter-wave plate, HM: half mirror, OL1 and OL2: objective lenses, S: sample, C: camera, SL: variable slit on a translational stage, and PD: photodetector).

Fig. 4.
Fig. 4.

PM-SRS spectrum of pure DMSO detected by the spectrally focused detection: (a) with the high-resolution setting derived by the polynomial fitting of the PM probe phase profile shown in Fig. 8(a) (delay: 730 fs, GDD: + 45000    fs 2 , TOD: + 3.6 × 10 6    fs 3 , detection bandwidth: 164    cm 1 ) and (b) with the defocused setting (squares) (delay: 1530 fs, GDD: + 70000    fs 2 , TOD: + 5.0 × 10 6    fs 3 , detection bandwidth: 125    cm 1 ). The spectrum measured with non-shaped LO pulses is also shown (triangles).

Fig. 5.
Fig. 5.

SRS signal versus DMSO concentration in water: (a) all the measured data (dots) and the linear fit calibration curve (dotted line) and (b) an enlarged view of the low concentration region. The error bars represent the stationary interference background on off-resonant frequencies.

Fig. 6.
Fig. 6.

PM-SRS imaging of a droplet of an anesthetic drug (sevoflurane) in water: (a) PM-SRS spectrum of sevoflurane (blue squares) and water (red circles), (b) near-infrared transmission image, (c) raw on-resonant SRS image at 730    cm 1 , (d) normalized SRS image at 730    cm 1 , and (e) normalized off-resonant SRS image at 620    cm 1 . No spatial filtering was used in the images. The scale bar is 20 μm.

Fig. 7.
Fig. 7.

Spectral phase compensation by MIIPS. (a) The spectral phase profiles before (dashed line) and after compensation (solid line) and the spectral intensity profile (dotted line) and (b) the phase profile after MIIPS compensation (solid line) compared to that measured with a commercial SPIDER system for reference (dashed line). The test pulses were sampled immediately after the 4f pulse shaper but before the bandpass filter (a silver mirror inserted prior to OI in Fig. 3). The strong negative chirp from the chirped mirrors was successfully compensated. (c) The SLM input level on an 8-bit grayscale after direct on-sample MIIPS compensation (solid line) and the 2 π -phase level (dashed line). The LO probe band is not yet allocated. All data here were recorded with the same SLM pattern after five MIIPS iterations.

Fig. 8.
Fig. 8.

Characterization of the PM probe pulse. (a) The spectral intensity profile measured by a spectrometer and the phase profile estimated by PRISM. The PRISM output is shown as a dotted line. The SLM (LCOS-SLM, X10468-02, Hamamatsu) had 256 gray levels and 800 pixels at 20    μm / pixel . The spectral resolution of the SLM near 780 nm was 0.24    nm / pixel . The PRISM measurement was performed with 800    samples / group × 4    groups = 3200    samples . Each group had randomly selected phase-modulated pixels (200 pixels) and non-modulated pixels (600 pixels). The phase advance per sample in the modulated pixels was uniformly distributed between π / 2 and π . The PRISM output was obtained by smoothing the raw output data with a 7-pixel median filter and a 5-pixel moving-average filter. The phase profile was further fitted with a fifth-degree polynomial (solid line). (b) The temporal amplitude profile recorded from the SFG cross-correlation measurement (solid line) and the temporal profile calculated from the PRISM data (dashed line). The discrepancy between the two results is seemingly caused by the limited spectral resolution of the 4f pulse shaper optics.

Fig. 9.
Fig. 9.

Power scaling of the PM-SRS signal: (a) lock-in amplifier output signal versus total input power plotted on a log–log scale, showing that the SRS signal is approximately scaled as a quadratic function ( Δ I SRS I total 1.98 ), and (b) linear dependence of the SRS signal on the detected DC level.

Equations (13)

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Δ n ( t ) χ ( 3 ) ( t τ ) | E pump ( τ ) | 2 d τ I ex ( Ω R ) χ ( 3 ) ( t ) , I ex ( Ω R ) = | E pump ( t ) | 2 exp ( i Ω R t ) d t , χ ( 3 ) ( t ) = U ( t ) Im { χ ( 3 ) ( Ω R ) } 2 π τ R exp ( t τ R ) sin ( Ω R t ) ,
Δ I SRS { i Δ n ( t ) E PM ( t , t PM ) E LO * ( t ) + c.c. } d t Im { χ ( 3 ) ( Ω R ) } 2 π τ R exp ( τ pr τ R ) × I pump I PM I LO cos ( 2 π f PM t PM + Δ ϕ offset ) ,
Δ n ( Ω ) χ ( 3 ) ( Ω ) E pump ( Ω ) E pump * ( Ω Ω ) d Ω ,
E SRS ( ω ) Δ n * ( Ω ) E PM ( ω Ω ) d Ω .
Δ I out = Δ I SRS ( ω ) d ω = E LO ( ω ) E SRS * ( ω ) d ω E LO ( ω ) Δ n ( Ω ) E PM * ( ω Ω ) d Ω d ω Δ n ( Ω ) R CC ( Ω ) d Ω ,
R CC ( Ω ) = E PM * ( ω Ω ) E LO ( ω ) d ω .
R CC ( Ω ) R AC ( Ω Δ ω pr ) = E LO * ( ω ( Ω Δ ω pr ) ) E LO ( ω ) d ω ,
R CC ( Ω ) = | E LO ( ω ) | | E PM * ( ω Ω ) | d ω .
Δ Ω SI = 2 π Δ τ SI = 2 π Δ τ LO ( ω ) Δ τ PM ( ω + Ω R ) = 2 π { β ( ω ω LO ) + τ pr } { β ( ω + Ω R ω PM ) + τ pr } = 2 π β Δ Ω R ,
Δ Ω R 2 π β Δ Ω pr .
Δ k SLM = λ 0 2 d SLM k 0 ,
Δ k 4 f = D beam 2 f k 0 ,
Δ τ cutoff = 2 π f Δ k 4 f c k 0 2 f g cos θ 0 ,

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