Abstract

We demonstrate, for the first time, single-beam heterodyne FAST CARS imaging without data post-processing and with nonresonant background subtraction in a simple setup via the real-time piezo modulation of the probe delay. Our fast signal acquisition scheme does not require a spatial light modulator in the pulse shaper, and is suitable for high-resolution imaging and time-resolved dynamics. In addition, the spectral detection of the back-scattered FAST CARS signal is incorporated into the pulse shaper, allowing for a compact and more efficient design. Such epi-detection capability is demonstrated by imaging Si and MoS2 microstructures.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2015 (5)

2014 (2)

J. M. Levitt, O. Katz, and Y. Silberberg, “Frequency-encoded multiplexed CARS microscopy by rapid pulse shaping,” J. Mod. Opt. 61(10), 872–876 (2014).
[Crossref]

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

2013 (1)

2012 (1)

A. Wipfler, T. Buckup, and M. Motzkus, ”Multiplexing single-beam coherent anti-Stokes Raman spectroscopy with heterodyne detection,” Appl. Phys. Lett. 100(7), 071102 (2012).
[Crossref]

2011 (1)

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. 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(3), 393–398 (2011).
[Crossref]

2010 (2)

B. Li, W. S. Warren, and M. C. Fischer, ”Phase-cycling coherent anti-Stokes Raman scattering using shaped femtosecond laser pulses,” Opt. Express 18(25), 25825–25832 (2010).
[Crossref] [PubMed]

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 research 70(23), 9562–9569 (2010).
[Crossref] [PubMed]

2009 (4)

2008 (1)

B.-C. Chen and S.-H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-Stokes Raman scattering microscopy,” J. Phys. Chem. B 112(12), 3653–3661 (2008).
[Crossref] [PubMed]

2007 (2)

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, ”Shot noise limited heterodyne detection of CARS signals,” Opt. Express 15(23), 15207–15213 (2007).
[Crossref] [PubMed]

2006 (4)

E. O. Potma, C. L. Evans, and X. S. Xie, ”Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31(2), 241–243 (2006).
[Crossref]

J. P. Ogilvie, E. Beaurepaire, A. Alexandrou, and M. Joffre, “Fourier-transform coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 31(4), 480–482 (2006).
[Crossref]

S.-H. Lim, A. G. Caster, O. Nicolet, and S. R. Leone, ”Chemical imaging by single pulse interferometric coherent anti-Stokes Raman scattering microscopy,” J. Phys. Chem. B 110(11), 5196–5204 (2006).
[Crossref] [PubMed]

B. von Vacano and M. Motzkus, ”Time-resolved two color single-beam CARS employing supercontinuum and femtosecond pulse shaping,” Opt. Commun. 264(2), 488–493 (2006).
[Crossref]

2004 (1)

D. L. Marks and S. A. Boppart, “Nonlinear interferometric vibrational imaging,” Phys. Rev. Lett. 92(12), 123905 (2004).
[Crossref] [PubMed]

2003 (1)

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90(21), 213902 (2003).
[Crossref] [PubMed]

2002 (2)

N. Dudovich, D. Oron, and Y. Silberberg, ”Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[Crossref] [PubMed]

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrný, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, “FAST CARS: Engineering a laser spectroscopic technique for rapid identification of bacterial spores,” Proc. Natl. Acad. Sci. U.S.A. 99(17), 10994–11001 (2002).
[Crossref] [PubMed]

2001 (2)

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref]

J.-X. Cheng, L. D. Book, and X. S. Xie, ”Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26(17), 1341–1343 (2001).
[Crossref]

2000 (1)

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

1984 (1)

F. L. Galeener, R. A. Barrio, E. Martinez, and R. J. Elliott, ”Vibrational decoupling of rings in amorphous solids,” Phys. Rev. Lett. 53(25), 2429 (1984).
[Crossref]

Alexandrou, A.

Ariunbold, G. O.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

Barrio, R. A.

F. L. Galeener, R. A. Barrio, E. Martinez, and R. J. Elliott, ”Vibrational decoupling of rings in amorphous solids,” Phys. Rev. Lett. 53(25), 2429 (1984).
[Crossref]

Beaurepaire, E.

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 research 70(23), 9562–9569 (2010).
[Crossref] [PubMed]

Book, L. D.

Boppart, S. A.

Y. Liu, M. D. King, H. Tu, Y. Zhao, and S. A. Boppart, “Broadband nonlinear vibrational spectroscopy by shaping a coherent fiber supercontinuum,” Opt. Express 21(7), 8269–8275 (2013).
[Crossref] [PubMed]

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 research 70(23), 9562–9569 (2010).
[Crossref] [PubMed]

D. L. Marks and S. A. Boppart, “Nonlinear interferometric vibrational imaging,” Phys. Rev. Lett. 92(12), 123905 (2004).
[Crossref] [PubMed]

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(22) 5204–5207 (2015).
[Crossref] [PubMed]

A. Wipfler, T. Buckup, and M. Motzkus, ”Multiplexing single-beam coherent anti-Stokes Raman spectroscopy with heterodyne detection,” Appl. Phys. Lett. 100(7), 071102 (2012).
[Crossref]

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, ”Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

Camp, C. H.

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

Caster, A. G.

S.-H. Lim, A. G. Caster, O. Nicolet, and S. R. Leone, ”Chemical imaging by single pulse interferometric coherent anti-Stokes Raman scattering microscopy,” J. Phys. Chem. B 110(11), 5196–5204 (2006).
[Crossref] [PubMed]

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 research 70(23), 9562–9569 (2010).
[Crossref] [PubMed]

Chen, B.-C.

B.-C. Chen and S.-H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-Stokes Raman scattering microscopy,” J. Phys. Chem. B 112(12), 3653–3661 (2008).
[Crossref] [PubMed]

Cheng, J.-X.

C.-S. Liao, M. N. Slipchenko, P. Wang, J. Li, S.-Y. Lee, R. A. Oglesbee, and J.-X. Cheng, ”Microsecond scale vibrational spectroscopic imaging by multiplex stimulated Raman scattering microscopy,” Light Sci. Appl. 4(3), e265 (2015).
[Crossref] [PubMed]

J.-X. Cheng, L. D. Book, and X. S. Xie, ”Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26(17), 1341–1343 (2001).
[Crossref]

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref]

J.-X. Cheng and X. S. Xie, Coherent Raman Scattering Microscopy (CRC, 2012).

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 research 70(23), 9562–9569 (2010).
[Crossref] [PubMed]

Cicerone, M. T.

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

Colthup, N. B.

N. B. Colthup, L. H. Daly, and S. E. Wiberley, Introduction to Infrared and Raman Spectroscopy (Academic, 1990).

Daly, L. H.

N. B. Colthup, L. H. Daly, and S. E. Wiberley, Introduction to Infrared and Raman Spectroscopy (Academic, 1990).

Dantus, M.

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. 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(3), 393–398 (2011).
[Crossref]

H. Li, D. A. Harris, B. Xu, P. J. Wrzesinski, V. V. Lozovoy, and M. Dantus, “Standoff and arms-length detection of chemicals with single-beam coherent anti-Stokes Raman scattering,” Appl. Opt. 48(4), B17–B22 (2009).
[Crossref] [PubMed]

Dogariu, A.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

Drexler, W.

Dudovich, N.

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90(21), 213902 (2003).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, ”Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[Crossref] [PubMed]

Elliott, R. J.

F. L. Galeener, R. A. Barrio, E. Martinez, and R. J. Elliott, ”Vibrational decoupling of rings in amorphous solids,” Phys. Rev. Lett. 53(25), 2429 (1984).
[Crossref]

Evans, C. L.

Fischer, M. C.

Galeener, F. L.

F. L. Galeener, R. A. Barrio, E. Martinez, and R. J. Elliott, ”Vibrational decoupling of rings in amorphous solids,” Phys. Rev. Lett. 53(25), 2429 (1984).
[Crossref]

Gord, J. R.

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. 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(3), 393–398 (2011).
[Crossref]

Gruebele, M.

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 research 70(23), 9562–9569 (2010).
[Crossref] [PubMed]

Harris, D. A.

Hartshorn, C. M.

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

Hashimoto, H.

Heddleston, J. M.

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

Hermann, B.

Hight Walker, A. R.

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

Huang, Y.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

Isobe, K.

Jia, Y.

Jiang, Z.

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 research 70(23), 9562–9569 (2010).
[Crossref] [PubMed]

Joffre, M.

Jurna, M.

Kamali, T.

Kannari, F.

Kattawar, G. W.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrný, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, “FAST CARS: Engineering a laser spectroscopic technique for rapid identification of bacterial spores,” Proc. Natl. Acad. Sci. U.S.A. 99(17), 10994–11001 (2002).
[Crossref] [PubMed]

Katz, O.

Kawano, H.

King, M. D.

Korterik, J. P.

Kumar, S.

Lathia, J. D.

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

Lee, S.-Y.

C.-S. Liao, M. N. Slipchenko, P. Wang, J. Li, S.-Y. Lee, R. A. Oglesbee, and J.-X. Cheng, ”Microsecond scale vibrational spectroscopic imaging by multiplex stimulated Raman scattering microscopy,” Light Sci. Appl. 4(3), e265 (2015).
[Crossref] [PubMed]

Lee, Y. J.

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

Leone, S. R.

S.-H. Lim, A. G. Caster, O. Nicolet, and S. R. Leone, ”Chemical imaging by single pulse interferometric coherent anti-Stokes Raman scattering microscopy,” J. Phys. Chem. B 110(11), 5196–5204 (2006).
[Crossref] [PubMed]

Levitt, J. M.

J. M. Levitt, O. Katz, and Y. Silberberg, “Frequency-encoded multiplexed CARS microscopy by rapid pulse shaping,” J. Mod. Opt. 61(10), 872–876 (2014).
[Crossref]

Levitte, J. M.

Li, B.

Li, H.

Li, J.

C.-S. Liao, M. N. Slipchenko, P. Wang, J. Li, S.-Y. Lee, R. A. Oglesbee, and J.-X. Cheng, ”Microsecond scale vibrational spectroscopic imaging by multiplex stimulated Raman scattering microscopy,” Light Sci. Appl. 4(3), e265 (2015).
[Crossref] [PubMed]

Liao, C.-S.

C.-S. Liao, M. N. Slipchenko, P. Wang, J. Li, S.-Y. Lee, R. A. Oglesbee, and J.-X. Cheng, ”Microsecond scale vibrational spectroscopic imaging by multiplex stimulated Raman scattering microscopy,” Light Sci. Appl. 4(3), e265 (2015).
[Crossref] [PubMed]

Lim, S.-H.

B.-C. Chen and S.-H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-Stokes Raman scattering microscopy,” J. Phys. Chem. B 112(12), 3653–3661 (2008).
[Crossref] [PubMed]

S.-H. Lim, A. G. Caster, O. Nicolet, and S. R. Leone, ”Chemical imaging by single pulse interferometric coherent anti-Stokes Raman scattering microscopy,” J. Phys. Chem. B 110(11), 5196–5204 (2006).
[Crossref] [PubMed]

Liu, Y.

Lozovoy, V. V.

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. 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(3), 393–398 (2011).
[Crossref]

H. Li, D. A. Harris, B. Xu, P. J. Wrzesinski, V. V. Lozovoy, and M. Dantus, “Standoff and arms-length detection of chemicals with single-beam coherent anti-Stokes Raman scattering,” Appl. Opt. 48(4), B17–B22 (2009).
[Crossref] [PubMed]

Lucht, R. P.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrný, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, “FAST CARS: Engineering a laser spectroscopic technique for rapid identification of bacterial spores,” Proc. Natl. Acad. Sci. U.S.A. 99(17), 10994–11001 (2002).
[Crossref] [PubMed]

Marks, D. L.

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 research 70(23), 9562–9569 (2010).
[Crossref] [PubMed]

D. L. Marks and S. A. Boppart, “Nonlinear interferometric vibrational imaging,” Phys. Rev. Lett. 92(12), 123905 (2004).
[Crossref] [PubMed]

Martinez, E.

F. L. Galeener, R. A. Barrio, E. Martinez, and R. J. Elliott, ”Vibrational decoupling of rings in amorphous solids,” Phys. Rev. Lett. 53(25), 2429 (1984).
[Crossref]

Midorikawa, K.

Miyawaki, A.

Mizuno, H.

Moffatt, D. J.

Motzkus, M.

L. Brückner, T. Buckup, and M. Motzkus, “Enhancement of coherent anti-Stokes Raman signal via tailored probing in spectral focusing,” Opt. Lett. 40(22) 5204–5207 (2015).
[Crossref] [PubMed]

A. Wipfler, T. Buckup, and M. Motzkus, ”Multiplexing single-beam coherent anti-Stokes Raman spectroscopy with heterodyne detection,” Appl. Phys. Lett. 100(7), 071102 (2012).
[Crossref]

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, ”Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

B. von Vacano and M. Motzkus, ”Time-resolved two color single-beam CARS employing supercontinuum and femtosecond pulse shaping,” Opt. Commun. 264(2), 488–493 (2006).
[Crossref]

Mukamel, S.

S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University, 1995).

Müller, C.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, ”Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

Murawski, R. K.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

Nicolet, O.

S.-H. Lim, A. G. Caster, O. Nicolet, and S. R. Leone, ”Chemical imaging by single pulse interferometric coherent anti-Stokes Raman scattering microscopy,” J. Phys. Chem. B 110(11), 5196–5204 (2006).
[Crossref] [PubMed]

Offerhaus, H. L.

Ogilvie, J. P.

Oglesbee, R. A.

C.-S. Liao, M. N. Slipchenko, P. Wang, J. Li, S.-Y. Lee, R. A. Oglesbee, and J.-X. Cheng, ”Microsecond scale vibrational spectroscopic imaging by multiplex stimulated Raman scattering microscopy,” Light Sci. Appl. 4(3), e265 (2015).
[Crossref] [PubMed]

Opatrný, T.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrný, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, “FAST CARS: Engineering a laser spectroscopic technique for rapid identification of bacterial spores,” Proc. Natl. Acad. Sci. U.S.A. 99(17), 10994–11001 (2002).
[Crossref] [PubMed]

Oron, D.

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90(21), 213902 (2003).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, ”Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[Crossref] [PubMed]

Otto, C.

Pegoraro, A. F.

Pestov, D.

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. 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(3), 393–398 (2011).
[Crossref]

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

Pezacki, J. P.

Pilloff, H.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrný, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, “FAST CARS: Engineering a laser spectroscopic technique for rapid identification of bacterial spores,” Proc. Natl. Acad. Sci. U.S.A. 99(17), 10994–11001 (2002).
[Crossref] [PubMed]

Potma, E. O.

Považay, B.

Rebane, A.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrný, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, “FAST CARS: Engineering a laser spectroscopic technique for rapid identification of bacterial spores,” Proc. Natl. Acad. Sci. U.S.A. 99(17), 10994–11001 (2002).
[Crossref] [PubMed]

Rich, J. N.

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

Ridsdale, A.

Rostovtsev, Y. V.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

Roy, S.

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. 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(3), 393–398 (2011).
[Crossref]

Sautenkov, V. A.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

Scully, M. O.

Y. Shen, D. V. Voronine, A. V. Sokolov, and M. O. Scully, ”Low-wavenumber efficient single-beam coherent anti-Stokes Raman scattering using a spectral hole,” Opt. Lett. 40(7), 1223–1226 (2015).
[Crossref] [PubMed]

Y. Shen, D. V. Voronine, A. V. Sokolov, and M. O. Scully, ”A versatile setup using femtosecond adaptive spectroscopic technique for coherent anti-Stokes Raman scattering,” Rev. Sci. Instrum. 86(8), 083107 (2015).
[Crossref] [PubMed]

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrný, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, “FAST CARS: Engineering a laser spectroscopic technique for rapid identification of bacterial spores,” Proc. Natl. Acad. Sci. U.S.A. 99(17), 10994–11001 (2002).
[Crossref] [PubMed]

Shen, Y.

Y. Shen, D. V. Voronine, A. V. Sokolov, and M. O. Scully, ”A versatile setup using femtosecond adaptive spectroscopic technique for coherent anti-Stokes Raman scattering,” Rev. Sci. Instrum. 86(8), 083107 (2015).
[Crossref] [PubMed]

Y. Shen, D. V. Voronine, A. V. Sokolov, and M. O. Scully, ”Low-wavenumber efficient single-beam coherent anti-Stokes Raman scattering using a spectral hole,” Opt. Lett. 40(7), 1223–1226 (2015).
[Crossref] [PubMed]

Silberberg, Y.

S. Kumar, T. Kamali, J. M. Levitte, O. Katz, B. Hermann, R. Werkmeister, B. Považay, W. Drexler, A. Unterhuber, and Y. Silberberg, “Single-pulse CARS based multimodal nonlinear optical microscope for bioimaging,” Opt. Express 23(10), 13082–13098 (2015).
[Crossref] [PubMed]

J. M. Levitt, O. Katz, and Y. Silberberg, “Frequency-encoded multiplexed CARS microscopy by rapid pulse shaping,” J. Mod. Opt. 61(10), 872–876 (2014).
[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(21), 213902 (2003).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, ”Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[Crossref] [PubMed]

Slipchenko, M. N.

C.-S. Liao, M. N. Slipchenko, P. Wang, J. Li, S.-Y. Lee, R. A. Oglesbee, and J.-X. Cheng, ”Microsecond scale vibrational spectroscopic imaging by multiplex stimulated Raman scattering microscopy,” Light Sci. Appl. 4(3), e265 (2015).
[Crossref] [PubMed]

Sokolov, A. V.

Y. Shen, D. V. Voronine, A. V. Sokolov, and M. O. Scully, ”A versatile setup using femtosecond adaptive spectroscopic technique for coherent anti-Stokes Raman scattering,” Rev. Sci. Instrum. 86(8), 083107 (2015).
[Crossref] [PubMed]

Y. Shen, D. V. Voronine, A. V. Sokolov, and M. O. Scully, ”Low-wavenumber efficient single-beam coherent anti-Stokes Raman scattering using a spectral hole,” Opt. Lett. 40(7), 1223–1226 (2015).
[Crossref] [PubMed]

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrný, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, “FAST CARS: Engineering a laser spectroscopic technique for rapid identification of bacterial spores,” Proc. Natl. Acad. Sci. U.S.A. 99(17), 10994–11001 (2002).
[Crossref] [PubMed]

Stolow, A.

Suda, A.

Tanaka, M.

Tu, H.

Unterhuber, A.

Volkmer, A.

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref]

von Vacano, B.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, ”Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

B. von Vacano and M. Motzkus, ”Time-resolved two color single-beam CARS employing supercontinuum and femtosecond pulse shaping,” Opt. Commun. 264(2), 488–493 (2006).
[Crossref]

Voronine, D. V.

Y. Shen, D. V. Voronine, A. V. Sokolov, and M. O. Scully, ”A versatile setup using femtosecond adaptive spectroscopic technique for coherent anti-Stokes Raman scattering,” Rev. Sci. Instrum. 86(8), 083107 (2015).
[Crossref] [PubMed]

Y. Shen, D. V. Voronine, A. V. Sokolov, and M. O. Scully, ”Low-wavenumber efficient single-beam coherent anti-Stokes Raman scattering using a spectral hole,” Opt. Lett. 40(7), 1223–1226 (2015).
[Crossref] [PubMed]

Wang, P.

C.-S. Liao, M. N. Slipchenko, P. Wang, J. Li, S.-Y. Lee, R. A. Oglesbee, and J.-X. Cheng, ”Microsecond scale vibrational spectroscopic imaging by multiplex stimulated Raman scattering microscopy,” Light Sci. Appl. 4(3), e265 (2015).
[Crossref] [PubMed]

Wang, X.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

Warren, W. S.

Weiner, A. M.

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

Werkmeister, R.

Wiberley, S. E.

N. B. Colthup, L. H. Daly, and S. E. Wiberley, Introduction to Infrared and Raman Spectroscopy (Academic, 1990).

Wipfler, A.

A. Wipfler, T. Buckup, and M. Motzkus, ”Multiplexing single-beam coherent anti-Stokes Raman spectroscopy with heterodyne detection,” Appl. Phys. Lett. 100(7), 071102 (2012).
[Crossref]

Wrzesinski, P. J.

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. 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(3), 393–398 (2011).
[Crossref]

H. Li, D. A. Harris, B. Xu, P. J. Wrzesinski, V. V. Lozovoy, and M. Dantus, “Standoff and arms-length detection of chemicals with single-beam coherent anti-Stokes Raman scattering,” Appl. Opt. 48(4), B17–B22 (2009).
[Crossref] [PubMed]

Xie, X. S.

E. O. Potma, C. L. Evans, and X. S. Xie, ”Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31(2), 241–243 (2006).
[Crossref]

J.-X. Cheng, L. D. Book, and X. S. Xie, ”Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26(17), 1341–1343 (2001).
[Crossref]

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref]

J.-X. Cheng and X. S. Xie, Coherent Raman Scattering Microscopy (CRC, 2012).

Xu, B.

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. 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(3), 393–398 (2011).
[Crossref]

H. Li, D. A. Harris, B. Xu, P. J. Wrzesinski, V. V. Lozovoy, and M. Dantus, “Standoff and arms-length detection of chemicals with single-beam coherent anti-Stokes Raman scattering,” Appl. Opt. 48(4), B17–B22 (2009).
[Crossref] [PubMed]

Zhao, Y.

Zhi, M.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

Zubairy, M. S.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrný, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, “FAST CARS: Engineering a laser spectroscopic technique for rapid identification of bacterial spores,” Proc. Natl. Acad. Sci. U.S.A. 99(17), 10994–11001 (2002).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Wipfler, T. Buckup, and M. Motzkus, ”Multiplexing single-beam coherent anti-Stokes Raman spectroscopy with heterodyne detection,” Appl. Phys. Lett. 100(7), 071102 (2012).
[Crossref]

Cancer research (1)

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 research 70(23), 9562–9569 (2010).
[Crossref] [PubMed]

J. Mod. Opt. (1)

J. M. Levitt, O. Katz, and Y. Silberberg, “Frequency-encoded multiplexed CARS microscopy by rapid pulse shaping,” J. Mod. Opt. 61(10), 872–876 (2014).
[Crossref]

J. Phys. Chem. B (2)

B.-C. Chen and S.-H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-Stokes Raman scattering microscopy,” J. Phys. Chem. B 112(12), 3653–3661 (2008).
[Crossref] [PubMed]

S.-H. Lim, A. G. Caster, O. Nicolet, and S. R. Leone, ”Chemical imaging by single pulse interferometric coherent anti-Stokes Raman scattering microscopy,” J. Phys. Chem. B 110(11), 5196–5204 (2006).
[Crossref] [PubMed]

J. Raman Spectrosc. (2)

P. J. Wrzesinski, D. Pestov, V. V. Lozovoy, B. 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(3), 393–398 (2011).
[Crossref]

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, ”Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

Light Sci. Appl. (1)

C.-S. Liao, M. N. Slipchenko, P. Wang, J. Li, S.-Y. Lee, R. A. Oglesbee, and J.-X. Cheng, ”Microsecond scale vibrational spectroscopic imaging by multiplex stimulated Raman scattering microscopy,” Light Sci. Appl. 4(3), e265 (2015).
[Crossref] [PubMed]

Nature (1)

N. Dudovich, D. Oron, and Y. Silberberg, ”Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[Crossref] [PubMed]

Nature Photonics (1)

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

Opt. Commun. (1)

B. von Vacano and M. Motzkus, ”Time-resolved two color single-beam CARS employing supercontinuum and femtosecond pulse shaping,” Opt. Commun. 264(2), 488–493 (2006).
[Crossref]

Opt. Express (6)

Opt. Lett. (5)

Phys. Rev. Lett. (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(21), 213902 (2003).
[Crossref] [PubMed]

D. L. Marks and S. A. Boppart, “Nonlinear interferometric vibrational imaging,” Phys. Rev. Lett. 92(12), 123905 (2004).
[Crossref] [PubMed]

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref]

F. L. Galeener, R. A. Barrio, E. Martinez, and R. J. Elliott, ”Vibrational decoupling of rings in amorphous solids,” Phys. Rev. Lett. 53(25), 2429 (1984).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrný, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, “FAST CARS: Engineering a laser spectroscopic technique for rapid identification of bacterial spores,” Proc. Natl. Acad. Sci. U.S.A. 99(17), 10994–11001 (2002).
[Crossref] [PubMed]

Rev. Sci. Instrum. (2)

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

Y. Shen, D. V. Voronine, A. V. Sokolov, and M. O. Scully, ”A versatile setup using femtosecond adaptive spectroscopic technique for coherent anti-Stokes Raman scattering,” Rev. Sci. Instrum. 86(8), 083107 (2015).
[Crossref] [PubMed]

Science (1)

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, ”Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316(5822), 265–268 (2007).
[Crossref] [PubMed]

Other (3)

N. B. Colthup, L. H. Daly, and S. E. Wiberley, Introduction to Infrared and Raman Spectroscopy (Academic, 1990).

J.-X. Cheng and X. S. Xie, Coherent Raman Scattering Microscopy (CRC, 2012).

S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University, 1995).

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Figures (6)

Fig. 1
Fig. 1 Schematic of the single-beam heterodyne FAST CARS. (a) Energy diagram of the FAST CARS scheme. (b) Spectral intensity of the excitation pulse with the probe and pump/Stokes parts marked with red and black lines, respectively. (c) Anti-Stokes signals I+(ω) (red) and I(ω) (blue) simulated corresponding to delays τ0 + δτ and τ0δτ, respectively, with τ0 ≈ 0. Inset shows the constructive (red) and destructive (blue) interferences between the FAST CARS signal and the FWM LO. (d) FAST CARS signal retrieved from the spectra in (c) using Eq. (1).
Fig. 2
Fig. 2 Single-beam heterodyne FAST CARS of TeCA using the forward detection: (a) 2D plot of the heterodyne FAST CARS spectra at different probe delays. (b) Heterodyne FAST CARS signal at 0 (black), 0.6 (red), and 1.2 ps (blue) delay. (c) FAST CARS signal of TeCA at zero probe delay from [29]. (d) Spontaneous Raman spectrum of TeCA. Spectra in (b) are normalized to the same factor.
Fig. 3
Fig. 3 FAST CARS spectra of fused silica using the forward detection at different probe delays: (a) 0 ps, (b) 0.2 ps, (c) 0.4 ps, (d) 0.6 ps, (e) 0.8 ps, and (f) 1 ps.
Fig. 4
Fig. 4 Input power and concentration dependence of the CCl4 FAST CARS signal measured in the forward detection. (a) Retrieved FAST CARS spectrum from CCl4 at zero probe delay. (b) Log-log plot of the intensity of the 459 cm−1 peak as a function of the laser power. (c) Intensity of the 459 cm−1 peak measured at different concentrations of CCl4 in acetone.
Fig. 5
Fig. 5 Epi-detection FAST CARS microscopy of Si and MoS2 microstructures. Optical images of the structured Si (a) and MoS2 flake (d) samples, with scale bars of 2μm. FAST CARS spectra of Si (b) and MoS2 (e) plotted in black lines compared to the background in red lines, with corresponding FAST CARS images in (c) and (f), respectively, using the Si peak at 520 cm−1 and the MoS2 peak at 385 cm−1. The two spectra in (b) were acquired at (6.4 μm, 6.4 μm) (black) and (4.0 μm, 4.0 μm) (red) corresponding to the image in (c), and the two spectra in (e) were acquired at (4.6 μm, 3.8 μm) (black) and (1.0 μm, 2.2 μm) (red) corresponding to (f).
Fig. 6
Fig. 6 Experimental setup: DC, chirp mirror pair for dispersion compensation; LPF, long-pass filter; G, grating; CM, concave mirror; M, mirror; SPF, short-pass filter; L, lens; Obj, microscope objective; S, sample on X–Y translation stage; spec, spectrometer. The excitation and FAST CARS beams are shown by red and green colors, respectively.

Equations (14)

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I CARS = I + ( ω ) I ( ω ) I + ( ω ) + I ( ω ) ,
I CARS ( Input power ) 1.5 .
P ( ω ) [ E pr ( ω Ω ) χ ( Ω ) + E p s ( ω Ω ) χ ( Ω ) ] A ( Ω ) d Ω ,
A ( Ω ) = E * ( ω ) E ( Ω + ω ) d ω ,
χ ( Ω ) = χ N R ( Ω ) + χ R ( Ω ) = χ N R ( Ω ) + m A m Ω R m Ω + i Γ R m .
P ( ω ) E pr ( ω Ω ) e i ( ω Ω ) τ χ ( Ω ) A ( Ω ) d Ω + P FWM ps ( ω ) .
f ( ω ) E pr ( ω Ω ) e i ( ω Ω ) τ 0 χ ( Ω ) A ( Ω ) d Ω ,
P + ( ω ) = { Re [ f ( ω ) ] cos ( ω pr δ τ ) + Im [ f ( ω ) ] sin ( ω pr δ τ ) } + i { Im [ f ( ω ) ] cos ( ω pr δ τ ) Re [ f ( ω ) ] sin ( ω pr δ τ ) } + P FWM ps ( ω ) ,
P ( ω ) = { Re [ f ( ω ) ] cos ( ω pr δ τ ) Im [ f ( ω ) ] sin ( ω pr δ τ ) } + i { Im [ f ( ω ) ] cos ( ω pr δ τ ) + Re [ f ( ω ) ] sin ( ω pr δ τ ) } + P FWM ps ( ω ) .
I + ( ω ) I ( ω ) | P + ( ω ) | 2 | P ( ω ) | 2 4 P FWM ps ( ω ) Im [ f ( ω ) ] sin ( ω pr δ τ ) ,
I CARS = I + ( ω ) I ( ω ) I + ( ω ) + I ( ω ) Im [ f ( ω ) ] .
I CARS E pr ( ω Ω ) A ( Ω ) { Im [ χ ( Ω ) ] cos [ ( ω Ω ) τ 0 ] Re [ χ ( Ω ) ] sin [ ( ω Ω ) τ 0 ] } d Ω .
I + ( ω ) I ( ω ) 4 sin ( ω pr δ τ ) { Re [ P FWM ps ( ω ) ] Im [ f ( ω ) ] Im [ P FWM ps ( ω ) ] Re [ f ( ω ) ] } ,
I CARS E pr ( ω Ω ) A ( Ω ) { Im [ χ ( Ω ) ] cos [ ( ω Ω ) τ 0 + θ ( ω ) ] Re [ χ ( Ω ) ] sin [ ( ω Ω ) τ 0 + θ ( ω ) ] } d Ω .

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