Abstract

Pulse shaping techniques are used to improve the selectivity of broadband CARS experiments, and to reject the overwhelming background. Knowledge about the fitness landscape and the capability of tailoring it is crucial for both fundamental insight and performing an efficient optimization of phase shapes. We use an evolutionary algorithm to find the optimal spectral phase of the broadband pump and probe beams in a background-suppressed shaped CARS process. We then investigate the shapes, symmetries, and topologies of the landscape contour lines around the optimal solution and also around the point corresponding to zero phase. We demonstrate the significance of the employed phase bases in achieving convex contour lines, suppressed local optima, and high optimization fitness with a few (and even a single) optimization parameter.

© 2010 OSA

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2010 (1)

P. van der Walle, H. L. Offerhaus, J. L. Herek, and A. Jafarpour, “Tailoring a coherent control solution landscape by linear transforms of spectral phase basis,” Opt. Express 18(2), 973–987 (2010).
[CrossRef]

2009 (7)

A. C. W. van Rhijn, S. Postma, J. P. Korterik, J. L. Herek, and H. L. Offerhaus, “Chemically selective imaging by spectral phase shaping for broadband CARS around 3000 cm−1,” J. Opt. Soc. Am. B 26(3), 559–563 (2009).
[CrossRef]

Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem. 60(1), 277–292 (2009).
[CrossRef] [PubMed]

S. Mukamel, “Controlling multidimensional off-resonant-Raman and infrared vibrational spectroscopy by finite pulse band shapes,” J. Chem. Phys. 130(5), 054110 (2009).
[CrossRef] [PubMed]

Y. J. Lee and M. T. Cicerone, “Single-shot interferometric approach to background free broadband coherent anti-Stokes Raman scattering spectroscopy,” Opt. Express 17(1), 123–135 (2009).
[CrossRef] [PubMed]

Y. Liu, Y. J. Lee, and M. T. Cicerone, “Fast extraction of resonant vibrational response from CARS spectra with arbitrary nonresonant background,” J. Raman Spectrosc. 40(7), 726–731 (2009).
[CrossRef]

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[CrossRef] [PubMed]

A. Jafarpour, J. Savolainen, R. de Jong, J. Middag, D. P. Sprünken, P. van der Walle, D. Yang, and J. L. Herek, “Robust orthogonal parameterization of evolution strategy for adaptive laser pulse shaping,” Opt. Express 17(14), 11986–12000 (2009).
[CrossRef] [PubMed]

2008 (6)

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. Pezeshki, M. Schreiber, and U. Kleinekathöfer, “Shaping femtosecond coherent anti-Stokes Raman spectra using optimal control theory,” Phys. Chem. Chem. Phys. 10(15), 2058–2066 (2008).
[CrossRef] [PubMed]

S. Postma, A. C. W. van Rhijn, J. P. Korterik, P. Gross, J. L. Herek, and H. L. Offerhaus, “Application of spectral phase shaping to high resolution CARS spectroscopy,” Opt. Express 16(11), 7985–7996 (2008).
[CrossRef] [PubMed]

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(8), 5499–5504 (2008).
[CrossRef] [PubMed]

X. G. Xu, S. O. Konorov, J. W. Hepburn, and V. Milner, “Noise autocorrelation spectroscopy with coherent Raman scattering,” Nat. Phys. 4(2), 125–129 (2008).
[CrossRef]

R. Fanciulli, L. Willmes, J. Savolainen, P. van der Walle, T. Bäck, and J. L. Herek, “Evolution strategies for laser pulse compression,” Lect. Notes Comput. Sci. 4926, 219–230 (2008).
[CrossRef]

2007 (7)

M. Telescu, N. Tanguy, P. Bréhonnet, and P. Vilbé, “Efficient Gram-matrix computation for irrational resonant systems using Kautz models,” Signal Process. 87(12), 3234–3240 (2007).
[CrossRef]

L. Cheng and D. Y. Kim, “Differential imaging in coherent anti-Stokes Raman scattering microscopy with Laguerre- Gaussian excitation beams,” Opt. Express 15(16), 10123–10134 (2007).
[CrossRef] [PubMed]

S. A. Malinovskaya and V. S. Malinovsky, “Chirped-pulse adiabatic control in coherent anti-Stokes Raman scattering for imaging of biological structure and dynamics,” Opt. Lett. 32(6), 707–709 (2007).
[CrossRef] [PubMed]

S.-H. Lim, A. G. Caster, and S. R. Leone, “Fourier transform spectral interferometric coherent anti-Stokes Raman scattering (FTSI-CARS) spectroscopy,” Opt. Lett. 32(10), 1332–1334 (2007).
[CrossRef] [PubMed]

S. Zhang, L. Zhang, X. Zhang, L. Ding, G. Chen, Z. Sun, and Z. Wang, “Selective excitation of CARS by adaptive pulse shaping based on genetic algorithm,” Chem. Phys. Lett. 433(4–6), 416–421 (2007).
[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]

S. O. Konorov, X. G. Xu, R. F. Turner, M. W. Blades, J. W. Hepburn, and V. Milner, “Pulse optimization for Raman spectroscopy with cross-correlation frequency resolved optical gating,” Opt. Express 15(12), 7564–7571 (2007).
[CrossRef] [PubMed]

2006 (3)

J. Konradi, A. K. Singh, A. V. Scaria, and A. Materny, “Selective spectral filtering of molecular modes of beta-carotene in solution using optimal control in four-wave-mixing spectroscopy,” J. Raman Spectrosc. 37(6), 697–704 (2006).
[CrossRef]

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

2005 (1)

J. Konradi, A. K. Singh, and A. Materny, “Mode-focusing in molecules by feedback-controlled shaping of femtosecond laser pulses,” Phys. Chem. Chem. Phys. 7, 3574–3579 (2005).
[CrossRef]

2004 (1)

J.-X. Cheng and X. S. Xie, “Coherent Anti-Stokes Raman Scattering Microscopy: Instrumentation, Theory, and Applications,” J. Phys. Chem. B 108(3), 827–840 (2004).
[CrossRef]

2003 (1)

T. Brixner, N. H. Damrauer, B. Kiefer, and G. Gerber, “Liquid-phase adaptive femtosecond quantum control: Removing intrinsic intensity dependencies,” J. Chem. Phys. 118(8), 3692 (2003).
[CrossRef]

2002 (4)

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, “Quantum control of coherent anti-Stokes Raman processes,” Phys. Rev. A 65(4), 043408 (2002).
[CrossRef]

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417(6888), 533–535 (2002).
[CrossRef] [PubMed]

J. X. Chen, A. Volkmer, L. D. Book, and ., “Multiplex coherent anti-stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106(34), 8493–8498 (2002).
[CrossRef]

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

1999 (2)

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60(2), 1287–1292 (1999).
[CrossRef]

U. Forssell and L. Ljung, “Closed-loop identification revisited,” Automatica 35(7), 1215–1241 (1999).
[CrossRef]

1992 (1)

R. S. Judson and H. Rabitz, “Teaching lasers to control molecules,” Phys. Rev. Lett. 68(10), 1500–1503 (1992).
[CrossRef] [PubMed]

1991 (1)

A. M. Weiner, D. E. Leaird, P. G. Wiederrecht, and K. A. Nelson, “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8(6), 1264–1275 (1991).
[CrossRef]

1986 (1)

P. Brumer and M. Shapiro, “Control of unimolecular reactions using coherent light,” Chem. Phys. Lett. 126(6), 541–546 (1986).
[CrossRef]

1976 (1)

J. J. Song, G. L. Eesley, and M. D. Levenson, “Background suppression in coherent Raman spectroscopy,” Appl. Phys. Lett. 29(9), 567 (1976).
[CrossRef]

1962 (1)

R. E. Kalman, “Canonical structure of linear dynamical systems,” Proc. Natl. Acad. Sci. U.S.A. 48(4), 596–600 (1962).
[CrossRef] [PubMed]

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]

Bäck, T.

R. Fanciulli, L. Willmes, J. Savolainen, P. van der Walle, T. Bäck, and J. L. Herek, “Evolution strategies for laser pulse compression,” Lect. Notes Comput. Sci. 4926, 219–230 (2008).
[CrossRef]

Blades, M. W.

S. O. Konorov, X. G. Xu, R. F. Turner, M. W. Blades, J. W. Hepburn, and V. Milner, “Pulse optimization for Raman spectroscopy with cross-correlation frequency resolved optical gating,” Opt. Express 15(12), 7564–7571 (2007).
[CrossRef] [PubMed]

Book, L. D.

J. X. Chen, A. Volkmer, L. D. Book, and ., “Multiplex coherent anti-stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106(34), 8493–8498 (2002).
[CrossRef]

Bréhonnet, P.

M. Telescu, N. Tanguy, P. Bréhonnet, and P. Vilbé, “Efficient Gram-matrix computation for irrational resonant systems using Kautz models,” Signal Process. 87(12), 3234–3240 (2007).
[CrossRef]

Brixner, T.

T. Brixner, N. H. Damrauer, B. Kiefer, and G. Gerber, “Liquid-phase adaptive femtosecond quantum control: Removing intrinsic intensity dependencies,” J. Chem. Phys. 118(8), 3692 (2003).
[CrossRef]

Brumer, P.

P. Brumer and M. Shapiro, “Control of unimolecular reactions using coherent light,” Chem. Phys. Lett. 126(6), 541–546 (1986).
[CrossRef]

Caster, A. G.

S.-H. Lim, A. G. Caster, and S. R. Leone, “Fourier transform spectral interferometric coherent anti-Stokes Raman scattering (FTSI-CARS) spectroscopy,” Opt. Lett. 32(10), 1332–1334 (2007).
[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]

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]

Chen, G.

S. Zhang, L. Zhang, X. Zhang, L. Ding, G. Chen, Z. Sun, and Z. Wang, “Selective excitation of CARS by adaptive pulse shaping based on genetic algorithm,” Chem. Phys. Lett. 433(4–6), 416–421 (2007).
[CrossRef]

Chen, J. X.

J. X. Chen, A. Volkmer, L. D. Book, and ., “Multiplex coherent anti-stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106(34), 8493–8498 (2002).
[CrossRef]

Cheng, J.-X.

J.-X. Cheng and X. S. Xie, “Coherent Anti-Stokes Raman Scattering Microscopy: Instrumentation, Theory, and Applications,” J. Phys. Chem. B 108(3), 827–840 (2004).
[CrossRef]

Cheng, L.

L. Cheng and D. Y. Kim, “Differential imaging in coherent anti-Stokes Raman scattering microscopy with Laguerre- Gaussian excitation beams,” Opt. Express 15(16), 10123–10134 (2007).
[CrossRef] [PubMed]

Cicerone, M. T.

Y. Liu, Y. J. Lee, and M. T. Cicerone, “Fast extraction of resonant vibrational response from CARS spectra with arbitrary nonresonant background,” J. Raman Spectrosc. 40(7), 726–731 (2009).
[CrossRef]

Y. J. Lee and M. T. Cicerone, “Single-shot interferometric approach to background free broadband coherent anti-Stokes Raman scattering spectroscopy,” Opt. Express 17(1), 123–135 (2009).
[CrossRef] [PubMed]

Cogdell, R. J.

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417(6888), 533–535 (2002).
[CrossRef] [PubMed]

Damrauer, N. H.

T. Brixner, N. H. Damrauer, B. Kiefer, and G. Gerber, “Liquid-phase adaptive femtosecond quantum control: Removing intrinsic intensity dependencies,” J. Chem. Phys. 118(8), 3692 (2003).
[CrossRef]

Dantus, M.

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(8), 5499–5504 (2008).
[CrossRef] [PubMed]

de Jong, R.

A. Jafarpour, J. Savolainen, R. de Jong, J. Middag, D. P. Sprünken, P. van der Walle, D. Yang, and J. L. Herek, “Robust orthogonal parameterization of evolution strategy for adaptive laser pulse shaping,” Opt. Express 17(14), 11986–12000 (2009).
[CrossRef] [PubMed]

Ding, L.

S. Zhang, L. Zhang, X. Zhang, L. Ding, G. Chen, Z. Sun, and Z. Wang, “Selective excitation of CARS by adaptive pulse shaping based on genetic algorithm,” Chem. Phys. Lett. 433(4–6), 416–421 (2007).
[CrossRef]

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]

Dudovich, N.

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, “Quantum control of coherent anti-Stokes Raman processes,” Phys. Rev. A 65(4), 043408 (2002).
[CrossRef]

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

Eesley, G. L.

J. J. Song, G. L. Eesley, and M. D. Levenson, “Background suppression in coherent Raman spectroscopy,” Appl. Phys. Lett. 29(9), 567 (1976).
[CrossRef]

Fanciulli, R.

R. Fanciulli, L. Willmes, J. Savolainen, P. van der Walle, T. Bäck, and J. L. Herek, “Evolution strategies for laser pulse compression,” Lect. Notes Comput. Sci. 4926, 219–230 (2008).
[CrossRef]

Forssell, U.

U. Forssell and L. Ljung, “Closed-loop identification revisited,” Automatica 35(7), 1215–1241 (1999).
[CrossRef]

Gerber, G.

T. Brixner, N. H. Damrauer, B. Kiefer, and G. Gerber, “Liquid-phase adaptive femtosecond quantum control: Removing intrinsic intensity dependencies,” J. Chem. Phys. 118(8), 3692 (2003).
[CrossRef]

Gross, P.

S. Postma, A. C. W. van Rhijn, J. P. Korterik, P. Gross, J. L. Herek, and H. L. Offerhaus, “Application of spectral phase shaping to high resolution CARS spectroscopy,” Opt. Express 16(11), 7985–7996 (2008).
[CrossRef] [PubMed]

Harris, D. A.

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(8), 5499–5504 (2008).
[CrossRef] [PubMed]

Hepburn, J. W.

X. G. Xu, S. O. Konorov, J. W. Hepburn, and V. Milner, “Noise autocorrelation spectroscopy with coherent Raman scattering,” Nat. Phys. 4(2), 125–129 (2008).
[CrossRef]

S. O. Konorov, X. G. Xu, R. F. Turner, M. W. Blades, J. W. Hepburn, and V. Milner, “Pulse optimization for Raman spectroscopy with cross-correlation frequency resolved optical gating,” Opt. Express 15(12), 7564–7571 (2007).
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P. van der Walle, H. L. Offerhaus, J. L. Herek, and A. Jafarpour, “Tailoring a coherent control solution landscape by linear transforms of spectral phase basis,” Opt. Express 18(2), 973–987 (2010).
[CrossRef]

A. C. W. van Rhijn, S. Postma, J. P. Korterik, J. L. Herek, and H. L. Offerhaus, “Chemically selective imaging by spectral phase shaping for broadband CARS around 3000 cm−1,” J. Opt. Soc. Am. B 26(3), 559–563 (2009).
[CrossRef]

A. Jafarpour, J. Savolainen, R. de Jong, J. Middag, D. P. Sprünken, P. van der Walle, D. Yang, and J. L. Herek, “Robust orthogonal parameterization of evolution strategy for adaptive laser pulse shaping,” Opt. Express 17(14), 11986–12000 (2009).
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M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[CrossRef] [PubMed]

S. Postma, A. C. W. van Rhijn, J. P. Korterik, P. Gross, J. L. Herek, and H. L. Offerhaus, “Application of spectral phase shaping to high resolution CARS spectroscopy,” Opt. Express 16(11), 7985–7996 (2008).
[CrossRef] [PubMed]

R. Fanciulli, L. Willmes, J. Savolainen, P. van der Walle, T. Bäck, and J. L. Herek, “Evolution strategies for laser pulse compression,” Lect. Notes Comput. Sci. 4926, 219–230 (2008).
[CrossRef]

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417(6888), 533–535 (2002).
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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).
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P. van der Walle, H. L. Offerhaus, J. L. Herek, and A. Jafarpour, “Tailoring a coherent control solution landscape by linear transforms of spectral phase basis,” Opt. Express 18(2), 973–987 (2010).
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A. Jafarpour, J. Savolainen, R. de Jong, J. Middag, D. P. Sprünken, P. van der Walle, D. Yang, and J. L. Herek, “Robust orthogonal parameterization of evolution strategy for adaptive laser pulse shaping,” Opt. Express 17(14), 11986–12000 (2009).
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M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
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S. Pezeshki, M. Schreiber, and U. Kleinekathöfer, “Shaping femtosecond coherent anti-Stokes Raman spectra using optimal control theory,” Phys. Chem. Chem. Phys. 10(15), 2058–2066 (2008).
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X. G. Xu, S. O. Konorov, J. W. Hepburn, and V. Milner, “Noise autocorrelation spectroscopy with coherent Raman scattering,” Nat. Phys. 4(2), 125–129 (2008).
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S. O. Konorov, X. G. Xu, R. F. Turner, M. W. Blades, J. W. Hepburn, and V. Milner, “Pulse optimization for Raman spectroscopy with cross-correlation frequency resolved optical gating,” Opt. Express 15(12), 7564–7571 (2007).
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J. Konradi, A. K. Singh, A. V. Scaria, and A. Materny, “Selective spectral filtering of molecular modes of beta-carotene in solution using optimal control in four-wave-mixing spectroscopy,” J. Raman Spectrosc. 37(6), 697–704 (2006).
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J. Konradi, A. K. Singh, and A. Materny, “Mode-focusing in molecules by feedback-controlled shaping of femtosecond laser pulses,” Phys. Chem. Chem. Phys. 7, 3574–3579 (2005).
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A. C. W. van Rhijn, S. Postma, J. P. Korterik, J. L. Herek, and H. L. Offerhaus, “Chemically selective imaging by spectral phase shaping for broadband CARS around 3000 cm−1,” J. Opt. Soc. Am. B 26(3), 559–563 (2009).
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M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
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S. Postma, A. C. W. van Rhijn, J. P. Korterik, P. Gross, J. L. Herek, and H. L. Offerhaus, “Application of spectral phase shaping to high resolution CARS spectroscopy,” Opt. Express 16(11), 7985–7996 (2008).
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A. M. Weiner, D. E. Leaird, P. G. Wiederrecht, and K. A. Nelson, “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8(6), 1264–1275 (1991).
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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).
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J. Konradi, A. K. Singh, A. V. Scaria, and A. Materny, “Selective spectral filtering of molecular modes of beta-carotene in solution using optimal control in four-wave-mixing spectroscopy,” J. Raman Spectrosc. 37(6), 697–704 (2006).
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D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60(2), 1287–1292 (1999).
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A. Jafarpour, J. Savolainen, R. de Jong, J. Middag, D. P. Sprünken, P. van der Walle, D. Yang, and J. L. Herek, “Robust orthogonal parameterization of evolution strategy for adaptive laser pulse shaping,” Opt. Express 17(14), 11986–12000 (2009).
[CrossRef] [PubMed]

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X. G. Xu, S. O. Konorov, J. W. Hepburn, and V. Milner, “Noise autocorrelation spectroscopy with coherent Raman scattering,” Nat. Phys. 4(2), 125–129 (2008).
[CrossRef]

S. O. Konorov, X. G. Xu, R. F. Turner, M. W. Blades, J. W. Hepburn, and V. Milner, “Pulse optimization for Raman spectroscopy with cross-correlation frequency resolved optical gating,” Opt. Express 15(12), 7564–7571 (2007).
[CrossRef] [PubMed]

Motzkus, M.

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

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417(6888), 533–535 (2002).
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A. M. Weiner, D. E. Leaird, P. G. Wiederrecht, and K. A. Nelson, “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8(6), 1264–1275 (1991).
[CrossRef]

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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]

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P. van der Walle, H. L. Offerhaus, J. L. Herek, and A. Jafarpour, “Tailoring a coherent control solution landscape by linear transforms of spectral phase basis,” Opt. Express 18(2), 973–987 (2010).
[CrossRef]

A. C. W. van Rhijn, S. Postma, J. P. Korterik, J. L. Herek, and H. L. Offerhaus, “Chemically selective imaging by spectral phase shaping for broadband CARS around 3000 cm−1,” J. Opt. Soc. Am. B 26(3), 559–563 (2009).
[CrossRef]

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[CrossRef] [PubMed]

S. Postma, A. C. W. van Rhijn, J. P. Korterik, P. Gross, J. L. Herek, and H. L. Offerhaus, “Application of spectral phase shaping to high resolution CARS spectroscopy,” Opt. Express 16(11), 7985–7996 (2008).
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D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, “Quantum control of coherent anti-Stokes Raman processes,” Phys. Rev. A 65(4), 043408 (2002).
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N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
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M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
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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).
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S. Pezeshki, M. Schreiber, and U. Kleinekathöfer, “Shaping femtosecond coherent anti-Stokes Raman spectra using optimal control theory,” Phys. Chem. Chem. Phys. 10(15), 2058–2066 (2008).
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A. C. W. van Rhijn, S. Postma, J. P. Korterik, J. L. Herek, and H. L. Offerhaus, “Chemically selective imaging by spectral phase shaping for broadband CARS around 3000 cm−1,” J. Opt. Soc. Am. B 26(3), 559–563 (2009).
[CrossRef]

S. Postma, A. C. W. van Rhijn, J. P. Korterik, P. Gross, J. L. Herek, and H. L. Offerhaus, “Application of spectral phase shaping to high resolution CARS spectroscopy,” Opt. Express 16(11), 7985–7996 (2008).
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R. S. Judson and H. Rabitz, “Teaching lasers to control molecules,” Phys. Rev. Lett. 68(10), 1500–1503 (1992).
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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).
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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).
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A. Jafarpour, J. Savolainen, R. de Jong, J. Middag, D. P. Sprünken, P. van der Walle, D. Yang, and J. L. Herek, “Robust orthogonal parameterization of evolution strategy for adaptive laser pulse shaping,” Opt. Express 17(14), 11986–12000 (2009).
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J. Konradi, A. K. Singh, A. V. Scaria, and A. Materny, “Selective spectral filtering of molecular modes of beta-carotene in solution using optimal control in four-wave-mixing spectroscopy,” J. Raman Spectrosc. 37(6), 697–704 (2006).
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S. Pezeshki, M. Schreiber, and U. Kleinekathöfer, “Shaping femtosecond coherent anti-Stokes Raman spectra using optimal control theory,” Phys. Chem. Chem. Phys. 10(15), 2058–2066 (2008).
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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).
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[CrossRef]

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

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60(2), 1287–1292 (1999).
[CrossRef]

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J. Konradi, A. K. Singh, A. V. Scaria, and A. Materny, “Selective spectral filtering of molecular modes of beta-carotene in solution using optimal control in four-wave-mixing spectroscopy,” J. Raman Spectrosc. 37(6), 697–704 (2006).
[CrossRef]

J. Konradi, A. K. Singh, and A. Materny, “Mode-focusing in molecules by feedback-controlled shaping of femtosecond laser pulses,” Phys. Chem. Chem. Phys. 7, 3574–3579 (2005).
[CrossRef]

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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]

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J. J. Song, G. L. Eesley, and M. D. Levenson, “Background suppression in coherent Raman spectroscopy,” Appl. Phys. Lett. 29(9), 567 (1976).
[CrossRef]

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A. Jafarpour, J. Savolainen, R. de Jong, J. Middag, D. P. Sprünken, P. van der Walle, D. Yang, and J. L. Herek, “Robust orthogonal parameterization of evolution strategy for adaptive laser pulse shaping,” Opt. Express 17(14), 11986–12000 (2009).
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S. Zhang, L. Zhang, X. Zhang, L. Ding, G. Chen, Z. Sun, and Z. Wang, “Selective excitation of CARS by adaptive pulse shaping based on genetic algorithm,” Chem. Phys. Lett. 433(4–6), 416–421 (2007).
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S. O. Konorov, X. G. Xu, R. F. Turner, M. W. Blades, J. W. Hepburn, and V. Milner, “Pulse optimization for Raman spectroscopy with cross-correlation frequency resolved optical gating,” Opt. Express 15(12), 7564–7571 (2007).
[CrossRef] [PubMed]

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P. van der Walle, H. L. Offerhaus, J. L. Herek, and A. Jafarpour, “Tailoring a coherent control solution landscape by linear transforms of spectral phase basis,” Opt. Express 18(2), 973–987 (2010).
[CrossRef]

A. Jafarpour, J. Savolainen, R. de Jong, J. Middag, D. P. Sprünken, P. van der Walle, D. Yang, and J. L. Herek, “Robust orthogonal parameterization of evolution strategy for adaptive laser pulse shaping,” Opt. Express 17(14), 11986–12000 (2009).
[CrossRef] [PubMed]

R. Fanciulli, L. Willmes, J. Savolainen, P. van der Walle, T. Bäck, and J. L. Herek, “Evolution strategies for laser pulse compression,” Lect. Notes Comput. Sci. 4926, 219–230 (2008).
[CrossRef]

van Rhijn, A. C. W.

A. C. W. van Rhijn, S. Postma, J. P. Korterik, J. L. Herek, and H. L. Offerhaus, “Chemically selective imaging by spectral phase shaping for broadband CARS around 3000 cm−1,” J. Opt. Soc. Am. B 26(3), 559–563 (2009).
[CrossRef]

S. Postma, A. C. W. van Rhijn, J. P. Korterik, P. Gross, J. L. Herek, and H. L. Offerhaus, “Application of spectral phase shaping to high resolution CARS spectroscopy,” Opt. Express 16(11), 7985–7996 (2008).
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M. Telescu, N. Tanguy, P. Bréhonnet, and P. Vilbé, “Efficient Gram-matrix computation for irrational resonant systems using Kautz models,” Signal Process. 87(12), 3234–3240 (2007).
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B. vonvacano and M. Motzkus, “Time-resolved two color single-beam CARS employing supercontinuum and femtosecond pulse shaping,” Opt. Commun. 264(2), 488–493 (2006).
[CrossRef]

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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]

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S. Zhang, L. Zhang, X. Zhang, L. Ding, G. Chen, Z. Sun, and Z. Wang, “Selective excitation of CARS by adaptive pulse shaping based on genetic algorithm,” Chem. Phys. Lett. 433(4–6), 416–421 (2007).
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A. M. Weiner, D. E. Leaird, P. G. Wiederrecht, and K. A. Nelson, “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8(6), 1264–1275 (1991).
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A. M. Weiner, D. E. Leaird, P. G. Wiederrecht, and K. A. Nelson, “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8(6), 1264–1275 (1991).
[CrossRef]

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R. Fanciulli, L. Willmes, J. Savolainen, P. van der Walle, T. Bäck, and J. L. Herek, “Evolution strategies for laser pulse compression,” Lect. Notes Comput. Sci. 4926, 219–230 (2008).
[CrossRef]

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J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417(6888), 533–535 (2002).
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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(8), 5499–5504 (2008).
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Figures (12)

Fig. 1
Fig. 1

Semi-classical description of the CARS process: (left) coupled interactions of the electric field E, the magnetic field H, and the linear/nonlinear components of polarization PL/PNL, and (right) the energy diagrams of resonant and non-resonant CARS, showing the pump ( = probe), the Stokes, and the CARS beams in green, red, and blue, respectively.

Fig. 2
Fig. 2

Amplitude/phase of polystyrene Raman spectrum and Stokes-shifted excitation pulse.

Fig. 3
Fig. 3

1D landscapes around the optimal point with (left) polynomials and (right) Kautz bases.

Fig. 4
Fig. 4

2D landscapes around the optimal point with polynomials (top row) even orders of 2,4, and 6 with the third order, (middle) even orders of 2,4, and 6 with the fifth order, and (bottom) orders with similar parities: 2-4, 2-6, 3-5, and 4-6.

Fig. 5
Fig. 5

2D landscapes around the optimal point with Kautz functions (top row) even orders of 0, 2, and 4 with the first order, (middle) even orders of 0, 2, and 4 with the third order, and (bottom) orders with similar parities: 0-2, 0-4, 1-3, and 2-4.

Fig. 6
Fig. 6

3D level sets around the optimal point corresponding to similar fitness values (56% of the maximum fitness) with (left) Kautz and (right) polynomial functions.

Fig. 7
Fig. 7

Modified 2D landscapes obtained by adding a scaled second order polynomial to (left) the third order and (right) the fourth order polynomials.

Fig. 8
Fig. 8

1D landscape around the zero phase with (left) polynomials and (right) Kautz bases.

Fig. 9
Fig. 9

2D landscape around the zero phase with polynomials

Fig. 10
Fig. 10

2D landscape around the zero phase with Kautz functions

Fig. 11
Fig. 11

3D level sets around the zero point corresponding to comparable fitness values (56% of the local maximum fitness in each case) with (left) Kautz and (right) polynomial functions.

Fig. 12
Fig. 12

(Left) Optimal phase profile for enhancing the background-suppressed CARS signal from polystyrene and reducing the corresponding signal from PMMA, and (right) the effect of giving different weights to the CARS energies of PMMA and polystyrene in the definition of the fitness function. The optimized profile shown in black in the left panel corresponds to the case of μ = 1. Solid lines on the right panel are just guides to the eye. The right panel has a linear scale in the interval [0,2].

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