Abstract

We experimentally demonstrate spatiotemporal focusing of light on single nanocrystals embedded inside a strongly scattering medium. Our approach is based on spatial wave front shaping of short pulses, using second harmonic generation inside the target nanocrystals as the feedback signal. We successfully develop a model both for the achieved pulse duration as well as the observed enhancement of the feedback signal. The approach enables exciting opportunities for studies of light propagation in the presence of strong scattering as well as for applications in imaging, micro- and nanomanipulation, coherent control and spectroscopy in complex media.

© 2012 OSA

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  1. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett.32(16), 2309–2311 (2007).
    [CrossRef] [PubMed]
  2. T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
    [CrossRef]
  3. E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
    [CrossRef] [PubMed]
  4. I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials, ” Opt. Express16(1), 67–80 (2008).
    [CrossRef] [PubMed]
  5. M. Fink, “Time reversed acoustics,” Phys. Today50(3), 34–40 (1997).
    [CrossRef]
  6. G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science315, 1120–1122 (2007).
    [CrossRef] [PubMed]
  7. M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express18(4), 3444–3455 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett.101, 081108 (2012).
    [CrossRef]
  10. J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
    [CrossRef] [PubMed]
  11. O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics5, 372–377 (2011).
    [CrossRef]
  12. J. Aulbach, A. Bretagne, M. Fink, M. Tanter, and A. Tourin, “Optimal spatiotemporal focusing through complex scattering media,” Phys. Rev. E85, 016605 (2012).
    [CrossRef]
  13. F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Meth.2, 932–940 (2005).
    [CrossRef]
  14. P. C. Ray, “Size and shape dependent second order nonlinear optical properties of nanomaterials and its application in biological and chemical sensing,” Chem. Rev.110(9), 5332–5365 (2010).
    [CrossRef] [PubMed]
  15. C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Second harmonic generation from nanocrystals under linearly and circularly polarized excitations,” Opt. Express18, 11917–11932 (2010).
    [CrossRef] [PubMed]
  16. L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
    [CrossRef]
  17. R. Grange, T. Lanvin, C. L. Hsieh, Y. Pu, and D. Psaltis, “Imaging with second-harmonic radiation probes in living tissue,” Biomed. Opt. Express2(9), 2532–2539 (2011).
    [CrossRef] [PubMed]
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  19. J. C. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt.24(9), 1270–1282 (1985).
    [CrossRef] [PubMed]
  20. D. J. Thouless, “Maximum metallic resistance in thin wires,” Phys. Rev. Lett.39, 1167–1169 (1977).
    [CrossRef]
  21. R. Landauer and M. Buttiker, “Diffusive traversal time: effective area in magnetically induced interference,” Phys. Rev. B36, 6255–6260 (1987).
    [CrossRef]
  22. I. M. Vellekoop, P. Lodahl, and A. Lagendijk, “Determination of the diffusion constant using phase-sensitive measurements,” Phys. Rev. E71, 056604 (2005).
    [CrossRef]
  23. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).
  24. S. Roke and G. Gonella, “Nonlinear light scattering and spectroscopy of particles and droplets in liquids,” Annu. Rev. Phys. Chem.63, 353–378 (2012)
    [CrossRef] [PubMed]
  25. E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Optimal concentration of light in turbid materials,” J. Opt. Soc. Am. B28(5), 1200–1203 (2011).
    [CrossRef]
  26. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A253, 358–379 (1959).
    [CrossRef]
  27. J. W. Goodman, Statistical Optics (Wiley, 2000).
  28. I. M. Vellekoop and A.P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281(11), 3071–3080 (2008).
    [CrossRef]
  29. D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” Opt. Express20(5), 4840–4849 (2012).
    [CrossRef] [PubMed]

2012 (4)

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett.101, 081108 (2012).
[CrossRef]

J. Aulbach, A. Bretagne, M. Fink, M. Tanter, and A. Tourin, “Optimal spatiotemporal focusing through complex scattering media,” Phys. Rev. E85, 016605 (2012).
[CrossRef]

S. Roke and G. Gonella, “Nonlinear light scattering and spectroscopy of particles and droplets in liquids,” Annu. Rev. Phys. Chem.63, 353–378 (2012)
[CrossRef] [PubMed]

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” Opt. Express20(5), 4840–4849 (2012).
[CrossRef] [PubMed]

2011 (5)

E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Optimal concentration of light in turbid materials,” J. Opt. Soc. Am. B28(5), 1200–1203 (2011).
[CrossRef]

R. Grange, T. Lanvin, C. L. Hsieh, Y. Pu, and D. Psaltis, “Imaging with second-harmonic radiation probes in living tissue,” Biomed. Opt. Express2(9), 2532–2539 (2011).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics5, 372–377 (2011).
[CrossRef]

2010 (5)

2009 (1)

2008 (2)

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials, ” Opt. Express16(1), 67–80 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop and A.P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281(11), 3071–3080 (2008).
[CrossRef]

2007 (2)

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science315, 1120–1122 (2007).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett.32(16), 2309–2311 (2007).
[CrossRef] [PubMed]

2006 (1)

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

2005 (2)

I. M. Vellekoop, P. Lodahl, and A. Lagendijk, “Determination of the diffusion constant using phase-sensitive measurements,” Phys. Rev. E71, 056604 (2005).
[CrossRef]

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

1997 (1)

M. Fink, “Time reversed acoustics,” Phys. Today50(3), 34–40 (1997).
[CrossRef]

1987 (1)

R. Landauer and M. Buttiker, “Diffusive traversal time: effective area in magnetically induced interference,” Phys. Rev. B36, 6255–6260 (1987).
[CrossRef]

1985 (1)

1977 (1)

D. J. Thouless, “Maximum metallic resistance in thin wires,” Phys. Rev. Lett.39, 1167–1169 (1977).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A253, 358–379 (1959).
[CrossRef]

Akbulut, D.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

Aulbach, J.

J. Aulbach, A. Bretagne, M. Fink, M. Tanter, and A. Tourin, “Optimal spatiotemporal focusing through complex scattering media,” Phys. Rev. E85, 016605 (2012).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

Bertolotti, J.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

Brasselet, S.

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

Bretagne, A.

J. Aulbach, A. Bretagne, M. Fink, M. Tanter, and A. Tourin, “Optimal spatiotemporal focusing through complex scattering media,” Phys. Rev. E85, 016605 (2012).
[CrossRef]

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics5, 372–377 (2011).
[CrossRef]

Brown, A. N.

Buttiker, M.

R. Landauer and M. Buttiker, “Diffusive traversal time: effective area in magnetically induced interference,” Phys. Rev. B36, 6255–6260 (1987).
[CrossRef]

Caravaca-Aguirre, A. M.

Chauvat, D.

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

Cizmar, T.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

Conkey, D. B.

Cui, M.

de Rosny, J.

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science315, 1120–1122 (2007).
[CrossRef] [PubMed]

Denk, W.

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

Dholakia, K.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

Diels, J. C.

Fink, M.

J. Aulbach, A. Bretagne, M. Fink, M. Tanter, and A. Tourin, “Optimal spatiotemporal focusing through complex scattering media,” Phys. Rev. E85, 016605 (2012).
[CrossRef]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science315, 1120–1122 (2007).
[CrossRef] [PubMed]

M. Fink, “Time reversed acoustics,” Phys. Today50(3), 34–40 (1997).
[CrossRef]

Fontaine, J. J.

Gacoin, T.

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

Gjonaj, B.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

Gonella, G.

S. Roke and G. Gonella, “Nonlinear light scattering and spectroscopy of particles and droplets in liquids,” Annu. Rev. Phys. Chem.63, 353–378 (2012)
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2000).

Grange, R.

Helmchen, F.

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

Hsieh, C. L.

Johnson, P. M.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

Katz, O.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics5, 372–377 (2011).
[CrossRef]

Lagendijk, A.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Optimal concentration of light in turbid materials,” J. Opt. Soc. Am. B28(5), 1200–1203 (2011).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials, ” Opt. Express16(1), 67–80 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop, P. Lodahl, and A. Lagendijk, “Determination of the diffusion constant using phase-sensitive measurements,” Phys. Rev. E71, 056604 (2005).
[CrossRef]

Landauer, R.

R. Landauer and M. Buttiker, “Diffusive traversal time: effective area in magnetically induced interference,” Phys. Rev. B36, 6255–6260 (1987).
[CrossRef]

Lanvin, T.

Lerosey, G.

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science315, 1120–1122 (2007).
[CrossRef] [PubMed]

Lodahl, P.

I. M. Vellekoop, P. Lodahl, and A. Lagendijk, “Determination of the diffusion constant using phase-sensitive measurements,” Phys. Rev. E71, 056604 (2005).
[CrossRef]

Marquier, F.

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

Mazilu, M.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

McMichael, I. C.

Mosk, A. P.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Optimal concentration of light in turbid materials,” J. Opt. Soc. Am. B28(5), 1200–1203 (2011).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials, ” Opt. Express16(1), 67–80 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett.32(16), 2309–2311 (2007).
[CrossRef] [PubMed]

Mosk, A.P.

I. M. Vellekoop and A.P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281(11), 3071–3080 (2008).
[CrossRef]

Perruchas, S.

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

Piestun, R.

Psaltis, D.

Pu, Y.

Ray, P. C.

P. C. Ray, “Size and shape dependent second order nonlinear optical properties of nanomaterials and its application in biological and chemical sensing,” Chem. Rev.110(9), 5332–5365 (2010).
[CrossRef] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A253, 358–379 (1959).
[CrossRef]

Roch, J.-F.

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

Roke, S.

S. Roke and G. Gonella, “Nonlinear light scattering and spectroscopy of particles and droplets in liquids,” Annu. Rev. Phys. Chem.63, 353–378 (2012)
[CrossRef] [PubMed]

Silberberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics5, 372–377 (2011).
[CrossRef]

Simoni, F.

Small, E.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics5, 372–377 (2011).
[CrossRef]

Tanter, M.

J. Aulbach, A. Bretagne, M. Fink, M. Tanter, and A. Tourin, “Optimal spatiotemporal focusing through complex scattering media,” Phys. Rev. E85, 016605 (2012).
[CrossRef]

Tard, C.

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

Thouless, D. J.

D. J. Thouless, “Maximum metallic resistance in thin wires,” Phys. Rev. Lett.39, 1167–1169 (1977).
[CrossRef]

Tourin, A.

J. Aulbach, A. Bretagne, M. Fink, M. Tanter, and A. Tourin, “Optimal spatiotemporal focusing through complex scattering media,” Phys. Rev. E85, 016605 (2012).
[CrossRef]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science315, 1120–1122 (2007).
[CrossRef] [PubMed]

Treussart, F.

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

van Putten, E. G.

Vellekoop, I. M.

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett.101, 081108 (2012).
[CrossRef]

I. M. Vellekoop and A.P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281(11), 3071–3080 (2008).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials, ” Opt. Express16(1), 67–80 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett.32(16), 2309–2311 (2007).
[CrossRef] [PubMed]

I. M. Vellekoop, P. Lodahl, and A. Lagendijk, “Determination of the diffusion constant using phase-sensitive measurements,” Phys. Rev. E71, 056604 (2005).
[CrossRef]

Vos, W. L.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A253, 358–379 (1959).
[CrossRef]

Xuan, L. L.

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

Yang, C.

Annu. Rev. Phys. Chem. (1)

S. Roke and G. Gonella, “Nonlinear light scattering and spectroscopy of particles and droplets in liquids,” Annu. Rev. Phys. Chem.63, 353–378 (2012)
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

L. L. Xuan, S. Brasselet, F. Treussart, J.-F. Roch, F. Marquier, D. Chauvat, S. Perruchas, C. Tard, and T. Gacoin, “Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters,” Appl. Phys. Lett.89(12), 121118 (2006).
[CrossRef]

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett.101, 081108 (2012).
[CrossRef]

Biomed. Opt. Express (1)

Chem. Rev. (1)

P. C. Ray, “Size and shape dependent second order nonlinear optical properties of nanomaterials and its application in biological and chemical sensing,” Chem. Rev.110(9), 5332–5365 (2010).
[CrossRef] [PubMed]

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

Nat. Meth. (1)

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

Nat. Photonics (2)

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4, 388–394 (2010).
[CrossRef]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics5, 372–377 (2011).
[CrossRef]

Opt. Commun. (1)

I. M. Vellekoop and A.P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281(11), 3071–3080 (2008).
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Figures (4)

Fig. 1
Fig. 1

Schematic illustration of the experiment. (Ti:Sa) Ti:sapphire laser, (MI) Michelson-type interferometer, (SLM) spatial light modulator, (NA) numerical aperture, (EMCCD) electron-multiplying CCD camera.

Fig. 2
Fig. 2

Sample backside imaged at the second harmonic wavelength λ = 420nm. (a) Average image obtained from 200 images, each with a different randomly generated illuminating phase pattern. Several nanocrystals are visible in the field of view. (b) Image after wave front shaping. The feedback signal for the optimization was the average count rate in a square of 1μmx1μm around the position of the selected particle, indicated by the dashed square. Here, the feedback signal was enhanced by a factor of ηexp = 3.0 · 102.

Fig. 3
Fig. 3

Second harmonic auto-correlation (AC) measured on an individual nanocrystal at the backside of the sample. The graphs show the mean count rate in a 1μmx1μm square around particle position. In particular, the measurements for particle 5 are shown (see Table 1). (a) AC before wave front shaping. The data shows a 3:2:1 contrast ratio between the quickly decaying correlation of the coherent part of the speckle pulse followed by a slower decay of the incoherent part of the speckle pulse towards the background. The data is fitted according to that model of Eq. (2). The only free parameter of the fit is the thickness of the medium. (b) AC measured on nanocrystal at the backside of a slab of disordered silica after wave front shaping. The FWHM of the fit based on the AC of a sech2 shaped pulse is 168fs, indicating a pulse duration of the fundamental pulse of 109fs at the particle position.

Fig. 4
Fig. 4

Fourier analysis of the feedback signal as a function of phase φa per segment during a sequence of the wave front shaping experiment. The graph on the left (a) shows the squared amplitude of the first non-zero frequency Fourier component |FT1|2 calculated by Eq. (14), the graph on the right (b) depicts the second component |FT2|2. The distributions are used to determine the amplitude distribution of the contributing segments and the noise level (see sections 3.2.5 and 4.2).

Tables (1)

Tables Icon

Table 1 Summary of the results of six wave front shaping experiments, each with a different particle visible in Fig. 2. The pulse duration τpulse is calculated from the Gaussian fit to the AC curve after optimization. The experimentally observed enhancement ηexp is calculated by the ratio of the average count rate in a 1μmx1μm square around the particle position after and before optimization. For each particle we calculated the enhancement ηmodel of the time-integrated SH according to our model, calculated by ηmodel = cτcαcrηcw. The theoretical enhancement of the SH in a hypothetical continuous wave experiment ηcw, is calculated based on the experimentally determined amplitude contribution. The factor cτ, which corrects the enhancement for speckle pulses, was calculated using Eq. (10), where the sample thickness to model 〈I(t)〉 is determined from the fits of the AC in Fig. 3(a). The particles 1–5 were all located in close vicinity, where we assume a constant thickness and an average value cτ = 0.12 was determined. Particle 6 was located on a different spot on the sample, where we obtained cτ = 0.17. The factors cα = 0.28 and cR = 0.57 include the polarization and the susceptibility tensor and the focal volume, respectively (see sections 3.2.3 and 3.2.4).

Equations (18)

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A C ( τ ) = d t I 2 ( t ) + 2 d t I ( t ) I ( t + τ ) .
A C ( τ ) A C ( τ = 0 ) = 1 + d t I d ( t ) I d ( t + τ ) d t I d ( t ) 2 + d t I 0 ( t ) I 0 ( t + τ ) d t ( I 0 ( t ) ) 2 .
P 2 ω = χ ( 2 ) E b 2 = χ ( 2 ) a = 1 N t a b E a a = 1 N t a b E a .
W 2 ω = c k 4 V 2 12 π ε 0 | P 2 ω | 2 ,
W 2 ω ( φ ) | E 1 2 | 2 + | E 2 2 | 2 + 4 | E 1 | 2 | E 2 | 2 + { 4 E 1 E 2 * | E 1 | 2 e i φ } + { 2 E 1 2 ( E 2 * ) 2 e 2 i φ } + { 4 E 1 E 2 * | E 2 | 2 e i φ } )
W 2 ω = 2 N ( N 1 ) | t a b | 2 2 + N | t a b | 4 .
W 2 ω wfs = W 2 ω + N ( N 1 ) | t a b | 2 2 + 6 N ( N 1 ) ( N 2 ) | t a b | 2 | t a b | 2 + 4 N ( N 1 ) | t a b | 3 | t a b | + N ( N 1 ) ( N 2 ) ( N 3 ) | t a b | 4 .
η cw W 2 ω wfs W 2 ω 0.5 ( | A | 2 | A | 2 ) 2 ( | t a b | 2 | t a b | 2 ) 2 N 2 ,
c τ η pulsed η cw .
c τ = t max τ c / 2 t max + τ c / 2 d t I ( t ) 2 + d t I ( t ) 2 .
P 2 ω = [ 0 0 0 0 d 15 0 0 0 0 d 15 0 0 d 31 d 31 d 33 0 0 0 ] ( E c x 2 E c y 2 E c z 2 2 E c y E c z 2 E c x E c z 2 E c x E c y ) ,
c R 1 V 0 R 0 π 0 2 π I 2 ω ( ϕ , θ , r ) I 2 ω , peak r 2 sin θ d r d ϕ d θ ,
η cw 0.5 ( | A a t a b | γ ( | A a t a b | , σ a , N φ ) 2 | A a b t a b | 2 ) 2 N 2 .
FT k , a n = 1 N φ { I 2 ω , a ( φ n ) } e i 2 π k N n .
p ( θ ; k ) = e 1 2 k 2 2 π + k cos ( θ ) 2 π e 1 2 k 2 sin 2 θ Ψ ( k cos ( θ ) )
Ψ ( x ) = 1 2 π x d y e 1 2 y 2 .
γ ( | A t a b | , σ a , N φ ) = 0 2 π d θ cos ( θ ) p ( θ ; k ( | A t a b | , σ a , N φ ) ) .
| FT 1 , a | 2 = 1 4 N φ 2 | A a t a b | 2 + N φ σ a 2 .

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