Abstract

Wavefront shaping is a powerful technique that can be used to focus light through scattering media, which can be important for imaging through scattering samples such as tissue. This method is based on the assumption that the field at the output of the medium is a linear superposition of the modes traveling through different paths in the medium. However, when the scattering medium also exhibits nonlinearity, as may occur in multiphoton microscopy, this assumption is violated and the applicability of wavefront shaping becomes unclear. Here, using a simple model system with a scattering layer followed by a nonlinear layer, we show that with adaptive optimization of the wavefront, light can still be controlled and focused through a scattering medium in the presence of nonlinearity. Notably, we find that moderate positive nonlinearity can serve to significantly increase the focused fraction of power, whereas negative nonlinearity reduces it.

© 2017 Optical Society of America

Full Article  |  PDF Article
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  1. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
    [Crossref]
  2. T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
    [Crossref]
  3. I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
    [Crossref]
  4. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
    [Crossref]
  5. 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]
  6. X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
    [Crossref]
  7. O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
    [Crossref]
  8. 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]
  9. D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
    [Crossref]
  10. Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
    [Crossref]
  11. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
    [Crossref]
  12. Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
    [Crossref]
  13. O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
    [Crossref]
  14. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
    [Crossref]
  15. C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3, 211–215 (2009).
    [Crossref]
  16. A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802 (2011).
    [Crossref]
  17. D. Yelin and Y. Silberberg, “Laser scanning third-harmonic-generation microscopy in biology,” Opt. Express 5, 169–175 (1999).
    [Crossref]
  18. C. L. Evans and X. Sunney Xie, “Coherent anti-Stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu. Rev. Anal. Chem. 1, 883–909 (2008).
    [Crossref]
  19. B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. Sunney Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010).
    [Crossref]
  20. C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
    [Crossref]
  21. A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74, 419–425 (2002).
    [Crossref]
  22. J. D. Bhawalker, N. D. Kumar, C.-F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15, 201–204 (1997).
  23. S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12, 635–639 (2012).
    [Crossref]
  24. T. Cizmar and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19, 18871–18884 (2011).
    [Crossref]
  25. L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9, 306–310 (2015).
    [Crossref]
  26. M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biologic medium,” IEEE J. Quantum Electron. 24, 693–696 (1988).
    [Crossref]
  27. W.-C. Lin, M. Motamedi, and A. J. Welch, “Dynamics of tissue optics during laser heating of turbid media,” Appl. Opt. 35, 3413–3420 (1996).
    [Crossref]
  28. Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics 4, 721–726 (2010).
    [Crossref]
  29. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  30. S. Derevyanko and E. Small, “Nonlinear propagation of an optical speckle field,” Phys. Rev. A 053816, 053816 (2012).
    [Crossref]
  31. C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8, 471–475 (2012).
    [Crossref]
  32. R. E. de Araujo and A. S. L. Gomes, “Nonlinear optical Kerr coefficients of disordered media,” Phys. Rev. A 57, 2037–2040 (1998).
    [Crossref]
  33. S. E. Skipetrov and R. Maynard, “Instabilities of waves in nonlinear disordered media,” Phys. Rev. Lett. 85, 736–739 (2000).
    [Crossref]
  34. Y. Wang and J. W. Fleischer, “A model of thick scattering media using a series of random diffraction gratings,” in Imaging and Applied Optics (2017), paper JTu5A.
  35. I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
    [Crossref]
  36. B. A. Rockwell, W. P. Roach, M. E. Rogers, M. W. Mayo, C. A. Toth, C. P. Cain, and G. D. Noojin, “Nonlinear refraction in vitreous humor,” Opt. Lett. 18, 1792–1794 (1993).
    [Crossref]
  37. E. O. Potma, W. P. De Boeij, and D. A. Wiersma, “Femtosecond dynamics of intracellular water probed with nonlinear optical Kerr effect microspectroscopy,” Biophys. J. 80, 3019–3024 (2001).
    [Crossref]
  38. N. T. Hunt, L. Kattner, R. P. Shanks, and K. Wynne, “The dynamics of water-protein interaction studied by ultrafast optical Kerr-effect spectroscopy,” J. Am. Chem. Soc. 129, 3168–3172 (2007).
    [Crossref]
  39. O. Katz, E. Small, Y. Guan, and Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1, 170–174 (2014).
    [Crossref]
  40. C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
    [Crossref]

2015 (1)

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9, 306–310 (2015).
[Crossref]

2014 (2)

O. Katz, E. Small, Y. Guan, and Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1, 170–174 (2014).
[Crossref]

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

2012 (6)

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12, 635–639 (2012).
[Crossref]

S. Derevyanko and E. Small, “Nonlinear propagation of an optical speckle field,” Phys. Rev. A 053816, 053816 (2012).
[Crossref]

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8, 471–475 (2012).
[Crossref]

2011 (9)

T. Cizmar and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19, 18871–18884 (2011).
[Crossref]

C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
[Crossref]

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]

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
[Crossref]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[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]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802 (2011).
[Crossref]

2010 (5)

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[Crossref]

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics 4, 721–726 (2010).
[Crossref]

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. Sunney Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010).
[Crossref]

2009 (1)

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3, 211–215 (2009).
[Crossref]

2008 (2)

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

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

2007 (2)

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

N. T. Hunt, L. Kattner, R. P. Shanks, and K. Wynne, “The dynamics of water-protein interaction studied by ultrafast optical Kerr-effect spectroscopy,” J. Am. Chem. Soc. 129, 3168–3172 (2007).
[Crossref]

2002 (1)

A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74, 419–425 (2002).
[Crossref]

2001 (1)

E. O. Potma, W. P. De Boeij, and D. A. Wiersma, “Femtosecond dynamics of intracellular water probed with nonlinear optical Kerr effect microspectroscopy,” Biophys. J. 80, 3019–3024 (2001).
[Crossref]

2000 (1)

S. E. Skipetrov and R. Maynard, “Instabilities of waves in nonlinear disordered media,” Phys. Rev. Lett. 85, 736–739 (2000).
[Crossref]

1999 (1)

1998 (1)

R. E. de Araujo and A. S. L. Gomes, “Nonlinear optical Kerr coefficients of disordered media,” Phys. Rev. A 57, 2037–2040 (1998).
[Crossref]

1997 (1)

J. D. Bhawalker, N. D. Kumar, C.-F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15, 201–204 (1997).

1996 (1)

1993 (1)

1988 (2)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biologic medium,” IEEE J. Quantum Electron. 24, 693–696 (1988).
[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]

Aulbach, J.

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]

Austin, D. R.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Barsi, C.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8, 471–475 (2012).
[Crossref]

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3, 211–215 (2009).
[Crossref]

Ben-Yakar, A.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

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]

Bhawalker, J. D.

J. D. Bhawalker, N. D. Kumar, C.-F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15, 201–204 (1997).

Bianchi, S.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12, 635–639 (2012).
[Crossref]

Boccara, A. C.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[Crossref]

Bondareff, P.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Bree, C.

C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
[Crossref]

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[Crossref]

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics 4, 721–726 (2010).
[Crossref]

Cain, C. P.

Chan, K. M. C.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

Chatel, B.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Cheong, W.-F.

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biologic medium,” IEEE J. Quantum Electron. 24, 693–696 (1988).
[Crossref]

Choi, W.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Choi, Y.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Christodoulides, D. N.

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9, 306–310 (2015).
[Crossref]

Cizmar, T.

T. Cizmar and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19, 18871–18884 (2011).
[Crossref]

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

Dasari, R. R.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

de Araujo, R. E.

R. E. de Araujo and A. S. L. Gomes, “Nonlinear optical Kerr coefficients of disordered media,” Phys. Rev. A 57, 2037–2040 (1998).
[Crossref]

De Boeij, W. P.

E. O. Potma, W. P. De Boeij, and D. A. Wiersma, “Femtosecond dynamics of intracellular water probed with nonlinear optical Kerr effect microspectroscopy,” Biophys. J. 80, 3019–3024 (2001).
[Crossref]

Demircan, A.

C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
[Crossref]

Derevyanko, S.

S. Derevyanko and E. Small, “Nonlinear propagation of an optical speckle field,” Phys. Rev. A 053816, 053816 (2012).
[Crossref]

Dholakia, K.

T. Cizmar and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19, 18871–18884 (2011).
[Crossref]

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

Di Leonardo, R.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12, 635–639 (2012).
[Crossref]

Dimarzio, C. A.

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Drommer, W.

A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74, 419–425 (2002).
[Crossref]

Ertmer, W.

A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74, 419–425 (2002).
[Crossref]

Evans, C. L.

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

Fang-Yen, C.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Feld, M. S.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

Feng, S.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

Ferhanoglu, O.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

Fink, M.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[Crossref]

Fleischer, J. W.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8, 471–475 (2012).
[Crossref]

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3, 211–215 (2009).
[Crossref]

Y. Wang and J. W. Fleischer, “A model of thick scattering media using a series of random diffraction gratings,” in Imaging and Applied Optics (2017), paper JTu5A.

Freudiger, C. W.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. Sunney Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010).
[Crossref]

Freund, I.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

Ghaffari, S. A.

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biologic medium,” IEEE J. Quantum Electron. 24, 693–696 (1988).
[Crossref]

Gigan, S.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[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]

Gomes, A. S. L.

R. E. de Araujo and A. S. L. Gomes, “Nonlinear optical Kerr coefficients of disordered media,” Phys. Rev. A 57, 2037–2040 (1998).
[Crossref]

Goy, A.

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802 (2011).
[Crossref]

Guan, Y.

Heisterkamp, A.

A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74, 419–425 (2002).
[Crossref]

Holtom, G. R.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. Sunney Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010).
[Crossref]

Hoy, C. L.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

Hunt, N. T.

N. T. Hunt, L. Kattner, R. P. Shanks, and K. Wynne, “The dynamics of water-protein interaction studied by ultrafast optical Kerr-effect spectroscopy,” J. Am. Chem. Soc. 129, 3168–3172 (2007).
[Crossref]

Jia, S.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8, 471–475 (2012).
[Crossref]

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]

Judkewitz, B.

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Kang, P.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Karajanagi, S. S.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

Kattner, L.

N. T. Hunt, L. Kattner, R. P. Shanks, and K. Wynne, “The dynamics of water-protein interaction studied by ultrafast optical Kerr-effect spectroscopy,” J. Am. Chem. Soc. 129, 3168–3172 (2007).
[Crossref]

Katz, O.

O. Katz, E. Small, Y. Guan, and Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1, 170–174 (2014).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[Crossref]

Kim, K. H.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

Kobler, J. B.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

Kumar, N. D.

J. D. Bhawalker, N. D. Kumar, C.-F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15, 201–204 (1997).

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (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]

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]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[Crossref]

Lahini, Y.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics 4, 721–726 (2010).
[Crossref]

Lee, K. J.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[Crossref]

Lin, W.-C.

Liu, H.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
[Crossref]

Lubatschowski, H.

A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74, 419–425 (2002).
[Crossref]

Mamom, T.

A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74, 419–425 (2002).
[Crossref]

Maynard, R.

S. E. Skipetrov and R. Maynard, “Instabilities of waves in nonlinear disordered media,” Phys. Rev. Lett. 85, 736–739 (2000).
[Crossref]

Mayo, M. W.

Mazilu, M.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (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]

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]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[Crossref]

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

Motamedi, M.

W.-C. Lin, M. Motamedi, and A. J. Welch, “Dynamics of tissue optics during laser heating of turbid media,” Appl. Opt. 35, 3413–3420 (1996).
[Crossref]

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biologic medium,” IEEE J. Quantum Electron. 24, 693–696 (1988).
[Crossref]

Noojin, G. D.

Picozzi, A.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8, 471–475 (2012).
[Crossref]

Popoff, S.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[Crossref]

Potma, E. O.

E. O. Potma, W. P. De Boeij, and D. A. Wiersma, “Femtosecond dynamics of intracellular water probed with nonlinear optical Kerr effect microspectroscopy,” Biophys. J. 80, 3019–3024 (2001).
[Crossref]

Prasad, P. N.

J. D. Bhawalker, N. D. Kumar, C.-F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15, 201–204 (1997).

Psaltis, D.

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802 (2011).
[Crossref]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

Reichman, J.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. Sunney Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010).
[Crossref]

Rica, S.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8, 471–475 (2012).
[Crossref]

Ripken, T.

A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74, 419–425 (2002).
[Crossref]

Roach, W. P.

Rockwell, B. A.

Rogers, M. E.

Rosenbluh, M.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

Saar, B. G.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. Sunney Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010).
[Crossref]

Shanks, R. P.

N. T. Hunt, L. Kattner, R. P. Shanks, and K. Wynne, “The dynamics of water-protein interaction studied by ultrafast optical Kerr-effect spectroscopy,” J. Am. Chem. Soc. 129, 3168–3172 (2007).
[Crossref]

Silberberg, Y.

O. Katz, E. Small, Y. Guan, and Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1, 170–174 (2014).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[Crossref]

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics 4, 721–726 (2010).
[Crossref]

D. Yelin and Y. Silberberg, “Laser scanning third-harmonic-generation microscopy in biology,” Opt. Express 5, 169–175 (1999).
[Crossref]

Skipetrov, S. E.

S. E. Skipetrov and R. Maynard, “Instabilities of waves in nonlinear disordered media,” Phys. Rev. Lett. 85, 736–739 (2000).
[Crossref]

Small, E.

O. Katz, E. Small, Y. Guan, and Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1, 170–174 (2014).
[Crossref]

S. Derevyanko and E. Small, “Nonlinear propagation of an optical speckle field,” Phys. Rev. A 053816, 053816 (2012).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[Crossref]

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics 4, 721–726 (2010).
[Crossref]

Stanley, C. M.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. Sunney Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010).
[Crossref]

Steinmeyer, G.

C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
[Crossref]

Sun, C.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8, 471–475 (2012).
[Crossref]

Sunney Xie, X.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. Sunney Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010).
[Crossref]

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

Tajalli, A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Tan, O. T.

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biologic medium,” IEEE J. Quantum Electron. 24, 693–696 (1988).
[Crossref]

Toth, C. A.

van Putten, E. G.

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]

Vellekoop, I. M.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[Crossref]

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

Walmsley, I. A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Wan, W.

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3, 211–215 (2009).
[Crossref]

Wang, L. V.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
[Crossref]

Wang, Y.

Y. Wang and J. W. Fleischer, “A model of thick scattering media using a series of random diffraction gratings,” in Imaging and Applied Optics (2017), paper JTu5A.

Wang, Y. M.

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Welch, A. J.

W.-C. Lin, M. Motamedi, and A. J. Welch, “Dynamics of tissue optics during laser heating of turbid media,” Appl. Opt. 35, 3413–3420 (1996).
[Crossref]

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biologic medium,” IEEE J. Quantum Electron. 24, 693–696 (1988).
[Crossref]

Welling, H.

A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74, 419–425 (2002).
[Crossref]

Wiersma, D. A.

E. O. Potma, W. P. De Boeij, and D. A. Wiersma, “Femtosecond dynamics of intracellular water probed with nonlinear optical Kerr effect microspectroscopy,” Biophys. J. 80, 3019–3024 (2001).
[Crossref]

Wise, F. W.

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9, 306–310 (2015).
[Crossref]

Wright, L. G.

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9, 306–310 (2015).
[Crossref]

Wynne, K.

N. T. Hunt, L. Kattner, R. P. Shanks, and K. Wynne, “The dynamics of water-protein interaction studied by ultrafast optical Kerr-effect spectroscopy,” J. Am. Chem. Soc. 129, 3168–3172 (2007).
[Crossref]

Xu, X.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
[Crossref]

Yang, C.

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

Yang, T. D.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

Yelin, D.

Yildirim, M.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

Zeitels, S. M.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

Zhao, C.-F.

J. D. Bhawalker, N. D. Kumar, C.-F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15, 201–204 (1997).

Annu. Rev. Anal. Chem. (1)

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

Appl. Opt. (1)

Appl. Phys. B (1)

A. Heisterkamp, T. Ripken, T. Mamom, W. Drommer, H. Welling, W. Ertmer, and H. Lubatschowski, “Nonlinear side effects of fs pulses inside corneal tissue during photodisruption,” Appl. Phys. B 74, 419–425 (2002).
[Crossref]

Biophys. J. (1)

E. O. Potma, W. P. De Boeij, and D. A. Wiersma, “Femtosecond dynamics of intracellular water probed with nonlinear optical Kerr effect microspectroscopy,” Biophys. J. 80, 3019–3024 (2001).
[Crossref]

IEEE J. Quantum Electron. (2)

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, “Clinical ultrafast laser surgery: recent advances and future directions,” IEEE J. Quantum Electron. 20, 7100814 (2014).
[Crossref]

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biologic medium,” IEEE J. Quantum Electron. 24, 693–696 (1988).
[Crossref]

J. Am. Chem. Soc. (1)

N. T. Hunt, L. Kattner, R. P. Shanks, and K. Wynne, “The dynamics of water-protein interaction studied by ultrafast optical Kerr-effect spectroscopy,” J. Am. Chem. Soc. 129, 3168–3172 (2007).
[Crossref]

J. Clin. Laser Med. Surg. (1)

J. D. Bhawalker, N. D. Kumar, C.-F. Zhao, and P. N. Prasad, “Two-photon photodynamic therapy,” J. Clin. Laser Med. Surg. 15, 201–204 (1997).

Lab Chip (1)

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12, 635–639 (2012).
[Crossref]

Nat. Commun. (3)

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[Crossref]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref]

Nat. Photonics (10)

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
[Crossref]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[Crossref]

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3, 211–215 (2009).
[Crossref]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9, 306–310 (2015).
[Crossref]

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nat. Photonics 4, 721–726 (2010).
[Crossref]

Nat. Phys. (1)

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8, 471–475 (2012).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Optica (1)

Phys. Rev. A (3)

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802 (2011).
[Crossref]

R. E. de Araujo and A. S. L. Gomes, “Nonlinear optical Kerr coefficients of disordered media,” Phys. Rev. A 57, 2037–2040 (1998).
[Crossref]

S. Derevyanko and E. Small, “Nonlinear propagation of an optical speckle field,” Phys. Rev. A 053816, 053816 (2012).
[Crossref]

Phys. Rev. Lett. (6)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

S. E. Skipetrov and R. Maynard, “Instabilities of waves in nonlinear disordered media,” Phys. Rev. Lett. 85, 736–739 (2000).
[Crossref]

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]

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]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
[Crossref]

Science (1)

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. Sunney Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010).
[Crossref]

Other (2)

Y. Wang and J. W. Fleischer, “A model of thick scattering media using a series of random diffraction gratings,” in Imaging and Applied Optics (2017), paper JTu5A.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Supplementary Material (1)

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» Supplement 1       Supplemental material

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Figures (5)

Fig. 1.
Fig. 1.

Simulation results of 2D speckle fields after propagation in a (a) linear medium, (b) nonlinear defocusing medium, and (c) nonlinear focusing medium. (d) Probability distribution of the intensities of the speckle fields shown in (a)–(c). (e) Power contained in the brightest speckle as a function of normalized nonlinearity, ηIink0n2L (without wavefront shaping). For η>0 (and n2>0) a larger fraction of the total power is contained within a small number of bright speckles, whereas for η<0 the total power is spread out more evenly among the speckles in the field, compared to the linear case.

Fig. 2.
Fig. 2.

Simulation results: (a) Fraction of the total incident power contained in the obtained focus after optimization, in a medium with defocusing nonlinearity, as a function of normalized nonlinearity ηIink0n2L. The focused power fraction declines with nonlinearity strength. (b) Same in a medium with focusing nonlinearity, where the focused power grows with nonlinearity strength. (c) Same in a composite scattering nonlinear focusing medium, consisting of multiple alternating scattering and nonlinear layers. The trend in (c) is similar to that in (b), showing a focused power fraction that grows with nonlinearity strength, though the trend shows less saturation and the η values are larger (see Supplement 1). All focused power fractions were calculated relative to those achieved in a linear scattering medium (η=0), and all data sets were fitted (black line) to simple functions of exponential form as a guide to the eye (see Section 6, Methods).

Fig. 3.
Fig. 3.

Simulation results: 1D cut through the propagation of a 2D speckle field, optimized to focus at the output of a layer (at propagation length=1) with (a) no nonlinearity, (b) defocusing nonlinearity, and (c) focusing nonlinearity. Tighter axial confinement (along the direction of propagation) of the focus is obtained in both the defocusing and focusing nonlinear cases than for the linear case. For focusing nonlinearity, the trajectories of neighboring bright speckles are altered by wavefront shaping such that they merge into the enhanced speckle.

Fig. 4.
Fig. 4.

Experimental setup. The wavefront of either a CW (for defocusing nonlinearity) or pulsed (for focusing nonlinearity) laser was shaped by a two-dimensional spatial light modulator (SLM) and then imaged with a telescope onto a thin diffuser. The generated speckle pattern was propagated through a nonlinear (NL) medium and the output facet of the NL medium was imaged onto a CCD camera.

Fig. 5.
Fig. 5.

Experimental results: focusing light through scattering media in the presence of nonlinearity. (a) The fraction of the total incident power contained in the obtained focus, after optimization in a defocusing nonlinear medium, as a function of the input laser power (blue circles). The scaled simulation results are plotted for comparison (black line). (b) Focused power fraction obtained in a focusing medium, as a function of the peak power incident on the diffuser (red circles), and the scaled simulation (black line). The fraction of light that can be controlled and focused rises (declines) with nonlinearity strength in a focusing (defocusing) medium, as predicted by the simulation. (c) A measurement of the “nonlinear memory effect” in the defocusing medium, i.e., the degree to which the optimal SLM phase can be used to obtain focusing as the nonlinearity strength of the medium is varied without reoptimization. The different colored lines represent the results for the different optimization powers shown in the legend. (d) Measurement of the “nonlinear memory effect” in the focusing medium. The white region is the range of peak powers used in (b). While for defocusing media the optimal SLM phase performs best for the optimization power and gradually declines in efficiency, for focusing media the optimal SLM phase is very robust and achieves a focus of similar quality for peak power 510 times larger than the optimization power.

Equations (1)

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iEz+12k0n0[2x2+2y2]E+k0n2|E|2E=0,

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