Abstract

Many materials, including biological tissue, attenuate light mostly by scattering. Because the scattered field is exquisitely sensitive to perturbations, control over the distribution of light after strong scattering is challenging. Though wavefront-shaping techniques enable arbitrary generation of light distributions within strongly scattering or turbid media in principle, the input wavefront necessary for the chosen light distribution is generally unknown. Using two different computational models, we demonstrate a technique called virtual aperture culling of the eigenmodes of a resonator (VACER), which uses weak spatial filtering mechanisms for noninvasive light focusing at arbitrary positions within turbid media. Compatibility with weak spatial filtering mechanisms is critical to innocuously focusing light within turbid media. One model represents an ideal system and could be physically implemented in some scenarios with digital optical phase conjugation, while the other model simulates phase conjugation via gain saturation, and its physical realization would operate fast enough to avoid the effects of speckle decorrelation in biological tissue. Modeling results establish that sound physical principles underlie VACER.

© 2014 Optical Society of America

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References

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  1. I. M. Vellekoop, A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
    [CrossRef]
  2. Z. Yaqoob, D. Psaltis, M. S. Feld, C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
    [CrossRef]
  3. I. M. Vellekoop, E. G. van Putten, A. Lagendijk, A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
    [CrossRef]
  4. I. M. Vellekoop, A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
    [CrossRef]
  5. M. Cui, E. J. McDowell, C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95, 123702 (2009).
    [CrossRef]
  6. M. Cui, E. J. McDowell, C. Yang, “An in vivo study of turbidity suppression by optical phase conjugation (TSOPC) on rabbit ear,” Opt. Express 18, 25–30 (2010).
    [CrossRef]
  7. M. Cui, C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18, 3444–3455 (2010).
    [CrossRef]
  8. I. M. Vellekoop, A. Lagendijk, A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
    [CrossRef]
  9. X. Xu, H. Liu, L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
    [CrossRef]
  10. Y. M. Wang, B. Judkewitz, C. A. DiMarzio, C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
    [CrossRef]
  11. F. Ramaz, B. Forget, M. Atlan, A. C. Boccara, M. Gross, P. Delaye, G. Roosen, “Photorefractive detection of tagged photons in ultrasound modulated optical tomography of thick biological tissues,” Opt. Express 12, 5469–5474 (2004).
    [CrossRef]
  12. P. Lai, X. Xu, L. V. Wang, “Ultrasound-modulated optical tomography at new depth,” J. Biomed. Opt. 17, 066006 (2012).
    [CrossRef]
  13. K. Si, R. Fiolka, M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).
    [CrossRef]
  14. C. Gu, P. Yeh, “Partial phase conjugation, fidelity, and reciprocity,” Opt. Commun. 107, 353–357 (1994).
    [CrossRef]
  15. S. Campbell, P. Yeh, C. Gu, Q. B. He, “Fidelity of image restoration by partial phase conjugation through multimode fibers,” Opt. Commun. 114, 50–56 (1995).
    [CrossRef]
  16. E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15, 025004 (2010).
    [CrossRef]
  17. K. Si, R. Fiolka, M. Cui, “Breaking the spatial resolution barrier via iterative sound-light interaction in deep tissue microscopy,” Sci. Rep. 2, 748 (2012).
    [CrossRef]
  18. W. J. Tom, “Focusing light within turbid media with virtual aperture culling of the eigenmodes of a resonator,” Ph.D. dissertation (University of Texas at Austin, 2012).
  19. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
    [CrossRef]
  20. S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
    [CrossRef]
  21. M. Pozniak, K. Zyczkowski, M. Kus, “Composed ensembles of random unitary matrices,” J. Phys. A 31, 1059–1071 (1998).
    [CrossRef]
  22. L. Shampine, M. Reichelt, “The MATLAB ODE suite,” SIAM J. Sci. Comput. 18, 1–22 (1997).
    [CrossRef]
  23. C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, T. Bifano, “Focusing through dynamic scattering media,” Opt. Express 20, 15086–15092 (2012).
    [CrossRef]
  24. R. Roy, P. A. Schulz, A. Walther, “Acousto-optic modulator as an electronically selectable unidirectional device in a ring laser,” Opt. Lett. 12, 672–674 (1987).
    [CrossRef]
  25. M. K. Reed, W. K. Bischel, “Acousto-optic modulators as unidirectional devices in ring lasers,” Opt. Lett. 17, 691–693 (1992).
    [CrossRef]
  26. W. Clarkson, A. Neilson, D. Hanna, “Unidirectional operation of ring lasers via the acoustooptic effect,” IEEE J. Quantum Electron. 32, 311–325 (1996).
    [CrossRef]
  27. Y. Wang, N. Saito, H. Tashiro, “Unidirectional operation of a ring laser by means of anisotropic acousto-optic device,” Opt. Commun. 207, 279–285 (2002).
    [CrossRef]
  28. G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
    [CrossRef]
  29. E. G. van Putten, A. Lagendijk, A. P. Mosk, “Optimal concentration of light in turbid materials,” J. Opt. Soc. Am. B 28, 1200–1203 (2011).
    [CrossRef]
  30. E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett. 106, 193905 (2011).
    [CrossRef]
  31. J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
    [CrossRef]

2013 (1)

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

2012 (5)

C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, T. Bifano, “Focusing through dynamic scattering media,” Opt. Express 20, 15086–15092 (2012).
[CrossRef]

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

P. Lai, X. Xu, L. V. Wang, “Ultrasound-modulated optical tomography at new depth,” J. Biomed. Opt. 17, 066006 (2012).
[CrossRef]

K. Si, R. Fiolka, M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).
[CrossRef]

K. Si, R. Fiolka, M. Cui, “Breaking the spatial resolution barrier via iterative sound-light interaction in deep tissue microscopy,” Sci. Rep. 2, 748 (2012).
[CrossRef]

2011 (4)

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[CrossRef]

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

E. G. van Putten, A. Lagendijk, A. P. Mosk, “Optimal concentration of light in turbid materials,” J. Opt. Soc. Am. B 28, 1200–1203 (2011).
[CrossRef]

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

2010 (5)

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15, 025004 (2010).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

M. Cui, E. J. McDowell, C. Yang, “An in vivo study of turbidity suppression by optical phase conjugation (TSOPC) on rabbit ear,” Opt. Express 18, 25–30 (2010).
[CrossRef]

M. Cui, C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18, 3444–3455 (2010).
[CrossRef]

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

2009 (1)

M. Cui, E. J. McDowell, C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95, 123702 (2009).
[CrossRef]

2008 (3)

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

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef]

I. M. Vellekoop, A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef]

2007 (2)

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

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef]

2004 (1)

2002 (1)

Y. Wang, N. Saito, H. Tashiro, “Unidirectional operation of a ring laser by means of anisotropic acousto-optic device,” Opt. Commun. 207, 279–285 (2002).
[CrossRef]

1998 (1)

M. Pozniak, K. Zyczkowski, M. Kus, “Composed ensembles of random unitary matrices,” J. Phys. A 31, 1059–1071 (1998).
[CrossRef]

1997 (1)

L. Shampine, M. Reichelt, “The MATLAB ODE suite,” SIAM J. Sci. Comput. 18, 1–22 (1997).
[CrossRef]

1996 (1)

W. Clarkson, A. Neilson, D. Hanna, “Unidirectional operation of ring lasers via the acoustooptic effect,” IEEE J. Quantum Electron. 32, 311–325 (1996).
[CrossRef]

1995 (1)

S. Campbell, P. Yeh, C. Gu, Q. B. He, “Fidelity of image restoration by partial phase conjugation through multimode fibers,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

1994 (1)

C. Gu, P. Yeh, “Partial phase conjugation, fidelity, and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

1992 (1)

1987 (1)

Akbulut, D.

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

Atlan, M.

Bertolotti, J.

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

Bifano, T.

Bischel, W. K.

Boccara, A. C.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

F. Ramaz, B. Forget, M. Atlan, A. C. Boccara, M. Gross, P. Delaye, G. Roosen, “Photorefractive detection of tagged photons in ultrasound modulated optical tomography of thick biological tissues,” Opt. Express 12, 5469–5474 (2004).
[CrossRef]

Campbell, S.

S. Campbell, P. Yeh, C. Gu, Q. B. He, “Fidelity of image restoration by partial phase conjugation through multimode fibers,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Cho, Y.-H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

Clarkson, W.

W. Clarkson, A. Neilson, D. Hanna, “Unidirectional operation of ring lasers via the acoustooptic effect,” IEEE J. Quantum Electron. 32, 311–325 (1996).
[CrossRef]

Cui, M.

K. Si, R. Fiolka, M. Cui, “Breaking the spatial resolution barrier via iterative sound-light interaction in deep tissue microscopy,” Sci. Rep. 2, 748 (2012).
[CrossRef]

K. Si, R. Fiolka, M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).
[CrossRef]

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15, 025004 (2010).
[CrossRef]

M. Cui, E. J. McDowell, C. Yang, “An in vivo study of turbidity suppression by optical phase conjugation (TSOPC) on rabbit ear,” Opt. Express 18, 25–30 (2010).
[CrossRef]

M. Cui, C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18, 3444–3455 (2010).
[CrossRef]

M. Cui, E. J. McDowell, C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95, 123702 (2009).
[CrossRef]

de Rosny, J.

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef]

Delaye, P.

DiMarzio, C. A.

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

Feld, M. S.

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

Fink, M.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef]

Fiolka, R.

K. Si, R. Fiolka, M. Cui, “Breaking the spatial resolution barrier via iterative sound-light interaction in deep tissue microscopy,” Sci. Rep. 2, 748 (2012).
[CrossRef]

K. Si, R. Fiolka, M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).
[CrossRef]

Forget, B.

Gigan, S.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Gross, M.

Gu, C.

S. Campbell, P. Yeh, C. Gu, Q. B. He, “Fidelity of image restoration by partial phase conjugation through multimode fibers,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

C. Gu, P. Yeh, “Partial phase conjugation, fidelity, and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

Han, S.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

Hanna, D.

W. Clarkson, A. Neilson, D. Hanna, “Unidirectional operation of ring lasers via the acoustooptic effect,” IEEE J. Quantum Electron. 32, 311–325 (1996).
[CrossRef]

He, Q. B.

S. Campbell, P. Yeh, C. Gu, Q. B. He, “Fidelity of image restoration by partial phase conjugation through multimode fibers,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

Hoffman, S.

Judkewitz, B.

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

Ko, S. H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

Kus, M.

M. Pozniak, K. Zyczkowski, M. Kus, “Composed ensembles of random unitary matrices,” J. Phys. A 31, 1059–1071 (1998).
[CrossRef]

Lagendijk, A.

E. G. van Putten, A. Lagendijk, A. P. Mosk, “Optimal concentration of light in turbid materials,” J. Opt. Soc. Am. B 28, 1200–1203 (2011).
[CrossRef]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, 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, A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef]

Lai, P.

P. Lai, X. Xu, L. V. Wang, “Ultrasound-modulated optical tomography at new depth,” J. Biomed. Opt. 17, 066006 (2012).
[CrossRef]

Lerosey, G.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef]

Liu, H.

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

Lu, Y.

McDowell, E. J.

M. Cui, E. J. McDowell, C. Yang, “An in vivo study of turbidity suppression by optical phase conjugation (TSOPC) on rabbit ear,” Opt. Express 18, 25–30 (2010).
[CrossRef]

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15, 025004 (2010).
[CrossRef]

M. Cui, E. J. McDowell, C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95, 123702 (2009).
[CrossRef]

Moore, J.

Mosk, A. P.

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

E. G. van Putten, A. Lagendijk, A. P. Mosk, “Optimal concentration of light in turbid materials,” J. Opt. Soc. Am. B 28, 1200–1203 (2011).
[CrossRef]

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

I. M. Vellekoop, A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef]

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

Nam, K. T.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

Neilson, A.

W. Clarkson, A. Neilson, D. Hanna, “Unidirectional operation of ring lasers via the acoustooptic effect,” IEEE J. Quantum Electron. 32, 311–325 (1996).
[CrossRef]

Park, C.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

Park, J.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

Park, J.-H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

Park, Y.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

Paxman, R.

Popoff, S. M.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Pozniak, M.

M. Pozniak, K. Zyczkowski, M. Kus, “Composed ensembles of random unitary matrices,” J. Phys. A 31, 1059–1071 (1998).
[CrossRef]

Psaltis, D.

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

Ramaz, F.

Reed, M. K.

Reichelt, M.

L. Shampine, M. Reichelt, “The MATLAB ODE suite,” SIAM J. Sci. Comput. 18, 1–22 (1997).
[CrossRef]

Roosen, G.

Roy, R.

Saito, N.

Y. Wang, N. Saito, H. Tashiro, “Unidirectional operation of a ring laser by means of anisotropic acousto-optic device,” Opt. Commun. 207, 279–285 (2002).
[CrossRef]

Schulz, P. A.

Senekerimyan, V.

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15, 025004 (2010).
[CrossRef]

Shampine, L.

L. Shampine, M. Reichelt, “The MATLAB ODE suite,” SIAM J. Sci. Comput. 18, 1–22 (1997).
[CrossRef]

Shin, J.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

Si, K.

K. Si, R. Fiolka, M. Cui, “Breaking the spatial resolution barrier via iterative sound-light interaction in deep tissue microscopy,” Sci. Rep. 2, 748 (2012).
[CrossRef]

K. Si, R. Fiolka, M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).
[CrossRef]

Stockbridge, C.

Tashiro, H.

Y. Wang, N. Saito, H. Tashiro, “Unidirectional operation of a ring laser by means of anisotropic acousto-optic device,” Opt. Commun. 207, 279–285 (2002).
[CrossRef]

Tom, W. J.

W. J. Tom, “Focusing light within turbid media with virtual aperture culling of the eigenmodes of a resonator,” Ph.D. dissertation (University of Texas at Austin, 2012).

Tourin, A.

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef]

Toussaint, K.

van Putten, E. G.

Vellekoop, I. M.

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

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15, 025004 (2010).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef]

I. M. Vellekoop, A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef]

I. M. Vellekoop, 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, A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett. 106, 193905 (2011).
[CrossRef]

Walther, A.

Wang, L. V.

P. Lai, X. Xu, L. V. Wang, “Ultrasound-modulated optical tomography at new depth,” J. Biomed. Opt. 17, 066006 (2012).
[CrossRef]

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

Wang, Y.

Y. Wang, N. Saito, H. Tashiro, “Unidirectional operation of a ring laser by means of anisotropic acousto-optic device,” Opt. Commun. 207, 279–285 (2002).
[CrossRef]

Wang, Y. M.

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

Xu, X.

P. Lai, X. Xu, L. V. Wang, “Ultrasound-modulated optical tomography at new depth,” J. Biomed. Opt. 17, 066006 (2012).
[CrossRef]

X. Xu, H. Liu, 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, C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[CrossRef]

M. Cui, E. J. McDowell, C. Yang, “An in vivo study of turbidity suppression by optical phase conjugation (TSOPC) on rabbit ear,” Opt. Express 18, 25–30 (2010).
[CrossRef]

M. Cui, C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18, 3444–3455 (2010).
[CrossRef]

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15, 025004 (2010).
[CrossRef]

M. Cui, E. J. McDowell, C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95, 123702 (2009).
[CrossRef]

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

Yaqoob, Z.

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15, 025004 (2010).
[CrossRef]

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

Yeh, P.

S. Campbell, P. Yeh, C. Gu, Q. B. He, “Fidelity of image restoration by partial phase conjugation through multimode fibers,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

C. Gu, P. Yeh, “Partial phase conjugation, fidelity, and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

Yu, H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

Zyczkowski, K.

M. Pozniak, K. Zyczkowski, M. Kus, “Composed ensembles of random unitary matrices,” J. Phys. A 31, 1059–1071 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

M. Cui, E. J. McDowell, C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett. 95, 123702 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. Clarkson, A. Neilson, D. Hanna, “Unidirectional operation of ring lasers via the acoustooptic effect,” IEEE J. Quantum Electron. 32, 311–325 (1996).
[CrossRef]

J. Biomed. Opt. (2)

P. Lai, X. Xu, L. V. Wang, “Ultrasound-modulated optical tomography at new depth,” J. Biomed. Opt. 17, 066006 (2012).
[CrossRef]

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15, 025004 (2010).
[CrossRef]

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

J. Phys. A (1)

M. Pozniak, K. Zyczkowski, M. Kus, “Composed ensembles of random unitary matrices,” J. Phys. A 31, 1059–1071 (1998).
[CrossRef]

Nat. Commun. (1)

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

Nat. Photonics (5)

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

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

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

K. Si, R. Fiolka, M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nat. Photonics 6, 657–661 (2012).
[CrossRef]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[CrossRef]

New J. Phys. (1)

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[CrossRef]

Opt. Commun. (3)

Y. Wang, N. Saito, H. Tashiro, “Unidirectional operation of a ring laser by means of anisotropic acousto-optic device,” Opt. Commun. 207, 279–285 (2002).
[CrossRef]

C. Gu, P. Yeh, “Partial phase conjugation, fidelity, and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

S. Campbell, P. Yeh, C. Gu, Q. B. He, “Fidelity of image restoration by partial phase conjugation through multimode fibers,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

Opt. Express (5)

Opt. Lett. (3)

Phys. Rev. Lett. (3)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

I. M. Vellekoop, A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef]

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

Sci. Rep. (1)

K. Si, R. Fiolka, M. Cui, “Breaking the spatial resolution barrier via iterative sound-light interaction in deep tissue microscopy,” Sci. Rep. 2, 748 (2012).
[CrossRef]

Science (1)

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef]

SIAM J. Sci. Comput. (1)

L. Shampine, M. Reichelt, “The MATLAB ODE suite,” SIAM J. Sci. Comput. 18, 1–22 (1997).
[CrossRef]

Other (1)

W. J. Tom, “Focusing light within turbid media with virtual aperture culling of the eigenmodes of a resonator,” Ph.D. dissertation (University of Texas at Austin, 2012).

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Figures (9)

Fig. 1.
Fig. 1.

(a) Pulse of seed light passes through the first phase conjugate mirror, PCM. Though some of the light is attenuated by absorbers (black circles) and scatterers (white circles) in the turbid medium (TM), some of the light reaches the second PCM. (b) The light which reaches the second PCM is phase conjugated and travels back toward the first PCM by traversing its path in the TM in the opposite direction. (c) The light which continually cycles from one PCM through the TM to the other PCM constitutes the stable modes of the phase conjugate resonator. An actual phase conjugate resonator may support countless optical modes. Moreover, cavity gain ensures that the modes contain many photons. The total circulating power of the phase conjugate resonator can be very high without causing damage because photons are concentrated in modes with low absorption. (d) Neither PCM is able to invert nonreciprocal effects such as the Faraday effect, which is the nonreciprocal polarization rotation of light in a medium with an axial magnetic field. Consequently, processes such as scattering that generally exhibit polarization dependence are altered with each pass through the TM. Modes can be perturbed such that light is lost from the phase conjugate resonator by absorption (upper mode) or scattering (lower mode). The modes which avoid the axial magnetic fields tend to be attenuated the least and have the highest probability of becoming stable modes (middle mode). The upper magnetic field (green) directed toward the right decreases with distance (diminishing green intensity) from an unseen magnet from above, while the lower magnetic field (blue) directed toward the left decreases with distance (diminishing blue intensity) from an unseen magnet from below.

Fig. 2.
Fig. 2.

In these three representative time series of the idealized VACER model, virtually all of the circulating power is in the selected mode (solid line) by the end of the simulations because the power in the seven culled modes (dashed lines) perpetually decays. In (a), the transmittance of the culled modes is 4% less than the transmittance of the selected mode, while in (b) and (c), the transmittance of the culled modes is 2% less. Though (a) and (b) result from simulations with the same randomly generated turbid medium, (c) originates from a distinct turbid medium.

Fig. 3.
Fig. 3.

In this time series with partial phase conjugation, the selected mode (solid line) eventually has more power than the seven culled modes (dashed lines), but the culled modes do not continually diminish. Generally, incomplete phase conjugation couples the selected mode to the culled modes, which even an idealized VACER system cannot prevent. The transmittance of the culled modes is 2% less than the transmittance of the selected mode.

Fig. 4.
Fig. 4.

In this time series with backscatter, the selected mode (solid line) eventually has more power than the seven culled modes (dashed lines), but the culled modes do not continually diminish. Generally, backscatter couples the selected mode to the culled modes, which even an idealized VACER system cannot prevent. In this example, the turbid medium backscatters about 7.5% of the incident light. The transmittance of the culled modes is 2% less than the transmittance of the selected mode.

Fig. 5.
Fig. 5.

In the idealized VACER model, the relative change per pass in the power of the culled modes is merely the relative transmittance of the culled modes.

Fig. 6.
Fig. 6.

Final power in the selected mode depends on the transmittance of the culled modes. While nearly all of the power is in the selected mode, given time, when the culled mode transmittance is less than the selected mode transmittance, the selected mode has negligible power when culled mode transmittance is greater than selected mode transmittance. Each plotted curve is from a different randomly generated turbid medium.

Fig. 7.
Fig. 7.

(a) After one cycle, very little power is in the selected mode at the center of the image. (b) After 250 cycles, the selected mode has the most power.

Fig. 8.
Fig. 8.

In these three representative time series of the fast VACER model, virtually all of the circulating power is in the selected mode (solid line) by the end of the simulations, though the power in the seven culled modes (dashed lines) initially rises with the selected mode power. In (a), the transmittance of the culled modes is 4% less than the transmittance of the selected mode, while in (b) and (c), the transmittance of the culled modes is 2% less. Though (a) and (b) result from simulations with the same randomly generated turbid medium, (c) originates from a distinct turbid medium. The turbid media and virtual aperture configurations used in (a)–(c) and in the corresponding plots in Fig. 2 are the same.

Fig. 9.
Fig. 9.

Final power in the selected mode depends on the transmittance of the culled modes. While most of the power is in the selected mode when culled mode transmittance is less than the selected mode transmittance, the selected mode has little power when culled mode transmittance is greater than the selected mode transmittance. Each plotted curve is from a different randomly generated turbid medium. Furthermore, corresponding curves in this plot and Fig. 6 used the same turbid medium.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

f ( n E n ) = n f ( E n )
f ( η E n ) = η f ( E n ) ,
g ( n E n ) = γ n f ( E n )
g ( η E n ) η g ( E n ) .
[ B m , 1 F m + 1 , 0 ] = M m [ F m , 1 B m + 1 , 0 ] ,
E p = A p exp ( i k p · r ) exp ( i ω t ) ,
2 i | k p | cos θ p A p ξ 2 i | k p | c A p t = μ ω 2 F p ,
c = 1 μ ϵ ,
P = p F p exp ( i k p · r ) exp ( i ω t ) = ϵ χ p E p ,
N t = R 1 τ n N n exp ( i K n · r ) c 2 τ I s n N n exp ( i K n · r ) Re [ ϵ p q E p E q * ] ,
I s = ω σ τ .
[ S u P u ] = 1 2 [ 1 i i 1 ] [ A u 0 ] .
[ A v x ] = 1 2 [ 1 i i 1 ] [ S v P v ] ,

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