Abstract

While a three-dimensional (3D) scattering medium is from the outset opaque, such a medium sustains intriguing transport channels with near-unity transmission that are pursued for fundamental reasons and for applications in solid-state lighting, random lasers, solar cells, and biomedical optics. Here, we study the 3D spatially resolved distribution of the energy density of light in a 3D scattering medium upon the excitation of highly transmitting channels. The coupling into these channels is excited by spatially shaping the incident optical wavefronts to a focus on the back surface. To probe the local energy density, we excite isolated fluorescent nanospheres distributed inside the medium. From the spatial fluorescent intensity pattern we obtain the position of each nanosphere, while the total fluorescent intensity gauges the energy density. Our 3D spatially resolved measurements reveal that the differential fluorescent enhancement changes with depth, up to 26× at the back surface of the medium, and the enhancement reveals a strong peak versus transverse position. We successfully interpret our results with a newly developed 3D model without adjustable parameters that considers the time-reversed diffusion starting from a point source at the back surface.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
    [Crossref]
  2. P. Sheng, Introduction to Wave Scattering, Localization, Mesoscopic Phenomena (Springer, 2006).
  3. E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).
  4. D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2013).
    [Crossref]
  5. C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).
    [Crossref]
  6. O. N. Dorokhov, “On the coexistence of localized and extended electronic states in the metallic phase,” Solid State Commun. 51, 381–384 (1984).
    [Crossref]
  7. I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
    [Crossref]
  8. S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112, 133903 (2014).
    [Crossref]
  9. 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]
  10. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
    [Crossref]
  11. I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
    [Crossref]
  12. 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]
  13. 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]
  14. I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
    [Crossref]
  15. R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
    [Crossref]
  16. M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
    [Crossref]
  17. W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q.-H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5, 11393 (2015).
    [Crossref]
  18. O. S. Ojambati, J. T. Hosmer-Quint, K. J. Gorter, A. P. Mosk, and W. L. Vos, “Controlling the intensity of light in large areas at the interfaces of a scattering medium,” Phys. Rev. A 94, 043834 (2016).
    [Crossref]
  19. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
    [Crossref]
  20. 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]
  21. J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
    [Crossref]
  22. D. Psaltis and I. N. Papadopoulos, “The fog clears,” Nature 491, 197–198 (2012).
  23. J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
    [Crossref]
  24. M. L. Meretska, A. Lagendijk, H. Thyrrestrup, A. P. Mosk, W. L. IJzerman, and W. L. Vos, “How to distinguish elastically scattered light from Stokes shifted light for solid-state lighting?” J. Appl. Phys. 119, 093102 (2016).
    [Crossref]
  25. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
    [Crossref]
  26. A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
    [Crossref]
  27. L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2012).
  28. C. Blum, A. P. Mosk, I. S. Nikolaev, V. Subramaniam, and W. L. Vos, “Color control of natural fluorescent proteins by photonic crystals,” Small 4, 492–496 (2008).
    [Crossref]
  29. O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
    [Crossref]
  30. W. Choi, A. P. Mosk, Q. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83, 134207 (2011).
    [Crossref]
  31. M. Davy, Z. Shi, and A. Z. Genack, “Focusing through random media: eigenchannel participation number and intensity correlation,” Phys. Rev. B 85, 035105 (2012).
    [Crossref]
  32. M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
    [Crossref]
  33. S. F. Liew and H. Cao, “Modification of light transmission channels by inhomogeneous absorption in random media,” Opt. Express 23, 11043 (2015).
    [Crossref]
  34. O. S. Ojambati, A. P. Mosk, I. M. Vellekoop, A. Lagendijk, and W. L. Vos, “Controlling waves in space and time for imaging and focusing in complex media,” Opt. Express 24, 18525 (2016).
    [Crossref]
  35. R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
    [Crossref]
  36. M. Koirala, R. Sarma, H. Cao, and A. Yamilov, “Inverse design of perfectly transmitting eigenchannels in scattering media,” Phys. Rev. B 96, 054209 (2017).
    [Crossref]
  37. Although the differential fluorescence enhancement (the slope) is proportional to the enhancement in the ideal limit of perfect fidelity [29], we focus here on the slope since it is directly obtained from the measurements.
  38. In Figs. 3(a) and 3(b), the maxima are centered at X0=3  μm and X0=1  μm, respectively, due to a slight misalignment of the nanosphere from the optical axis. This misalignment is due to the weakness of the signal from fluorescent particles that are close to the back surface of the sample.
  39. H. Yılmaz, W. L. Vos, and A. P. Mosk, “Optimal control of light propagation through multiple-scattering media in the presence of noise,” Biomed. Opt. Express 4, 1759–1768 (2013).
    [Crossref]
  40. Our procedure is an innovation beyond Ref. [29] where we extrapolated to perfect fidelity; the present one solely exploits measured quantities.
  41. J. B. Pendry, A. MacKinnon, and A. B. Pretre, “Maximal fluctuations—a new phenomenon in disordered systems,” Physica A 168, 400–407 (1990).
    [Crossref]
  42. J. B. Pendry, A. MacKinnon, and P. J. Roberts, “Universality classes and fluctuations in disordered systems,” Proc. R. Soc. London Ser. A 437, 67–83 (1992).
    [Crossref]
  43. A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
    [Crossref]

2017 (1)

M. Koirala, R. Sarma, H. Cao, and A. Yamilov, “Inverse design of perfectly transmitting eigenchannels in scattering media,” Phys. Rev. B 96, 054209 (2017).
[Crossref]

2016 (5)

O. S. Ojambati, A. P. Mosk, I. M. Vellekoop, A. Lagendijk, and W. L. Vos, “Controlling waves in space and time for imaging and focusing in complex media,” Opt. Express 24, 18525 (2016).
[Crossref]

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[Crossref]

O. S. Ojambati, J. T. Hosmer-Quint, K. J. Gorter, A. P. Mosk, and W. L. Vos, “Controlling the intensity of light in large areas at the interfaces of a scattering medium,” Phys. Rev. A 94, 043834 (2016).
[Crossref]

M. L. Meretska, A. Lagendijk, H. Thyrrestrup, A. P. Mosk, W. L. IJzerman, and W. L. Vos, “How to distinguish elastically scattered light from Stokes shifted light for solid-state lighting?” J. Appl. Phys. 119, 093102 (2016).
[Crossref]

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

2015 (4)

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref]

S. F. Liew and H. Cao, “Modification of light transmission channels by inhomogeneous absorption in random media,” Opt. Express 23, 11043 (2015).
[Crossref]

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q.-H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5, 11393 (2015).
[Crossref]

2014 (1)

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112, 133903 (2014).
[Crossref]

2013 (2)

2012 (7)

M. Davy, Z. Shi, and A. Z. Genack, “Focusing through random media: eigenchannel participation number and intensity correlation,” Phys. Rev. B 85, 035105 (2012).
[Crossref]

A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (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]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (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]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

D. Psaltis and I. N. Papadopoulos, “The fog clears,” Nature 491, 197–198 (2012).

2011 (3)

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]

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]

W. Choi, A. P. Mosk, Q. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83, 134207 (2011).
[Crossref]

2010 (2)

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

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

2008 (3)

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

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

C. Blum, A. P. Mosk, I. S. Nikolaev, V. Subramaniam, and W. L. Vos, “Color control of natural fluorescent proteins by photonic crystals,” Small 4, 492–496 (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]

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

1999 (1)

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

1997 (1)

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).
[Crossref]

1995 (1)

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
[Crossref]

1994 (1)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[Crossref]

1992 (1)

J. B. Pendry, A. MacKinnon, and P. J. Roberts, “Universality classes and fluctuations in disordered systems,” Proc. R. Soc. London Ser. A 437, 67–83 (1992).
[Crossref]

1990 (1)

J. B. Pendry, A. MacKinnon, and A. B. Pretre, “Maximal fluctuations—a new phenomenon in disordered systems,” Physica A 168, 400–407 (1990).
[Crossref]

1984 (1)

O. N. Dorokhov, “On the coexistence of localized and extended electronic states in the metallic phase,” Solid State Commun. 51, 381–384 (1984).
[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]

Akkermans, E.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).

Atwater, H. A.

A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[Crossref]

Balachandran, R. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[Crossref]

Beenakker, C. W. J.

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).
[Crossref]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[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]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

C. Blum, A. P. Mosk, I. S. Nikolaev, V. Subramaniam, and W. L. Vos, “Color control of natural fluorescent proteins by photonic crystals,” Small 4, 492–496 (2008).
[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]

Bromberg, Y.

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[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]

Cao, H.

M. Koirala, R. Sarma, H. Cao, and A. Yamilov, “Inverse design of perfectly transmitting eigenchannels in scattering media,” Phys. Rev. B 96, 054209 (2017).
[Crossref]

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[Crossref]

S. F. Liew and H. Cao, “Modification of light transmission channels by inhomogeneous absorption in random media,” Opt. Express 23, 11043 (2015).
[Crossref]

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112, 133903 (2014).
[Crossref]

Choi, W.

W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q.-H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5, 11393 (2015).
[Crossref]

W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q.-H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5, 11393 (2015).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
[Crossref]

W. Choi, A. P. Mosk, Q. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83, 134207 (2011).
[Crossref]

W. Choi, A. P. Mosk, Q. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83, 134207 (2011).
[Crossref]

Choi, Y.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
[Crossref]

Coltrin, M. E.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Crawford, M. H.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Davy, M.

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref]

M. Davy, Z. Shi, and A. Z. Genack, “Focusing through random media: eigenchannel participation number and intensity correlation,” Phys. Rev. B 85, 035105 (2012).
[Crossref]

Derode, A.

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
[Crossref]

Dorokhov, O. N.

O. N. Dorokhov, “On the coexistence of localized and extended electronic states in the metallic phase,” Solid State Commun. 51, 381–384 (1984).
[Crossref]

Fang-Yen, C.

W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q.-H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5, 11393 (2015).
[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]

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
[Crossref]

Fischer, A. J.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Genack, A. Z.

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref]

M. Davy, Z. Shi, and A. Z. Genack, “Focusing through random media: eigenchannel participation number and intensity correlation,” Phys. Rev. B 85, 035105 (2012).
[Crossref]

Gigan, 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]

Goetschy, A.

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112, 133903 (2014).
[Crossref]

Gomes, A. S. L.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[Crossref]

Gorter, K. J.

O. S. Ojambati, J. T. Hosmer-Quint, K. J. Gorter, A. P. Mosk, and W. L. Vos, “Controlling the intensity of light in large areas at the interfaces of a scattering medium,” Phys. Rev. A 94, 043834 (2016).
[Crossref]

Horstmeyer, R.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

Hosmer-Quint, J. T.

O. S. Ojambati, J. T. Hosmer-Quint, K. J. Gorter, A. P. Mosk, and W. L. Vos, “Controlling the intensity of light in large areas at the interfaces of a scattering medium,” Phys. Rev. A 94, 043834 (2016).
[Crossref]

IJzerman, W. L.

M. L. Meretska, A. Lagendijk, H. Thyrrestrup, A. P. Mosk, W. L. IJzerman, and W. L. Vos, “How to distinguish elastically scattered light from Stokes shifted light for solid-state lighting?” J. Appl. Phys. 119, 093102 (2016).
[Crossref]

Katz, O.

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, D.

W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q.-H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5, 11393 (2015).
[Crossref]

Kim, J.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
[Crossref]

Kim, M.

W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q.-H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5, 11393 (2015).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
[Crossref]

Koirala, M.

M. Koirala, R. Sarma, H. Cao, and A. Yamilov, “Inverse design of perfectly transmitting eigenchannels in scattering media,” Phys. Rev. B 96, 054209 (2017).
[Crossref]

Krames, M. R.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Lagendijk, A.

M. L. Meretska, A. Lagendijk, H. Thyrrestrup, A. P. Mosk, W. L. IJzerman, and W. L. Vos, “How to distinguish elastically scattered light from Stokes shifted light for solid-state lighting?” J. Appl. Phys. 119, 093102 (2016).
[Crossref]

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

O. S. Ojambati, A. P. Mosk, I. M. Vellekoop, A. Lagendijk, and W. L. Vos, “Controlling waves in space and time for imaging and focusing in complex media,” Opt. Express 24, 18525 (2016).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (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]

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

Lawandy, N. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[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]

Liew, S. F.

S. F. Liew and H. Cao, “Modification of light transmission channels by inhomogeneous absorption in random media,” Opt. Express 23, 11043 (2015).
[Crossref]

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112, 133903 (2014).
[Crossref]

MacKinnon, A.

J. B. Pendry, A. MacKinnon, and P. J. Roberts, “Universality classes and fluctuations in disordered systems,” Proc. R. Soc. London Ser. A 437, 67–83 (1992).
[Crossref]

J. B. Pendry, A. MacKinnon, and A. B. Pretre, “Maximal fluctuations—a new phenomenon in disordered systems,” Physica A 168, 400–407 (1990).
[Crossref]

Meretska, M. L.

M. L. Meretska, A. Lagendijk, H. Thyrrestrup, A. P. Mosk, W. L. IJzerman, and W. L. Vos, “How to distinguish elastically scattered light from Stokes shifted light for solid-state lighting?” J. Appl. Phys. 119, 093102 (2016).
[Crossref]

Montambaux, G.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).

Mosk, A. P.

M. L. Meretska, A. Lagendijk, H. Thyrrestrup, A. P. Mosk, W. L. IJzerman, and W. L. Vos, “How to distinguish elastically scattered light from Stokes shifted light for solid-state lighting?” J. Appl. Phys. 119, 093102 (2016).
[Crossref]

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

O. S. Ojambati, J. T. Hosmer-Quint, K. J. Gorter, A. P. Mosk, and W. L. Vos, “Controlling the intensity of light in large areas at the interfaces of a scattering medium,” Phys. Rev. A 94, 043834 (2016).
[Crossref]

O. S. Ojambati, A. P. Mosk, I. M. Vellekoop, A. Lagendijk, and W. L. Vos, “Controlling waves in space and time for imaging and focusing in complex media,” Opt. Express 24, 18525 (2016).
[Crossref]

H. Yılmaz, W. L. Vos, and A. P. Mosk, “Optimal control of light propagation through multiple-scattering media in the presence of noise,” Biomed. Opt. Express 4, 1759–1768 (2013).
[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]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

W. Choi, A. P. Mosk, Q. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83, 134207 (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, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[Crossref]

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

C. Blum, A. P. Mosk, I. S. Nikolaev, V. Subramaniam, and W. L. Vos, “Color control of natural fluorescent proteins by photonic crystals,” Small 4, 492–496 (2008).
[Crossref]

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

Mueller, G. O.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Mueller-Mach, R.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Nieuwenhuizen, T. M.

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

Nikolaev, I. S.

C. Blum, A. P. Mosk, I. S. Nikolaev, V. Subramaniam, and W. L. Vos, “Color control of natural fluorescent proteins by photonic crystals,” Small 4, 492–496 (2008).
[Crossref]

Ohno, Y.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Ojambati, O. S.

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

O. S. Ojambati, J. T. Hosmer-Quint, K. J. Gorter, A. P. Mosk, and W. L. Vos, “Controlling the intensity of light in large areas at the interfaces of a scattering medium,” Phys. Rev. A 94, 043834 (2016).
[Crossref]

O. S. Ojambati, A. P. Mosk, I. M. Vellekoop, A. Lagendijk, and W. L. Vos, “Controlling waves in space and time for imaging and focusing in complex media,” Opt. Express 24, 18525 (2016).
[Crossref]

Papadopoulos, I. N.

D. Psaltis and I. N. Papadopoulos, “The fog clears,” Nature 491, 197–198 (2012).

Park, J.

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref]

Park, Q.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
[Crossref]

W. Choi, A. P. Mosk, Q. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83, 134207 (2011).
[Crossref]

Park, Q.-H.

W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q.-H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5, 11393 (2015).
[Crossref]

Pendry, J. B.

J. B. Pendry, A. MacKinnon, and P. J. Roberts, “Universality classes and fluctuations in disordered systems,” Proc. R. Soc. London Ser. A 437, 67–83 (1992).
[Crossref]

J. B. Pendry, A. MacKinnon, and A. B. Pretre, “Maximal fluctuations—a new phenomenon in disordered systems,” Physica A 168, 400–407 (1990).
[Crossref]

Petrenko, S.

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[Crossref]

Phillips, J. M.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Polman, A.

A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (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]

Popoff, S. M.

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112, 133903 (2014).
[Crossref]

Pretre, A. B.

J. B. Pendry, A. MacKinnon, and A. B. Pretre, “Maximal fluctuations—a new phenomenon in disordered systems,” Physica A 168, 400–407 (1990).
[Crossref]

Psaltis, D.

D. Psaltis and I. N. Papadopoulos, “The fog clears,” Nature 491, 197–198 (2012).

Roberts, P. J.

J. B. Pendry, A. MacKinnon, and P. J. Roberts, “Universality classes and fluctuations in disordered systems,” Proc. R. Soc. London Ser. A 437, 67–83 (1992).
[Crossref]

Rohwer, L. E. S.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Roux, P.

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
[Crossref]

Ruan, H.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

Sarma, R.

M. Koirala, R. Sarma, H. Cao, and A. Yamilov, “Inverse design of perfectly transmitting eigenchannels in scattering media,” Phys. Rev. B 96, 054209 (2017).
[Crossref]

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[Crossref]

Sauvain, E.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[Crossref]

Sheng, P.

P. Sheng, Introduction to Wave Scattering, Localization, Mesoscopic Phenomena (Springer, 2006).

Shi, Z.

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref]

M. Davy, Z. Shi, and A. Z. Genack, “Focusing through random media: eigenchannel participation number and intensity correlation,” Phys. Rev. B 85, 035105 (2012).
[Crossref]

Silberberg, Y.

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]

Simmons, J. A.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Small, E.

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]

Stone, A. D.

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112, 133903 (2014).
[Crossref]

Subramaniam, V.

C. Blum, A. P. Mosk, I. S. Nikolaev, V. Subramaniam, and W. L. Vos, “Color control of natural fluorescent proteins by photonic crystals,” Small 4, 492–496 (2008).
[Crossref]

Thyrrestrup, H.

M. L. Meretska, A. Lagendijk, H. Thyrrestrup, A. P. Mosk, W. L. IJzerman, and W. L. Vos, “How to distinguish elastically scattered light from Stokes shifted light for solid-state lighting?” J. Appl. Phys. 119, 093102 (2016).
[Crossref]

Tian, C.

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref]

Tsao, J. Y.

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[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, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[Crossref]

van Rossum, M. C. W.

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

Vellekoop, I. M.

Vos, W. L.

O. S. Ojambati, J. T. Hosmer-Quint, K. J. Gorter, A. P. Mosk, and W. L. Vos, “Controlling the intensity of light in large areas at the interfaces of a scattering medium,” Phys. Rev. A 94, 043834 (2016).
[Crossref]

M. L. Meretska, A. Lagendijk, H. Thyrrestrup, A. P. Mosk, W. L. IJzerman, and W. L. Vos, “How to distinguish elastically scattered light from Stokes shifted light for solid-state lighting?” J. Appl. Phys. 119, 093102 (2016).
[Crossref]

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

O. S. Ojambati, A. P. Mosk, I. M. Vellekoop, A. Lagendijk, and W. L. Vos, “Controlling waves in space and time for imaging and focusing in complex media,” Opt. Express 24, 18525 (2016).
[Crossref]

H. Yılmaz, W. L. Vos, and A. P. Mosk, “Optimal control of light propagation through multiple-scattering media in the presence of noise,” Biomed. Opt. Express 4, 1759–1768 (2013).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[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]

C. Blum, A. P. Mosk, I. S. Nikolaev, V. Subramaniam, and W. L. Vos, “Color control of natural fluorescent proteins by photonic crystals,” Small 4, 492–496 (2008).
[Crossref]

Wang, L. V.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2012).

Wiersma, D. S.

D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2013).
[Crossref]

Wu, H.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2012).

Yamilov, A.

M. Koirala, R. Sarma, H. Cao, and A. Yamilov, “Inverse design of perfectly transmitting eigenchannels in scattering media,” Phys. Rev. B 96, 054209 (2017).
[Crossref]

Yamilov, A. G.

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[Crossref]

Yang, C.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

Yilmaz, H.

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

H. Yılmaz, W. L. Vos, and A. P. Mosk, “Optimal control of light propagation through multiple-scattering media in the presence of noise,” Biomed. Opt. Express 4, 1759–1768 (2013).
[Crossref]

Yoon, C.

W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q.-H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5, 11393 (2015).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
[Crossref]

Biomed. Opt. Express (1)

J. Appl. Phys. (1)

M. L. Meretska, A. Lagendijk, H. Thyrrestrup, A. P. Mosk, W. L. IJzerman, and W. L. Vos, “How to distinguish elastically scattered light from Stokes shifted light for solid-state lighting?” J. Appl. Phys. 119, 093102 (2016).
[Crossref]

Laser Photon. Rev. (1)

J. M. Phillips, M. E. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1, 307–333 (2007).
[Crossref]

Nat. Commun. (2)

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[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]

Nat. Mater. (1)

A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[Crossref]

Nat. Photonics (7)

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]

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

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 581–585 (2012).
[Crossref]

D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2013).
[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]

Nature (3)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

D. Psaltis and I. N. Papadopoulos, “The fog clears,” Nature 491, 197–198 (2012).

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[Crossref]

New J. Phys. (1)

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (1)

O. S. Ojambati, J. T. Hosmer-Quint, K. J. Gorter, A. P. Mosk, and W. L. Vos, “Controlling the intensity of light in large areas at the interfaces of a scattering medium,” Phys. Rev. A 94, 043834 (2016).
[Crossref]

Phys. Rev. B (3)

W. Choi, A. P. Mosk, Q. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83, 134207 (2011).
[Crossref]

M. Davy, Z. Shi, and A. Z. Genack, “Focusing through random media: eigenchannel participation number and intensity correlation,” Phys. Rev. B 85, 035105 (2012).
[Crossref]

M. Koirala, R. Sarma, H. Cao, and A. Yamilov, “Inverse design of perfectly transmitting eigenchannels in scattering media,” Phys. Rev. B 96, 054209 (2017).
[Crossref]

Phys. Rev. Lett. (5)

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117, 086803 (2016).
[Crossref]

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

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112, 133903 (2014).
[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]

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75, 4206–4209 (1995).
[Crossref]

Physica A (1)

J. B. Pendry, A. MacKinnon, and A. B. Pretre, “Maximal fluctuations—a new phenomenon in disordered systems,” Physica A 168, 400–407 (1990).
[Crossref]

Proc. R. Soc. London Ser. A (1)

J. B. Pendry, A. MacKinnon, and P. J. Roberts, “Universality classes and fluctuations in disordered systems,” Proc. R. Soc. London Ser. A 437, 67–83 (1992).
[Crossref]

Rev. Mod. Phys. (2)

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).
[Crossref]

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

Sci. Rep. (1)

W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q.-H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5, 11393 (2015).
[Crossref]

Small (1)

C. Blum, A. P. Mosk, I. S. Nikolaev, V. Subramaniam, and W. L. Vos, “Color control of natural fluorescent proteins by photonic crystals,” Small 4, 492–496 (2008).
[Crossref]

Solid State Commun. (1)

O. N. Dorokhov, “On the coexistence of localized and extended electronic states in the metallic phase,” Solid State Commun. 51, 381–384 (1984).
[Crossref]

Other (6)

P. Sheng, Introduction to Wave Scattering, Localization, Mesoscopic Phenomena (Springer, 2006).

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2012).

Although the differential fluorescence enhancement (the slope) is proportional to the enhancement in the ideal limit of perfect fidelity [29], we focus here on the slope since it is directly obtained from the measurements.

In Figs. 3(a) and 3(b), the maxima are centered at X0=3  μm and X0=1  μm, respectively, due to a slight misalignment of the nanosphere from the optical axis. This misalignment is due to the weakness of the signal from fluorescent particles that are close to the back surface of the sample.

Our procedure is an innovation beyond Ref. [29] where we extrapolated to perfect fidelity; the present one solely exploits measured quantities.

Supplementary Material (1)

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Figures (7)

Fig. 1.
Fig. 1. Schematic of our method to probe the 3D ( x , y , z ) spatially resolved local energy density that is enhanced by wavefront shaping. Incident green light is wavefront shaped to an optimized focus at the back surface of a scattering medium (ensemble of ZnO nanospheres) to preferentially excite open transmission channels. The scattering medium is sparsely doped with fluorescent nanospheres that probe the local energy density of the green incident light at different positions ( x , y , z ) by emitting orange light in proportion to the local energy density of the green excitation light.
Fig. 2.
Fig. 2. Measured differential fluorescence enhancement η f / F (blue circles with error bars) versus depth z and scaled depth z / for two samples with thicknesses of (a)  L = 8    μm and (b)  L = 16    μm . The vertical error bars are comparable to the symbol size. The fluorescent nanospheres are centered on the optical axis at ( x 0 , y 0 ) . The red curve is the energy density enhancement predicted by our 3D model. The green dashed–dotted curve indicates a hypothetical absence of control of the energy density.
Fig. 3.
Fig. 3. Differential fluorescence enhancement η f / F versus transverse displacement Δ x relative to the optical axis for scattering samples with thicknesses of (a)  L = 8    μm [nanosphere at ( y , z ) = ( 0 , 5.9 ± 0.1 )    μm ] and (b)  L = 16    μm [nanosphere at ( y , z ) = ( 0 , 14.7 ± 0.2 )    μm ]. Red circles are the measured data with error bars. The light blue surface map and the blue solid line are the differential energy densities along the transverse x position at y = 0 , as predicted by our 3D model.
Fig. 4.
Fig. 4. Determining the depth z of a fluorescent sphere in the L = 8    μm sample. (a) Fluorescence image measured in real space by averaging m 1 = 41 data sets, each with a different random incident wavefront. (b) Fourier transform of the data in panel (a). Intensities in (a) and (b) are normalized to their maxima. (c) Solution of the diffusion equation with a single fluorescent nanosphere at depth z = 3.3 ± 0.3    μm . (d) Cross sections through the centers of (b) (blue circles) and (c) (red line), respectively, showing a good match.
Fig. 5.
Fig. 5. Measured fidelity F versus the phase perturbation factor δ ϕ m on the optimized phase pattern. The red curve is a guide to the eye.
Fig. 6.
Fig. 6. Measured fluorescence enhancement η f versus fidelity F (blue squares) at a depth z = 3.3 ± 0.3    μm in the L = 8    μm thick sample. Red dashed line: Eq. (2) with unity intercept and differential fluorescence enhancement η f / F = 6.9 ± 0.7 as the only adjustable parameter, with the error at the 95% confidence interval (red dotted lines). Magenta circles are rebinned data (101 raw data per bin), which give a similar result: η f / F = 6.7 ± 0.6 (green dashed–dotted line).
Fig. 7.
Fig. 7. (a) Transverse ( x , y ) cross sections of the calculated energy densities of optimized light at various depths z inside a scattering medium with thickness L = 8    μm . The scale bar is 10 μm. (b) Energy densities of optimized light W o integrated over the transverse ( x , y ) -plane (red solid curve), unoptimized light W uo (green short-dashed curve), and the energy density of the fundamental diffusion mode W m = 1 as a function of depth z . (c) The energy densities W o ( x = 0 , y = 0 , z ) (red solid curve) and W uo ( x = 0 , y = 0 , z ) (green dashed curve) as a function of z . I 0 and D are the incident intensity and the diffusion constant, respectively.

Equations (4)

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W e ( x , y , z ) = F · W o ( x , y , z ) + ( 1 F ) · W uo ( x , y , z ) .
η f ( x , y , z ) = 1 + F · η f F ,
ϕ p ( i , j ) = ϕ o ( i , j ) + δ ϕ ( i , j ) ,
W o ( x , y , z ) = W of ( x , y , z ) + W bg ( x , y , z ) ,

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