Abstract

In recent years, wavefront shaping has been utilized to control and correct distorted light for enhancing a bright spot, generation of a Bessel beam or darkening a complete area at the output of a scattering system. All these outcomes can be thought of as enhancing a particular mode of the output field. In this letter, we study the relation between the attainable enhancement factor, corresponding to the efficiency of mode conversion, and the field distribution of the target mode. Working in the limit of a thin diffuser enables not only a comparison between experimental and simulated results, but also allows for derivation of an analytic formula. These results shed light on the ability to use a scattering medium as a mode converter and on the relationship between the desired shape and the efficiency.

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

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2017 (4)

S. Rotter and S. Gigan, “Light fields in complex media: mesoscopic scattering meets wave control,” Rev. Mod. Phys. 89(1), 015005 (2017).
[Crossref]

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. Douglas Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13(5), 497–502 (2017).
[Crossref]

R. Fickler, M. Ginoya, and R. W. Boyd, “Custom-tailored spatial mode sorting by controlled random scattering,” Phys. Rev. B 95(16), 161108 (2017).
[Crossref]

A. Boniface, M. Mounaix, B. Blochet, R. Piestun, and S. Gigan, “Transmission-matrix-based point-spread-function engineering through a complex medium,” Optica 4(1), 54–59 (2017).
[Crossref]

2016 (5)

A. Malavalli, M. Ackermann, and C. M. Aegerter, “Structured illumination behind turbid media,” Opt. Express 24(20), 23018–23026 (2016).
[Crossref] [PubMed]

A. Daniel, L. Liberman, and Y. Silberberg, “Wave front shaping for glare reduction,” Optica 3(10), 1104–1106 (2016).
[Crossref]

D. Di Battista, D. Ancora, M. Leonetti, and G. Zacharakis, “Tailoring non-diffractive beams from amorphous light speckles,” Appl. Phys. Lett. 109(12), 121110 (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(4), 043834 (2016).
[Crossref]

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116(25), 253901 (2016).
[Crossref] [PubMed]

2015 (1)

J. Carpenter, B. J. Eggleton, and J. Schröder, “Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre,” Nat. Photonics 9(11), 751–757 (2015).
[Crossref]

2013 (1)

2012 (3)

2011 (6)

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(19), 193905 (2011).
[Crossref] [PubMed]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2(1), 447 (2011).
[Crossref] [PubMed]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19(1), 247–254 (2011).
[Crossref] [PubMed]

2010 (4)

I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Opt. Lett. 35(8), 1245–1247 (2010).
[Crossref] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and 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(10), 100601 (2010).
[Crossref] [PubMed]

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010).
[Crossref]

2009 (1)

2007 (1)

Ackermann, M.

Aegerter, C. M.

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(19), 193905 (2011).
[Crossref] [PubMed]

Ancora, D.

D. Di Battista, D. Ancora, M. Leonetti, and G. Zacharakis, “Tailoring non-diffractive beams from amorphous light speckles,” Appl. Phys. Lett. 109(12), 121110 (2016).
[Crossref]

Andreoli, D.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116(25), 253901 (2016).
[Crossref] [PubMed]

Aulbach, J.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

Austin, D. R.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2(1), 447 (2011).
[Crossref] [PubMed]

Baddour, N.

Bertolotti, J.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

Bianchi, S.

Blochet, B.

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and 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(10), 100601 (2010).
[Crossref] [PubMed]

Bondareff, P.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2(1), 447 (2011).
[Crossref] [PubMed]

Boniface, A.

Boyd, R. W.

R. Fickler, M. Ginoya, and R. W. Boyd, “Custom-tailored spatial mode sorting by controlled random scattering,” Phys. Rev. B 95(16), 161108 (2017).
[Crossref]

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Brown, A. N.

Cao, H.

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. Douglas Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13(5), 497–502 (2017).
[Crossref]

Caravaca-Aguirre, A. M.

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and 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(10), 100601 (2010).
[Crossref] [PubMed]

Carpenter, J.

J. Carpenter, B. J. Eggleton, and J. Schröder, “Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre,” Nat. Photonics 9(11), 751–757 (2015).
[Crossref]

Chatel, B.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2(1), 447 (2011).
[Crossref] [PubMed]

Choi, W.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

Choi, Y.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

Cizmar, T.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

Conkey, D. B.

Daniel, A.

Dasari, R. R.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

Defienne, H.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116(25), 253901 (2016).
[Crossref] [PubMed]

Dholakia, K.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

Di Battista, D.

D. Di Battista, D. Ancora, M. Leonetti, and G. Zacharakis, “Tailoring non-diffractive beams from amorphous light speckles,” Appl. Phys. Lett. 109(12), 121110 (2016).
[Crossref]

Di Leonardo, R.

Douglas Stone, A.

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. Douglas Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13(5), 497–502 (2017).
[Crossref]

Eggleton, B. J.

J. Carpenter, B. J. Eggleton, and J. Schröder, “Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre,” Nat. Photonics 9(11), 751–757 (2015).
[Crossref]

Fang-Yen, C.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

Feld, M. S.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

Fickler, R.

R. Fickler, M. Ginoya, and R. W. Boyd, “Custom-tailored spatial mode sorting by controlled random scattering,” Phys. Rev. B 95(16), 161108 (2017).
[Crossref]

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and 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(10), 100601 (2010).
[Crossref] [PubMed]

Gigan, S.

S. Rotter and S. Gigan, “Light fields in complex media: mesoscopic scattering meets wave control,” Rev. Mod. Phys. 89(1), 015005 (2017).
[Crossref]

A. Boniface, M. Mounaix, B. Blochet, R. Piestun, and S. Gigan, “Transmission-matrix-based point-spread-function engineering through a complex medium,” Optica 4(1), 54–59 (2017).
[Crossref]

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116(25), 253901 (2016).
[Crossref] [PubMed]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2(1), 447 (2011).
[Crossref] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and 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(10), 100601 (2010).
[Crossref] [PubMed]

Ginoya, M.

R. Fickler, M. Ginoya, and R. W. Boyd, “Custom-tailored spatial mode sorting by controlled random scattering,” Phys. Rev. B 95(16), 161108 (2017).
[Crossref]

Gjonaj, B.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

Goetschy, A.

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. Douglas Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13(5), 497–502 (2017).
[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(4), 043834 (2016).
[Crossref]

Grésillon, S.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116(25), 253901 (2016).
[Crossref] [PubMed]

Guan, Y.

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(4), 043834 (2016).
[Crossref]

Hsu, C. W.

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. Douglas Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13(5), 497–502 (2017).
[Crossref]

Johnson, P. M.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

Kang, P.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

Katz, O.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116(25), 253901 (2016).
[Crossref] [PubMed]

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(8), 549–553 (2012).
[Crossref]

Y. Guan, O. Katz, E. Small, J. Zhou, and Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37(22), 4663–4665 (2012).
[Crossref] [PubMed]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Lagendijk, A.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010).
[Crossref]

Lee, K. J.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

Leonetti, M.

D. Di Battista, D. Ancora, M. Leonetti, and G. Zacharakis, “Tailoring non-diffractive beams from amorphous light speckles,” Appl. Phys. Lett. 109(12), 121110 (2016).
[Crossref]

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and 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(10), 100601 (2010).
[Crossref] [PubMed]

Liberman, L.

Liew, S. F.

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. Douglas Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13(5), 497–502 (2017).
[Crossref]

Malavalli, A.

Mazilu, M.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2(1), 447 (2011).
[Crossref] [PubMed]

Mosk, A. P.

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(4), 043834 (2016).
[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(19), 193905 (2011).
[Crossref] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010).
[Crossref]

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

Mounaix, M.

A. Boniface, M. Mounaix, B. Blochet, R. Piestun, and S. Gigan, “Transmission-matrix-based point-spread-function engineering through a complex medium,” Optica 4(1), 54–59 (2017).
[Crossref]

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116(25), 253901 (2016).
[Crossref] [PubMed]

Ojambati, O. S.

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(4), 043834 (2016).
[Crossref]

Piestun, R.

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and 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(10), 100601 (2010).
[Crossref] [PubMed]

Rotter, S.

S. Rotter and S. Gigan, “Light fields in complex media: mesoscopic scattering meets wave control,” Rev. Mod. Phys. 89(1), 015005 (2017).
[Crossref]

Schröder, J.

J. Carpenter, B. J. Eggleton, and J. Schröder, “Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre,” Nat. Photonics 9(11), 751–757 (2015).
[Crossref]

Silberberg, Y.

A. Daniel, L. Liberman, and Y. Silberberg, “Wave front shaping for glare reduction,” Optica 3(10), 1104–1106 (2016).
[Crossref]

Y. Guan, O. Katz, E. Small, J. Zhou, and Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37(22), 4663–4665 (2012).
[Crossref] [PubMed]

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(8), 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(6), 372–377 (2011).
[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(8), 549–553 (2012).
[Crossref]

Y. Guan, O. Katz, E. Small, J. Zhou, and Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37(22), 4663–4665 (2012).
[Crossref] [PubMed]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Tajalli, A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2(1), 447 (2011).
[Crossref] [PubMed]

Toussaint, K. C.

Tripathi, S.

van Putten, E. G.

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

Vellekoop, I. M.

Volpe, G.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116(25), 253901 (2016).
[Crossref] [PubMed]

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(4), 043834 (2016).
[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(19), 193905 (2011).
[Crossref] [PubMed]

Walmsley, I. A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2(1), 447 (2011).
[Crossref] [PubMed]

Yang, T. D.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

Zacharakis, G.

D. Di Battista, D. Ancora, M. Leonetti, and G. Zacharakis, “Tailoring non-diffractive beams from amorphous light speckles,” Appl. Phys. Lett. 109(12), 121110 (2016).
[Crossref]

Zhou, J.

Appl. Phys. Lett. (1)

D. Di Battista, D. Ancora, M. Leonetti, and G. Zacharakis, “Tailoring non-diffractive beams from amorphous light speckles,” Appl. Phys. Lett. 109(12), 121110 (2016).
[Crossref]

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

Nat. Commun. (1)

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2(1), 447 (2011).
[Crossref] [PubMed]

Nat. Photonics (5)

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(8), 549–553 (2012).
[Crossref]

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 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(6), 372–377 (2011).
[Crossref]

J. Carpenter, B. J. Eggleton, and J. Schröder, “Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre,” Nat. Photonics 9(11), 751–757 (2015).
[Crossref]

Nat. Phys. (1)

C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. Douglas Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13(5), 497–502 (2017).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Optica (2)

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(4), 043834 (2016).
[Crossref]

Phys. Rev. B (1)

R. Fickler, M. Ginoya, and R. W. Boyd, “Custom-tailored spatial mode sorting by controlled random scattering,” Phys. Rev. B 95(16), 161108 (2017).
[Crossref]

Phys. Rev. Lett. (5)

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett. 106(19), 193905 (2011).
[Crossref] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and 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(10), 100601 (2010).
[Crossref] [PubMed]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107(2), 023902 (2011).
[Crossref] [PubMed]

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116(25), 253901 (2016).
[Crossref] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

S. Rotter and S. Gigan, “Light fields in complex media: mesoscopic scattering meets wave control,” Rev. Mod. Phys. 89(1), 015005 (2017).
[Crossref]

Other (2)

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of the optical setup used for enhancing a particular mode of a light by wave front shaping (a helical mode in this case). A speckle field propagates and encounters a helical phase plate (PP) at the far field (or at the Fourier plane of lens L1, as shown). The resulting field is then focused on a CCD camera by lens L2. Using a feedback algorithm, the phases on the SLM are adjusted to maximize the focus, which corresponds to a uniform phase distribution at the output of the phase mask. A variable size aperture (A), attached to the mask, enables the control the size of the target mode. (b) Intensity autocorrelation of the speckle pattern: the size of the autocorrelation spot is approximately 12 pixels, each pixel is 5.3 µm. Therefore the full width is ~60 µm. Since we take the FWHM of the distribution as the speckle size, the diameter is smaller than the full width by a factor of about 1.5, namely ~40 µm. (c) The intensity distribution (to scale) of the scattered light before and after optimization for a particular aperture size as observed at the aperture plane (target plane). A doughnut shape which is associated with the helical phase distribution is obtained.
Fig. 2
Fig. 2 Experimentally measured field enhancement (enhancement factor is defined as the ratio between the optimized intensity on the target CCD pixel and the initial average intensity before optimization) for different target modes. The enhancement factor is plotted as a function of aperture diameter for no mask (blue) helical phase mask of topological charge 2 (red) and a random phase mask (black). The upper axis indicates the aperture diameter in terms of average speckle diameter. Error bars were determined from multiple realizations of the scattering medium. Note that for helical phase, the minimum pinhole size is 150 μm, which is limited by the finite singularity dimension of the phase mask. For the constant and the random masks, the minimum pinhole size is 25 μm, which is approximately half the size of a single speckle at the pinhole plane.
Fig. 3
Fig. 3 Simulations (a) and theoretical estimates (b) showing the optimized enhancements for a flat field with no mask (red), a field with spiral phase of charge 2 (green) and a field with random phase structure (gray), as a function of aperture diameter S (normalized by the speckle size d). (The derivation of the random phase is not valid for small apertures (details in theoretical derivation section). The enhancement factor is defined as the ratio between the optimized intensity on the target pixel and the initial average intensity before optimization.
Fig. 4
Fig. 4 (a) The simplified geometry for estimating the maximal possible enhancement. (b) To estimate the number of effective control elements and their contributions, we consider a wave propagating backwards from the target to the SLM plane. The distribution of light on the SLM is determined by the convolution of the phase mask and the aperture. For a constant phase, as illustrated here, as the aperture is closed the diffracted beam broadens, covering more pixels on the SLM, enabling higher enhancement.
Fig. 5
Fig. 5 Optimal enhancement of phase-singular fields vs aperture radius for m = 1 (red), m = 2 (green), m = 4 (blue).

Equations (15)

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E( q )=F{ circ( 2r S ) }= I 0 [ 2 J 1 ( x ) x ]; I( q )= I 0 [ 2 J 1 (x) x ] 2 .
I rp = 4 π N c π q m 2 2π 0 q m qI( q )dq = 4 π N c π q m 2 4π  ( λL πS   ) 2  [ 1- J 0 2 (   πS q m λL )- J 1 2 (   πS q m λL ) ] =  4 π 4 N c   ( d S   ) 2  [ 1 J 0 2 (   S d ) J 1 2 (   S d ) ].
E opt = N c π q m 2 2π 0 q m q| E( q ) |dq =4 N c   ( d S   ) 2  [ 12 J 0 ( z 1 )+2 J 0 ( z 2 ) J 0 (   S d ) ].
F f = | E opt | 2 I rp = π 4 4 N c ( d S ) 2 [ 12 J 0 ( z 1 )+2 J 0 ( z 2 ) J 0 ( S d ) ] 2 [ 1 J 0 2 (   S d ) J 1 2 (   S d ) ] .
E( q,φ )=F{ T(r,θ) }=F{ circ( 2r S )exp( i2θ ) }.
E( q,φ )=2πexp( 2iφ ) 0 S/2 J 2 ( 2πrq λL ) r dr.
J 2 ( x ) x dx =2 J 0 x J 1 ,
E( q,φ )=2πexp( i2φ ) ( λL 2πq ) 2 [ 22 J 0 ( πsq λL ) πsq λL J 1 ( πsq λL ) ],
E opt = N c π q m 2 2π 0 q m q| E( q ) |dq = N c π q m 2 ( 2π ) 2 ( λL 2π ) 2 0 S/d x 1 | 22 J 0 ( x )x J 1 ( x ) |dx.
I rp = 4 π N c π q m 2 2π 0 q m qI( q )dq= = 4 π N c π q m 2 8 π 3   ( λL 2π   ) 4   ( d S ) 2   0 S/d x 3 [ 22 J 0 ( x )x J 1 ( x ) ] 2 dx,
F s = | E opt | 2 I rp = π 4 2 N c   ( d S   ) 2 [ 0 S/d x 1 | 22 J 0 ( x )x J 1 ( x ) |dx ] 2 0 S/d x 3 | 22 J 0 ( x )x J 1 ( x ) | 2 dx .
P( I )= 1 2 σ 2 exp( I 2 σ 2 ), P( | E | )= | E | σ 2 exp( E 2 2 σ 2 ),
E opt = 2π N c π q m 2 | E( q,φ ) |qdq =  N c   E = N c EP( E )dE= N c σ 2 2π .
I rp = 2π 4 π N c π q m 2 I(q,φ)qdq = 4 π N c   I = 4 π N c IP( I )dI= 4 π N c 2 σ 2 .
F r = | E opt | 2 I rp = ( π 4 ) 2 N c .

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