Abstract

We study the effect of frequency detuning on light focused through turbid media. By shaping the wavefront of the incident beam light is focused through an opaque scattering layer. When detuning the laser we observe a gradual decrease of the focus intensity, while the position, size,and shape of the focus remain the same within experimental accuracy. The frequency dependence of the focus intensity follows a measured speckle correlation function. We support our experimental findings with calculations based on transport theory. Our results imply wavefront shaping methods can be generalized to allow focusing of optical pulses in turbid media.

© 2011 Optical Society of America

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  1. S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
    [CrossRef] [PubMed]
  2. I. Freund, Physica A 168, 49 (1990).
    [CrossRef]
  3. S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, Phys. Rev. Lett. 99, 063902 (2007).
    [CrossRef] [PubMed]
  4. M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
    [CrossRef]
  5. G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, Science 315, 1120 (2007).
    [CrossRef] [PubMed]
  6. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
    [CrossRef]
  7. I. M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309 (2007).
    [CrossRef] [PubMed]
  8. C.-L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, Opt. Express 18, 12283 (2010).
    [CrossRef] [PubMed]
  9. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 1 (2010).
    [CrossRef]
  10. T. W. Kohlgraf-Owensand and A. Dogariu, Opt. Lett. 35, 2236 (2010).
    [CrossRef]
  11. E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, Appl. Opt. 47, 2076 (2008).
    [CrossRef] [PubMed]
  12. I. M. Vellekoop and A. P. Mosk, Phys. Rev. Lett. 101, 120601 (2008).
    [CrossRef] [PubMed]
  13. J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
    [CrossRef]
  14. I. Edrei and M. Kaveh, Phys. Rev. B 38, 950 (1988).
    [CrossRef]
  15. R. K. Tyson, Principles of Adaptive Optics, 2nd ed.(Academic Press, 1998).

2010

2008

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, Appl. Opt. 47, 2076 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef] [PubMed]

2007

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309 (2007).
[CrossRef] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, Science 315, 1120 (2007).
[CrossRef] [PubMed]

2000

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

1992

J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
[CrossRef]

1990

I. Freund, Physica A 168, 49 (1990).
[CrossRef]

1988

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

I. Edrei and M. Kaveh, Phys. Rev. B 38, 950 (1988).
[CrossRef]

Boccara, A. C.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 1 (2010).
[CrossRef]

Cassereau, D.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

de Boer, J. F.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
[CrossRef]

de Rosny, J.

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, Science 315, 1120 (2007).
[CrossRef] [PubMed]

Derode, A.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Dogariu, A.

Edrei, I.

I. Edrei and M. Kaveh, Phys. Rev. B 38, 950 (1988).
[CrossRef]

Feld, M. S.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Feng, S.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

Fink, M.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 1 (2010).
[CrossRef]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, Science 315, 1120 (2007).
[CrossRef] [PubMed]

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Freund, I.

I. Freund, Physica A 168, 49 (1990).
[CrossRef]

Genack, A. Z.

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

Gigan, S.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 1 (2010).
[CrossRef]

Grange, R.

Hsieh, C.-L.

Hu, B.

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

Kaveh, M.

I. Edrei and M. Kaveh, Phys. Rev. B 38, 950 (1988).
[CrossRef]

Kohlgraf-Owensand, T. W.

Lagendijk, A.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
[CrossRef]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

Lerosey, G.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 1 (2010).
[CrossRef]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, Science 315, 1120 (2007).
[CrossRef] [PubMed]

Mosk, A. P.

Popoff, S.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 1 (2010).
[CrossRef]

Prada, C.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Psaltis, D.

C.-L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, Opt. Express 18, 12283 (2010).
[CrossRef] [PubMed]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Pu, Y.

Roux, P.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Sebbah, P.

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

Tanter, M.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Thomas, J. L.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Tourin, A.

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, Science 315, 1120 (2007).
[CrossRef] [PubMed]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics, 2nd ed.(Academic Press, 1998).

van Albada, M. P.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
[CrossRef]

van Putten, E. G.

Vellekoop, I. M.

Wu, F.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Yang, C.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Zhang, S.

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

Appl. Opt.

Nat. Commun.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 1 (2010).
[CrossRef]

Nat. Photon.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon. 2, 110 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
[CrossRef]

I. Edrei and M. Kaveh, Phys. Rev. B 38, 950 (1988).
[CrossRef]

Phys. Rev. Lett.

I. M. Vellekoop and A. P. Mosk, Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

S. Zhang, B. Hu, P. Sebbah, and A. Z. Genack, Phys. Rev. Lett. 99, 063902 (2007).
[CrossRef] [PubMed]

Physica A

I. Freund, Physica A 168, 49 (1990).
[CrossRef]

Rep. Prog. Phys.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, Rep. Prog. Phys. 63, 1933 (2000).
[CrossRef]

Science

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, Science 315, 1120 (2007).
[CrossRef] [PubMed]

Other

R. K. Tyson, Principles of Adaptive Optics, 2nd ed.(Academic Press, 1998).

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Figures (4)

Fig. 1
Fig. 1

Illustration of our experiment. (a) Light is focused through an opaque scattering layer using a wavefront synthesizer at a frequency ω 0 . (b) The frequency is detuned until at sufficiently large detuning a regular speckle pattern remains.

Fig. 2
Fig. 2

Experimental setup. PBS, polarizing beam splitter; A, aperture; L 1 and L 2 , lenses; 63 × , microscope objective; 20 × , microscope objective; S, sample; P, polarizer.

Fig. 3
Fig. 3

(a)–(c) Focus intensity while the frequency detuning is increased from 0 to 2.3 GHz . The intensity decreases, while its position, shape, and size remain roughly the same.

Fig. 4
Fig. 4

(a) Normalized intensity of the focus versus the frequency detuning Δ ω . Black squares, correlation C ( Δ ω ) of the background speckle. The intensity and correlation show identical behavior. (b) Frequency width of the focus and correlation versus enhancement. The symbols represent a single measurement, and the error is smaller than the symbol size.

Tables (1)

Tables Icon

Table 1 Average Over 20 Sample Realizations and the Standard Deviation (σ) of the FWHM Frequency of the Focus ( Δ ω I ) and the Speckle Correlation Function ( Δ ω C ) for Two Samples of Different Thickness

Equations (3)

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E b ( ω ) = { a } N s t b a ( ω ) E a .
E a opt , β ( ω 0 ) = T β 1 / 2 t β a * ( ω 0 ) ,
I β opt ( ω 0 + Δ ω ) I β ( ω 0 ) η C ( Δ ω ) ,

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