Abstract

The numerical aperture (NA) of a multimode optical fiber sets the limit of the information transport capacity along the spatial degree of freedom. In this Letter, we report that the application of a highly disordered medium can overcome the capacity limit set by the fiber NA. Specifically, we coated the input surface of a multimode fiber with a disordered medium made of ZnO nanoparticles and transported a wide-field image through the fiber with a spatial resolution beyond the diffraction limit given by the fiber NA. This was made possible because multiple scatterings induced by the disordered medium physically increased the NA of the entire system. Our study will lead to enhancing the spatial resolution of fiber-based endoscopic imaging and also improving the information transport capacity in optical communications.

© 2013 Optical Society of America

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References

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2013 (2)

2012 (5)

C. Yoon, Y. Choi, M. Kim, J. Moon, and W. Choi, Opt. Lett. 37, 4558 (2012).
[CrossRef]

S. Bianchi and R. Di Leonardo, Lab Chip 12, 635 (2012).
[CrossRef]

T. Cizmar and K. Dholakia, Nat. Commun. 3, 1027 (2012).
[CrossRef]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Phys. Rev. Lett. 109, 203901 (2012).
[CrossRef]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, Nat. Photonics 6, 581 (2012).

2011 (1)

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

2005 (1)

2000 (1)

H. R. Stuart, Science 289, 281 (2000).
[CrossRef]

1996 (1)

1985 (1)

B. F. a. S. Sternklar, Appl. Phys. Lett. 46, 113 (1985).
[CrossRef]

1981 (1)

A. L. Aan de Kerk, Int. Ophthalmol. 3, 191 (1981).
[CrossRef]

1978 (1)

Aan de Kerk, A. L.

A. L. Aan de Kerk, Int. Ophthalmol. 3, 191 (1981).
[CrossRef]

Bianchi, S.

S. Bianchi and R. Di Leonardo, Lab Chip 12, 635 (2012).
[CrossRef]

Bobrinev, V. I.

Cho, Y. H.

Choi, W.

C. Yoon, Y. Choi, M. Kim, J. Moon, and W. Choi, Opt. Lett. 37, 4558 (2012).
[CrossRef]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Phys. Rev. Lett. 109, 203901 (2012).
[CrossRef]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, Nat. Photonics 6, 581 (2012).

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, Nat. Photonics 6, 581 (2012).

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Choi, Y.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Phys. Rev. Lett. 109, 203901 (2012).
[CrossRef]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, Nat. Photonics 6, 581 (2012).

C. Yoon, Y. Choi, M. Kim, J. Moon, and W. Choi, Opt. Lett. 37, 4558 (2012).
[CrossRef]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Cizmar, T.

T. Cizmar and K. Dholakia, Nat. Commun. 3, 1027 (2012).
[CrossRef]

Dasari, R. R.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Phys. Rev. Lett. 109, 203901 (2012).
[CrossRef]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, Opt. Lett. 30, 1165 (2005).
[CrossRef]

Dholakia, K.

T. Cizmar and K. Dholakia, Nat. Commun. 3, 1027 (2012).
[CrossRef]

Di Leonardo, R.

S. Bianchi and R. Di Leonardo, Lab Chip 12, 635 (2012).
[CrossRef]

Eom, Y. S.

Fang-Yen, C.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Phys. Rev. Lett. 109, 203901 (2012).
[CrossRef]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Farahi, S.

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, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, Opt. Lett. 30, 1165 (2005).
[CrossRef]

Friesem, A. A.

Gu, R. Y.

Ikeda, T.

Jeon, H. W.

Kahn, J. M.

Kang, P.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Kim, J.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, Nat. Photonics 6, 581 (2012).

Kim, M.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, Nat. Photonics 6, 581 (2012).

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Phys. Rev. Lett. 109, 203901 (2012).
[CrossRef]

C. Yoon, Y. Choi, M. Kim, J. Moon, and W. Choi, Opt. Lett. 37, 4558 (2012).
[CrossRef]

Lee, K. J.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Phys. Rev. Lett. 109, 203901 (2012).
[CrossRef]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Levy, U.

Mahalati, R. N.

Moon, J.

Moser, C.

Papadopoulos, I. N.

Park, Q.-H.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, Nat. Photonics 6, 581 (2012).

Popescu, G.

Psaltis, D.

Son, J. Y.

Sternklar, B. F. a. S.

B. F. a. S. Sternklar, Appl. Phys. Lett. 46, 113 (1985).
[CrossRef]

Stuart, H. R.

H. R. Stuart, Science 289, 281 (2000).
[CrossRef]

Yang, T. D.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Phys. Rev. Lett. 109, 203901 (2012).
[CrossRef]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Yoon, C.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Phys. Rev. Lett. 109, 203901 (2012).
[CrossRef]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, Nat. Photonics 6, 581 (2012).

C. Yoon, Y. Choi, M. Kim, J. Moon, and W. Choi, Opt. Lett. 37, 4558 (2012).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

B. F. a. S. Sternklar, Appl. Phys. Lett. 46, 113 (1985).
[CrossRef]

Biomed. Opt. Express (1)

Int. Ophthalmol. (1)

A. L. Aan de Kerk, Int. Ophthalmol. 3, 191 (1981).
[CrossRef]

Lab Chip (1)

S. Bianchi and R. Di Leonardo, Lab Chip 12, 635 (2012).
[CrossRef]

Nat. Commun. (1)

T. Cizmar and K. Dholakia, Nat. Commun. 3, 1027 (2012).
[CrossRef]

Nat. Photonics (1)

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, Nat. Photonics 6, 581 (2012).

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (2)

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Phys. Rev. Lett. 109, 203901 (2012).
[CrossRef]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Science (1)

H. R. Stuart, Science 289, 281 (2000).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the experimental setup. BSi, i-th beam splitter; PBS, polarizing beam splitter; GM, galvanometer mirror; OP, object plane; IP, image plane; OL and OLT, objective lenses. The red arrows indicate the direction of polarization. The photograph next to the OLT shows the bright-field image of the input surface of the fiber coated by nanoparticles. (b), (c) Representative measured output images as a function of the incident angle (sinθi) of plane waves at OP, for the intact fiber (b) and the nanoparticle-coated fiber (c), respectively. Scale bar, 25 μm.

Fig. 2.
Fig. 2.

(a) Measured transmission matrix of the intact fiber. The matrix elements were acquired up to the fiber NA. (b) Measured transmission matrix of the random fiber. The measurable input range was extended over the fiber NA (yellow dashed line). Vertical and horizontal indices represent the position at IP and input angle θi at OP, respectively. Color bar: arbitrary intensity unit. (c) Average intensity of the column of the transmission matrix as a function of incident angle. The intensity was normalized with respect to that of θi=0. The dashed line denotes the fiber NA.

Fig. 3.
Fig. 3.

(a) Reconstructed image transported through the intact fiber. The smallest structures in group 4 are blurred due to the lack of resolving power. (b) Reconstructed image from the output through the nanoparticle-coated fiber. The structural details in group 4 can be resolved. Scale bar: 10 μm. (c) Section profiles along the lines shown in (a) and (b). The improved resolution is verified by the comparison of the two section profiles.

Equations (1)

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EOP(ξ,η)=T1EIP(x,y).

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