Abstract

We propose a reconfigurable cylindrical concentrator designed using a transformation-optics approach when the core of the device contains a material with Kerr nonlinearity. We demonstrate that in the case of focusing Kerr nonlinearity of the material in the device, it functions as an axicon-like lens with a variable focus line that can be tuned by changing the incident electromagnetic field. We also numerically study the cases where the core of the device is made of a material with defocusing Kerr nonlinearity or consists of a negative index material and predict beam splitting or localized field enhancement at the boundary of the core, respectively.

© 2012 Optical Society of America

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  1. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photon. Nanostruct. Fundam. Appl. 6, 87 (2008).
    [CrossRef]
  2. W. Wang, L. Lin, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, Opt. Express 16, 11431 (2008).
    [CrossRef]
  3. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef]
  4. U. Leonhardt and T. G. Philbin, Prog. Opt. 53, 69(2009).
    [CrossRef]
  5. N. M. Litchinitser and V. M. Shalaev, J. Opt. Soc. Am. B 26, B161 (2009).
    [CrossRef]
  6. E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
    [CrossRef]
  7. Y. Lai, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
    [CrossRef]
  8. N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Opt. Express 20, 14954 (2012).
    [CrossRef]
  9. I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, Phys. Rev. Lett. 109, 083902 (2012).
    [CrossRef]
  10. H. Odabasi, F. L. Teixeira, and W. C. Chew, J. Opt. Soc. Am. B 28, 1317 (2011).
    [CrossRef]
  11. H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, Appl. Phys. Lett. 82, 2691 (2003).
    [CrossRef]
  12. L. H. Lee and W. C. Chen, J. Mater. Chem. 13, 1475(2003).
    [CrossRef]
  13. I. Bogaert, J. Peeters, and F. Olyslager, Metamaterials 2, 101 (2008).
    [CrossRef]

2012 (2)

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, Phys. Rev. Lett. 109, 083902 (2012).
[CrossRef]

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Opt. Express 20, 14954 (2012).
[CrossRef]

2011 (1)

2009 (4)

N. M. Litchinitser and V. M. Shalaev, J. Opt. Soc. Am. B 26, B161 (2009).
[CrossRef]

U. Leonhardt and T. G. Philbin, Prog. Opt. 53, 69(2009).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Y. Lai, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

2008 (3)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photon. Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

I. Bogaert, J. Peeters, and F. Olyslager, Metamaterials 2, 101 (2008).
[CrossRef]

W. Wang, L. Lin, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, Opt. Express 16, 11431 (2008).
[CrossRef]

2006 (1)

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

2003 (2)

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, Appl. Phys. Lett. 82, 2691 (2003).
[CrossRef]

L. H. Lee and W. C. Chen, J. Mater. Chem. 13, 1475(2003).
[CrossRef]

Bogaert, I.

I. Bogaert, J. Peeters, and F. Olyslager, Metamaterials 2, 101 (2008).
[CrossRef]

Chan, C. T.

Y. Lai, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Chen, H. Y.

Y. Lai, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Chen, W. C.

L. H. Lee and W. C. Chen, J. Mater. Chem. 13, 1475(2003).
[CrossRef]

Chew, W. C.

Cui, J.

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photon. Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Du, C.

Elim, H. I.

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, Appl. Phys. Lett. 82, 2691 (2003).
[CrossRef]

Han, D. Z.

Y. Lai, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Ji, W.

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, Appl. Phys. Lett. 82, 2691 (2003).
[CrossRef]

Kapitanova, P. V.

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, Phys. Rev. Lett. 109, 083902 (2012).
[CrossRef]

Kildishev, A. V.

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Kivshar, Y. S.

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Opt. Express 20, 14954 (2012).
[CrossRef]

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, Phys. Rev. Lett. 109, 083902 (2012).
[CrossRef]

Lai, Y.

Y. Lai, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Lee, L. H.

L. H. Lee and W. C. Chen, J. Mater. Chem. 13, 1475(2003).
[CrossRef]

Leonhardt, U.

U. Leonhardt and T. G. Philbin, Prog. Opt. 53, 69(2009).
[CrossRef]

Lin, L.

Litchinitser, N. M.

Luo, X.

Ma, J.

Maslovski, S. I.

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, Phys. Rev. Lett. 109, 083902 (2012).
[CrossRef]

Narimanov, E. E.

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Odabasi, H.

Olyslager, F.

I. Bogaert, J. Peeters, and F. Olyslager, Metamaterials 2, 101 (2008).
[CrossRef]

Peeters, J.

I. Bogaert, J. Peeters, and F. Olyslager, Metamaterials 2, 101 (2008).
[CrossRef]

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photon. Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, Prog. Opt. 53, 69(2009).
[CrossRef]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photon. Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photon. Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photon. Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, Phys. Rev. Lett. 109, 083902 (2012).
[CrossRef]

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Opt. Express 20, 14954 (2012).
[CrossRef]

Shalaev, V. M.

Smith, D. R.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photon. Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

Teixeira, F. L.

Wang, C.

Wang, J.

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, Appl. Phys. Lett. 82, 2691 (2003).
[CrossRef]

Wang, W.

Xiao, J. J.

Y. Lai, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Xue, J. M.

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, Appl. Phys. Lett. 82, 2691 (2003).
[CrossRef]

Yuwono, A. H.

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, Appl. Phys. Lett. 82, 2691 (2003).
[CrossRef]

Zhang, Z.-Q.

Y. Lai, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Zharov, A. A.

Zharova, N. A.

Appl. Phys. Lett. (2)

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

H. I. Elim, W. Ji, A. H. Yuwono, J. M. Xue, and J. Wang, Appl. Phys. Lett. 82, 2691 (2003).
[CrossRef]

J. Mater. Chem. (1)

L. H. Lee and W. C. Chen, J. Mater. Chem. 13, 1475(2003).
[CrossRef]

J. Opt. Soc. Am. B (2)

Metamaterials (1)

I. Bogaert, J. Peeters, and F. Olyslager, Metamaterials 2, 101 (2008).
[CrossRef]

Opt. Express (2)

Photon. Nanostruct. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photon. Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

Y. Lai, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, Phys. Rev. Lett. 109, 083902 (2012).
[CrossRef]

Prog. Opt. (1)

U. Leonhardt and T. G. Philbin, Prog. Opt. 53, 69(2009).
[CrossRef]

Science (1)

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of (a) wave concentrator based on self-action of a single high-intensity beam, (b) nonlinear concentrator for a weak signal propagating in nonlinear medium with refractive index modified by a strong pump, and (c) and (d) power flows in a linear and nonlinear concentrator of type (a), respectively.

Fig. 2.
Fig. 2.

Schematic of lens.

Fig. 3.
Fig. 3.

Time-averaged power flow illustrating the predicted lensing effect in the case of focusing nonlinearity. Focal line shifts toward the lens as the incident field is varied from (a) 50MV/m to (b) 90MV/m and to (c) 150MV/m as shown by dashed lines.

Fig. 4.
Fig. 4.

Surface plot of time-averaged power flow when the core of the device is made of (a) defocusing nonlinearity and (b) NIM. The inset shows the enhancement at the boundary of the shell and the core.

Equations (2)

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εri,j=μri,j={[10001000(R2/R1)2]0rR1[(r+M)/r000r/(r+M)000N(r+M)/r]R1<rR3,
ε=εl±χ(3)|E|2.

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