Abstract

The performance of an optical hyperlens made of metal–dielectric layers can be improved by incorporating self-focusing nonlinearity in the dielectric layers. Using a modified beam propagation method in cylindrical coordinates, we show increased bandwidth and better propagation length, which can improve the spatial and temporal resolution of the device.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Z. Jacob, L. Alekseyev, and E. Narimanov, Opt. Express 14, 8247 (2006).
    [CrossRef]
  2. A. Salandrino, and N. Engheta, Phys. Rev. B 74, 075103 (2006).
    [CrossRef]
  3. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
    [CrossRef]
  4. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
    [CrossRef]
  5. J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
    [CrossRef]
  6. E. Abbe, Archiv f. Mikr. Anat. 9, 413 (1873).
    [CrossRef]
  7. D. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
    [CrossRef]
  8. M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. Centini, A. Mandatori, C. Sibilia, N. Akozbek, M. G. Cappeddu, M. Fowler, and J. W. Haus, Opt. Express 15, 508 (2007).
    [CrossRef]
  9. A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
    [CrossRef]
  10. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
    [CrossRef]
  11. P. Belov and Y. Hao, Phys. Rev. B 73, 1 (2006).
    [CrossRef]
  12. J. Schilling, Phys. Rev. E 74, 046618 (2006).
    [CrossRef]
  13. B. Wood, J. Pendry, and D. Tsai, Phys. Rev. B 1, 1 (2006).
    [CrossRef]
  14. Y. Liu, G. Bartal, D. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
    [CrossRef]
  15. D. Bergman, Phys. Rep. 43, 377 (1978).
    [CrossRef]
  16. P. Johnson and R. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  17. R. Morandotti, H. Eisenberg, Y. Silberberg, M. Sorel, and J. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef]
  18. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 4 (2002).
    [CrossRef]
  19. A. Sharma, and A. Agrawal, J. Opt. Soc. Am. A 21, 1082 (2004).
    [CrossRef]
  20. J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, Appl. Phys. Lett. 90, 191109 (2007).
    [CrossRef]
  21. A. L. Stepanov, Rev. Adv. Mater. Sci. 27115 (2011).

2011

A. L. Stepanov, Rev. Adv. Mater. Sci. 27115 (2011).

2010

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
[CrossRef]

2008

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef]

2007

Y. Liu, G. Bartal, D. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. Centini, A. Mandatori, C. Sibilia, N. Akozbek, M. G. Cappeddu, M. Fowler, and J. W. Haus, Opt. Express 15, 508 (2007).
[CrossRef]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, Appl. Phys. Lett. 90, 191109 (2007).
[CrossRef]

2006

Z. Jacob, L. Alekseyev, and E. Narimanov, Opt. Express 14, 8247 (2006).
[CrossRef]

A. Salandrino, and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

P. Belov and Y. Hao, Phys. Rev. B 73, 1 (2006).
[CrossRef]

J. Schilling, Phys. Rev. E 74, 046618 (2006).
[CrossRef]

B. Wood, J. Pendry, and D. Tsai, Phys. Rev. B 1, 1 (2006).
[CrossRef]

2004

2003

D. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

2002

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 4 (2002).
[CrossRef]

2001

R. Morandotti, H. Eisenberg, Y. Silberberg, M. Sorel, and J. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

1978

D. Bergman, Phys. Rep. 43, 377 (1978).
[CrossRef]

1972

P. Johnson and R. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1873

E. Abbe, Archiv f. Mikr. Anat. 9, 413 (1873).
[CrossRef]

Abbe, E.

E. Abbe, Archiv f. Mikr. Anat. 9, 413 (1873).
[CrossRef]

Agrawal, A.

Aitchison, J.

R. Morandotti, H. Eisenberg, Y. Silberberg, M. Sorel, and J. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

Akozbek, N.

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Z. Jacob, L. Alekseyev, and E. Narimanov, Opt. Express 14, 8247 (2006).
[CrossRef]

Avrutsky, I.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, Appl. Phys. Lett. 90, 191109 (2007).
[CrossRef]

Bartal, G.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
[CrossRef]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef]

Y. Liu, G. Bartal, D. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Belov, P.

P. Belov and Y. Hao, Phys. Rev. B 73, 1 (2006).
[CrossRef]

Bergman, D.

D. Bergman, Phys. Rep. 43, 377 (1978).
[CrossRef]

Bloemer, M. J.

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 4 (2002).
[CrossRef]

Cappeddu, M. G.

Centini, M.

Choi, H.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
[CrossRef]

Christy, R.

P. Johnson and R. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

D’Aguanno, G.

Davis, C. C.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

de Ceglia, D.

Eisenberg, H.

R. Morandotti, H. Eisenberg, Y. Silberberg, M. Sorel, and J. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

Elser, J.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, Appl. Phys. Lett. 90, 191109 (2007).
[CrossRef]

Engheta, N.

A. Salandrino, and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Fowler, M.

Franz, K. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Genov, D.

Y. Liu, G. Bartal, D. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Gmachl, C.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Hao, Y.

P. Belov and Y. Hao, Phys. Rev. B 73, 1 (2006).
[CrossRef]

Haus, J. W.

Hoffman, A. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Howard, S. S.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Hung, Y.-J.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Jacob, Z.

Johnson, P.

P. Johnson and R. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 4 (2002).
[CrossRef]

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Liu, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef]

Y. Liu, G. Bartal, D. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Liu, Z.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
[CrossRef]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Mandatori, A.

Mattiucci, N.

Morandotti, R.

R. Morandotti, H. Eisenberg, Y. Silberberg, M. Sorel, and J. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

Narimanov, E.

Narimanov, E. E.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Pendry, J.

B. Wood, J. Pendry, and D. Tsai, Phys. Rev. B 1, 1 (2006).
[CrossRef]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 4 (2002).
[CrossRef]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 4 (2002).
[CrossRef]

Podolskiy, V. A.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, Appl. Phys. Lett. 90, 191109 (2007).
[CrossRef]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Rho, J.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
[CrossRef]

Salakhutdinov, I.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, Appl. Phys. Lett. 90, 191109 (2007).
[CrossRef]

Salandrino, A.

A. Salandrino, and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Scalora, M.

Schilling, J.

J. Schilling, Phys. Rev. E 74, 046618 (2006).
[CrossRef]

Schurig, D.

D. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Sharma, A.

Sibilia, C.

Silberberg, Y.

R. Morandotti, H. Eisenberg, Y. Silberberg, M. Sorel, and J. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

Sivco, D. L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Smith, D.

D. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Smolyaninov, I. I.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Sorel, M.

R. Morandotti, H. Eisenberg, Y. Silberberg, M. Sorel, and J. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

Stacy, A. M.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef]

Stepanov, A. L.

A. L. Stepanov, Rev. Adv. Mater. Sci. 27115 (2011).

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Tsai, D.

B. Wood, J. Pendry, and D. Tsai, Phys. Rev. B 1, 1 (2006).
[CrossRef]

Wang, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef]

Wasserman, D.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Wood, B.

B. Wood, J. Pendry, and D. Tsai, Phys. Rev. B 1, 1 (2006).
[CrossRef]

Xiong, Y.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Yao, J.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef]

Ye, Z.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
[CrossRef]

Yin, X.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
[CrossRef]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 4 (2002).
[CrossRef]

Zhang, X.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
[CrossRef]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef]

Y. Liu, G. Bartal, D. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Appl. Phys. Lett.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, Appl. Phys. Lett. 90, 191109 (2007).
[CrossRef]

Archiv f. Mikr. Anat.

E. Abbe, Archiv f. Mikr. Anat. 9, 413 (1873).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Commun.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
[CrossRef]

Nat. Mater.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef]

Opt. Express

Phys. Rep.

D. Bergman, Phys. Rep. 43, 377 (1978).
[CrossRef]

Phys. Rev. B

P. Johnson and R. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

P. Belov and Y. Hao, Phys. Rev. B 73, 1 (2006).
[CrossRef]

A. Salandrino, and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

B. Wood, J. Pendry, and D. Tsai, Phys. Rev. B 1, 1 (2006).
[CrossRef]

Phys. Rev. E

J. Schilling, Phys. Rev. E 74, 046618 (2006).
[CrossRef]

Phys. Rev. Lett.

R. Morandotti, H. Eisenberg, Y. Silberberg, M. Sorel, and J. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 4 (2002).
[CrossRef]

D. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Y. Liu, G. Bartal, D. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Rev. Adv. Mater. Sci.

A. L. Stepanov, Rev. Adv. Mater. Sci. 27115 (2011).

Science

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Dispersion relation: (a) real and (b) imaginary parts of the propagation constant at λ=385nm (solid line) and λ=365nm (dashed curve). Close to resonance (solid line) the dispersion is flat, indicating diffractionless propagation. However, the losses, corresponding to the imaginary part of kz are high, farther from resonance (dashed curves), the dispersion is curved hence diffraction emerges. On the other hand, losses are decreased.

Fig. 2.
Fig. 2.

Imaging of two super-Gaussian sources 90 nm apart. Linear propagation (a) close to resonance at λ=385nm and (b)  far from resonance at λ=365nm. (c) Nonlinear propagation at λ=365nm. (d) Output intensities: close to resonance [curve (a)] the image is resolved but suffers high loss; far from resonance [dotted curve (b)] the image is smeared due to strong diffraction; the nonlinear propagation in the medium [dashed curve (c)] resolves the image with better efficiency.

Fig. 3.
Fig. 3.

Imaging of two Gaussian sources 75 nm apart in a hyperlens with inner and outer radii of 240 and 1000 nm, respectively. (a)–(d) Similar to Fig. 2.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

zΨ(x,z)=iMT(x)Ψ(x,z),Ψ=(HzEx),
MT=(0k0εxk01k0x(1εzx)0).
Ψ(x,y,z+Δz)=eiMNLΔzDΔz{Ψ(x,z)}+O[(Δz)3].
Ψ(x,z+Δz)=DΔz{Ψ(x,z)}=kxC(kx,z0)eikz(kx)Δz,
P⃗NL=12ε0χ(3)[|E|2E⃗+12(E⃗·E⃗)E⃗*]=εx(NL)Exx^+εz(NL)Ezz^.
Φm(ρ,ϕ)=[Jimεϕ|ερ|(k0εϕρ)+iYimεϕ|ερ|(k0εϕρ)]eimϕ.
ρΨ(ρ,ϕ)=iMT(Cyl)Ψ(ρ,ϕ),Ψ=(HzEϕ),
MT(Cyl)=(0iεϕk0ik0iρ2ερk02ϕ21ρ).
Ψ(ρ0+Δρ)=DΔρ{Ψ(ρ0)}=mAm(ρ0)·Φm(ρ=ρ0+Δρ,ϕ),

Metrics