Abstract

This study aims to give a general theory that enables the design of flat lenses based on hyperbolic metamaterials. We derive a lens equation that is demonstrated to involve the curvature of the dispersion relation. Guided by this theory, hyperbolic lenses of focal length ranging from zero to a few wavelength are simulated. High transmission efficiency is also obtained by reducing the amount of metal compared to the dielectric material.

© 2012 Optical Society of America

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  1. C. M. Soukoulis and M. Wegener, Nat. Photonics. 5, 523 (2011).
    [CrossRef]
  2. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
    [CrossRef]
  3. Y. Fu and X. Zhou, Plasmonics 5, 287 (2010).
    [CrossRef]
  4. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef]
  5. N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
    [CrossRef]
  6. K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (2007).
    [CrossRef]
  7. V. G. Veselago, Sov Phys Uspekhi 10, 509 (1968).
    [CrossRef]
  8. P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110(2006).
    [CrossRef]
  9. Z. Liu, H. Lee, X. Yi, C. Sun, and X. Zhang, Science 315, 1686 (2007).
    [CrossRef]
  10. N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, Opt. Express 17, 17517 (2009).
    [CrossRef]
  11. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
    [CrossRef]
  12. J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).
    [CrossRef]
  13. Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 94, 203108 (2009).
    [CrossRef]
  14. A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103 (2006).
    [CrossRef]
  15. Z. Jacob, L. V. Alekseyev, and E. Narimanov, Opt. Express 14, 8247 (2006).
    [CrossRef]
  16. 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]
  17. R. Pollès, E. Centeno, J. Arlandis, and A. Moreau, Opt. Express 19, 6149 (2011).
    [CrossRef]
  18. J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, Phys. Rev. Lett. 108, 037401 (2012).
    [CrossRef]
  19. Z. Jacob, L. V. Alekseyev, and E. Narimanov, J. Opt. Soc. Am. A 24, A52 (2007).
    [CrossRef]
  20. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1991).
  21. F. Krayzel, R. Pollès, A. Moreau, and M. Mihailovic, J. Europ. Opt. Soc. Rap. Pub. 5, 10025 (2010).
    [CrossRef]

2012 (1)

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

2011 (2)

2010 (3)

Y. Fu and X. Zhou, Plasmonics 5, 287 (2010).
[CrossRef]

F. Krayzel, R. Pollès, A. Moreau, and M. Mihailovic, J. Europ. Opt. Soc. Rap. Pub. 5, 10025 (2010).
[CrossRef]

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

2009 (2)

2007 (5)

Z. Liu, H. Lee, X. Yi, 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]

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]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, J. Opt. Soc. Am. A 24, A52 (2007).
[CrossRef]

K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (2007).
[CrossRef]

2006 (4)

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110(2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

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

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

2005 (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

1968 (1)

V. G. Veselago, Sov Phys Uspekhi 10, 509 (1968).
[CrossRef]

Akozbek, N.

Alekseyev, L. V.

Arlandis, J.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

R. Pollès, E. Centeno, J. Arlandis, and A. Moreau, Opt. Express 19, 6149 (2011).
[CrossRef]

Aydin, K.

K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (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]

Belov, P. A.

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110(2006).
[CrossRef]

Bloemer, M. J.

Bulu, I.

K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (2007).
[CrossRef]

Campos, J.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

Cappeddu, M. G.

Centeno, E.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

R. Pollès, E. Centeno, J. Arlandis, and A. Moreau, Opt. Express 19, 6149 (2011).
[CrossRef]

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]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[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.

Engheta, N.

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

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Fowler, M.

Fu, Y.

Y. Fu and X. Zhou, Plasmonics 5, 287 (2010).
[CrossRef]

Gauthier-Lafaye, O.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

Hao, Y.

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110(2006).
[CrossRef]

Haus, J. W.

Hung, Y.-J.

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

Jacob, Z.

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Krayzel, F.

F. Krayzel, R. Pollès, A. Moreau, and M. Mihailovic, J. Europ. Opt. Soc. Rap. Pub. 5, 10025 (2010).
[CrossRef]

Lee, H.

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

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[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]

Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 94, 203108 (2009).
[CrossRef]

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

Mandatori, A.

Mattiucci, N.

Mihailovic, M.

F. Krayzel, R. Pollès, A. Moreau, and M. Mihailovic, J. Europ. Opt. Soc. Rap. Pub. 5, 10025 (2010).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Monmayrant, A.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

Moreau, A.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

R. Pollès, E. Centeno, J. Arlandis, and A. Moreau, Opt. Express 19, 6149 (2011).
[CrossRef]

F. Krayzel, R. Pollès, A. Moreau, and M. Mihailovic, J. Europ. Opt. Soc. Rap. Pub. 5, 10025 (2010).
[CrossRef]

Narimanov, E.

Ozbay, E.

K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (2007).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1991).

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Pollès, R.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

R. Pollès, E. Centeno, J. Arlandis, and A. Moreau, Opt. Express 19, 6149 (2011).
[CrossRef]

F. Krayzel, R. Pollès, A. Moreau, and M. Mihailovic, J. Europ. Opt. Soc. Rap. Pub. 5, 10025 (2010).
[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]

Salandrino, A.

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

Scalora, M.

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Sibilia, C.

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Smolyaninov, I. I.

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

Soukoulis, C. M.

C. M. Soukoulis and M. Wegener, Nat. Photonics. 5, 523 (2011).
[CrossRef]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Sun, C.

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

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Veselago, V. G.

V. G. Veselago, Sov Phys Uspekhi 10, 509 (1968).
[CrossRef]

Wegener, M.

C. M. Soukoulis and M. Wegener, Nat. Photonics. 5, 523 (2011).
[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]

Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 94, 203108 (2009).
[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]

Yi, X.

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

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]

Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 94, 203108 (2009).
[CrossRef]

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

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Zhou, X.

Y. Fu and X. Zhou, Plasmonics 5, 287 (2010).
[CrossRef]

Appl. Phys. Lett. (2)

K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (2007).
[CrossRef]

Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 94, 203108 (2009).
[CrossRef]

J. Europ. Opt. Soc. Rap. Pub. (1)

F. Krayzel, R. Pollès, A. Moreau, and M. Mihailovic, J. Europ. Opt. Soc. Rap. Pub. 5, 10025 (2010).
[CrossRef]

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

Nat. Commun. (1)

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

Nat. Photonics. (1)

C. M. Soukoulis and M. Wegener, Nat. Photonics. 5, 523 (2011).
[CrossRef]

Opt. Express (4)

Phys. Rev. B (2)

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

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110(2006).
[CrossRef]

Phys. Rev. Lett. (2)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

Plasmonics (1)

Y. Fu and X. Zhou, Plasmonics 5, 287 (2010).
[CrossRef]

Science (4)

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Z. Liu, H. Lee, X. Yi, 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]

Sov Phys Uspekhi (1)

V. G. Veselago, Sov Phys Uspekhi 10, 509 (1968).
[CrossRef]

Other (1)

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1991).

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Figures (3)

Fig. 1.
Fig. 1.

Design and transmission diagram of the hyperlens with and without antireflection coating (AR).

Fig. 2.
Fig. 2.

(a) IFCs computed for Ag/Diamond layers with the metal losses. (b) Curvature index versus the reduced frequency.

Fig. 3.
Fig. 3.

Focal distance versus de reduced frequency D/λ. The bold and dashed lines obtained with Eq. (6) are computed with and without silver losses. The circles corresponds to the focal distance fi computed for a hyperbolic lens of 20 periods. (a)–(d) Magnetic field maps of axis in units of λ. The image is focalized at the focal distances 0, λ/4, λ/2 and λ.

Equations (6)

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

ϵx=ϵ1d1+ϵ2d2D,ϵy=[ϵ11d1+ϵ21d2D]1,
|ϵ2|ϵ1<d2d1<ϵ1|ϵ2|,ϵ1<ϵ2<ϵ1.
U(x,y)=dkxU˜(kx,0)eikxxeiky(kx)y,
ky(ω,kx)=ky(ω,0)kx22k01nc,
U(x,L)=eiky(ω,0)LdkxU(kx,0)eikxxeiLkx22k01nc,
fo+fi=NDnc.

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