Abstract

Metamaterials are being used to model various exotic “optical spaces” for such applications as novel lenses and cloaking. While most efforts are directed toward the engineering of continuously changing dielectric permittivity and magnetic permeability tensors, an alternative approach may be based on lattices of metamaterial waveguides. Here we demonstrate the power of the latter technique by presenting metamaterial lattice models of various four-dimensional spaces.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  2. U. Leonhardt, Science 312, 1777 (2006).
    [CrossRef] [PubMed]
  3. U. Leonhardt and T. G. Philbin, New J. Phys. 8, 247 (2006).
    [CrossRef]
  4. X. Liu, C. Li, K. Yao, X. Meng, and F. Li, IEEE Antennas Wireless Propagat. Lett. 8, 1154 (2009).
    [CrossRef]
  5. P. Alitalo, F. Bongard, J.-F. Zürcher, J. Mosig, and S. Tretyakov, Appl. Phys. Lett. 94, 014103 (2009).
    [CrossRef]
  6. U. Leonhardt and T. Tyc, Science 323, 110 (2009).
    [CrossRef]
  7. A. Louri, S. Furlonge, and C. Neocleous, Appl. Opt. 35, 6909 (1996).
    [CrossRef] [PubMed]
  8. J. Gray, Ideas of Space: Euclidean, Non-Euclidean, and Relativistic (Clarendon, 1989).
  9. I. I. Smolyaninov, Phys. Rev. D 65, 047503 (2002).
    [CrossRef]
  10. B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
    [CrossRef] [PubMed]
  11. I. I. Smolyaninov, J. Opt. 13, 024004 (2011).
    [CrossRef]

2011 (1)

I. I. Smolyaninov, J. Opt. 13, 024004 (2011).
[CrossRef]

2009 (3)

X. Liu, C. Li, K. Yao, X. Meng, and F. Li, IEEE Antennas Wireless Propagat. Lett. 8, 1154 (2009).
[CrossRef]

P. Alitalo, F. Bongard, J.-F. Zürcher, J. Mosig, and S. Tretyakov, Appl. Phys. Lett. 94, 014103 (2009).
[CrossRef]

U. Leonhardt and T. Tyc, Science 323, 110 (2009).
[CrossRef]

2008 (1)

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

2006 (3)

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

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, New J. Phys. 8, 247 (2006).
[CrossRef]

2002 (1)

I. I. Smolyaninov, Phys. Rev. D 65, 047503 (2002).
[CrossRef]

1996 (1)

1989 (1)

J. Gray, Ideas of Space: Euclidean, Non-Euclidean, and Relativistic (Clarendon, 1989).

Alitalo, P.

P. Alitalo, F. Bongard, J.-F. Zürcher, J. Mosig, and S. Tretyakov, Appl. Phys. Lett. 94, 014103 (2009).
[CrossRef]

Alu, A.

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Bongard, F.

P. Alitalo, F. Bongard, J.-F. Zürcher, J. Mosig, and S. Tretyakov, Appl. Phys. Lett. 94, 014103 (2009).
[CrossRef]

Edwards, B.

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Engheta, N.

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Furlonge, S.

Gray, J.

J. Gray, Ideas of Space: Euclidean, Non-Euclidean, and Relativistic (Clarendon, 1989).

Leonhardt, U.

U. Leonhardt and T. Tyc, Science 323, 110 (2009).
[CrossRef]

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, New J. Phys. 8, 247 (2006).
[CrossRef]

Li, C.

X. Liu, C. Li, K. Yao, X. Meng, and F. Li, IEEE Antennas Wireless Propagat. Lett. 8, 1154 (2009).
[CrossRef]

Li, F.

X. Liu, C. Li, K. Yao, X. Meng, and F. Li, IEEE Antennas Wireless Propagat. Lett. 8, 1154 (2009).
[CrossRef]

Liu, X.

X. Liu, C. Li, K. Yao, X. Meng, and F. Li, IEEE Antennas Wireless Propagat. Lett. 8, 1154 (2009).
[CrossRef]

Louri, A.

Meng, X.

X. Liu, C. Li, K. Yao, X. Meng, and F. Li, IEEE Antennas Wireless Propagat. Lett. 8, 1154 (2009).
[CrossRef]

Mosig, J.

P. Alitalo, F. Bongard, J.-F. Zürcher, J. Mosig, and S. Tretyakov, Appl. Phys. Lett. 94, 014103 (2009).
[CrossRef]

Neocleous, C.

Pendry, J. B.

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

Philbin, T. G.

U. Leonhardt and T. G. Philbin, New J. Phys. 8, 247 (2006).
[CrossRef]

Schurig, D.

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

Silveirinha, M.

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Smith, D. R.

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

Smolyaninov, I. I.

I. I. Smolyaninov, J. Opt. 13, 024004 (2011).
[CrossRef]

I. I. Smolyaninov, Phys. Rev. D 65, 047503 (2002).
[CrossRef]

Tretyakov, S.

P. Alitalo, F. Bongard, J.-F. Zürcher, J. Mosig, and S. Tretyakov, Appl. Phys. Lett. 94, 014103 (2009).
[CrossRef]

Tyc, T.

U. Leonhardt and T. Tyc, Science 323, 110 (2009).
[CrossRef]

Yao, K.

X. Liu, C. Li, K. Yao, X. Meng, and F. Li, IEEE Antennas Wireless Propagat. Lett. 8, 1154 (2009).
[CrossRef]

Young, M. E.

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Zürcher, J.-F.

P. Alitalo, F. Bongard, J.-F. Zürcher, J. Mosig, and S. Tretyakov, Appl. Phys. Lett. 94, 014103 (2009).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. Alitalo, F. Bongard, J.-F. Zürcher, J. Mosig, and S. Tretyakov, Appl. Phys. Lett. 94, 014103 (2009).
[CrossRef]

IEEE Antennas Wireless Propagat. Lett. (1)

X. Liu, C. Li, K. Yao, X. Meng, and F. Li, IEEE Antennas Wireless Propagat. Lett. 8, 1154 (2009).
[CrossRef]

J. Opt. (1)

I. I. Smolyaninov, J. Opt. 13, 024004 (2011).
[CrossRef]

New J. Phys. (1)

U. Leonhardt and T. G. Philbin, New J. Phys. 8, 247 (2006).
[CrossRef]

Phys. Rev. D (1)

I. I. Smolyaninov, Phys. Rev. D 65, 047503 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Science (3)

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

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. Tyc, Science 323, 110 (2009).
[CrossRef]

Other (1)

J. Gray, Ideas of Space: Euclidean, Non-Euclidean, and Relativistic (Clarendon, 1989).

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 (4)

Fig. 1
Fig. 1

(a) Perspective projection of an elementary unit of a 4D hypercubic spatial lattice, which shows the ( x , y , z , w ) coordinates of each vertex. The elementary unit is filled with metal, except for the black lines, which represent pieces of thin single-mode waveguides engineered to have the same impedance and the same optical length. (b) Perspective projection of a 2 × 2 × 2 × 2 region of the hypercubic lattice: three 2 × 2 × 2 elements of the cubic lattice are shifted along the projected “fourth orthogonal direction.”

Fig. 2
Fig. 2

(a) HFSS simulations of electric field magnitude inside the 2 × 2 × 2 × 2 hypercubic lattice of waveguides. Radiation source is placed at the origin ( 0 , 0 , 0 , 0 ) . (b) HFSS simulations of electric field magnitude inside the 3 × 3 × 3 × 3 hypercubic lattice of waveguides. For the sake of clarity, the field magnitude is shown only for four 3D sections of the hypercube.

Fig. 3
Fig. 3

Field intensity measured at the lattice vertices plotted as a function of R 3 is consistent with the 4D character of field propagation at large Rs.

Fig. 4
Fig. 4

HFSS simulations of a Kaluza–Klein mode propagation inside a lattice of waveguides, which emulates the 5D space–time described by Eq. (2). The inset in the top right corner shows field magnitude inside an individual waveguide, which is oriented along the projected “fifth spatial dimension.” Standing wave character of the Kaluza–Klein mode along the emulated fifth lattice dimension is clearly demonstrated.

Equations (2)

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

Z = 1 2 π μ ε ln D d
d s 2 = g α β d x α d x β + 2 g α 5 d x α d ϕ + g 55 d ϕ 2

Metrics