Abstract

In this paper, a spatially dispersive finite-difference time-domain (FDTD) method to model wire media is developed and validated. Sub-wavelength imaging properties of the finite wire medium slabs are examined. It is demonstrated that the slab with its thickness equal to an integer number of half-wavelengths is capable of transporting images with sub-wavelength resolution from one interface of the slab to another. It is also shown that the operation of such transmission devices is not sensitive to their transverse dimensions, which can be made even comparable to the wavelength. In this case, the edge diffractions are negligible and do not disturb the image formation.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Pendry, "Negative refraction index makes perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  2. V. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  3. P. A. Belov, C. R. Simovski, and P. Ikonen, "Canalization of sub-wavelength images by electromagnetic crystals," Phys. Rev. B. 71, 193105 (2005).
    [CrossRef]
  4. P. Ikonen, P. A. Belov, C. R. Simovski, and S. I. Maslovski, "Experimental demonstration of subwavelength field channeling at microwave frequencies using a capacitively loaded wire medium," Phys. Rev. B 73, 073102 (2006).
    [CrossRef]
  5. P. A. Belov, Y. Hao, and S. Sudhakaran, "Subwavelength microwave imaging using an array of parallel conducting wires as a lens," Phys. Rev. B 73, 033108 (2006).
    [CrossRef]
  6. P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113110 (2006).
    [CrossRef]
  7. P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silverinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B 67, 113103 (2003).
    [CrossRef]
  8. M. G. Silveirinha, "Nonlocal homogenization model for a periodic array of epsilon-negative rods," accepted to Phys. Rev. E (arXiv: cond-mat/0602471) (2006).
  9. W. Rotman, "Plasma simulations by artificial dielectrics and parallel-plate media," IRE Trans. Ant. Propag. 10, 82-95 (1962).
    [CrossRef]
  10. J. Brown, "Artificial Dielectrics," Progress in dielectrics 2, 195-225 (1960).
  11. J. Pendry, A. Holden, W. Steward, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
    [CrossRef] [PubMed]
  12. P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, "Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires," J. Electromagn. Waves Applic. 16, 1153-1170 (2002).
    [CrossRef]
  13. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propgat. 14, 302-307 (1966).
    [CrossRef]
  14. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Norwood, MA: Artech House, 1995).
  15. F. B. Hildebrand, Introduction to Numerical Analysis (New York: Mc-Graw-Hill, 1956).
  16. Y. Zhao, P. A. Belov, and Y. Hao, "Modelling of wave propagation in wire media using spatially dispersive finite-difference time-domain method: numerical aspects," submitted to IEEE Trans. Antennas Propagat. (arXiv: cond-mat/0604012) (2006).
  17. K. P. Prokopidis, E. P. Kosmidou, and T. D. Tsiboukis, "An FDTD algorithm for wave propagation in dispersive media using higher-order schemes," J. Electromagn. Waves Appl. 18, 1171-1194 (2004).
    [CrossRef]
  18. C. R. Simovski and P. A. Belov, "Low-frequency spatial dispersion in wire media," Phys. Rev. E 70, 046616 (2004).
    [CrossRef]
  19. M. Silveirinha and C. Fernandes, "Homogenization of 3D connected and non-connected wire metamaterials," IEEE Trans. Microwave Theory Tech. 54, 1418-1430 (2005).
    [CrossRef]
  20. M. Silveirinha and C. Fernandes, "Homogenization of metamaterial surfaces and slabs: the crossed wire mesh canonical problem," IEEE Trans. Antennas Propgat. 53, 59-69 (2005).
    [CrossRef]
  21. J. R. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computat. Phys. 114, 185-200 (1994).
    [CrossRef]
  22. P. A. Belov and M. G. Silveirinha, "Resolution of sub-wavelength lenses formed by the wire medium," accepted to Phys. Rev. E (arXiv: physics/0511139) (2006).

2006 (3)

P. Ikonen, P. A. Belov, C. R. Simovski, and S. I. Maslovski, "Experimental demonstration of subwavelength field channeling at microwave frequencies using a capacitively loaded wire medium," Phys. Rev. B 73, 073102 (2006).
[CrossRef]

P. A. Belov, Y. Hao, and S. Sudhakaran, "Subwavelength microwave imaging using an array of parallel conducting wires as a lens," Phys. Rev. B 73, 033108 (2006).
[CrossRef]

P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113110 (2006).
[CrossRef]

2005 (3)

P. A. Belov, C. R. Simovski, and P. Ikonen, "Canalization of sub-wavelength images by electromagnetic crystals," Phys. Rev. B. 71, 193105 (2005).
[CrossRef]

M. Silveirinha and C. Fernandes, "Homogenization of 3D connected and non-connected wire metamaterials," IEEE Trans. Microwave Theory Tech. 54, 1418-1430 (2005).
[CrossRef]

M. Silveirinha and C. Fernandes, "Homogenization of metamaterial surfaces and slabs: the crossed wire mesh canonical problem," IEEE Trans. Antennas Propgat. 53, 59-69 (2005).
[CrossRef]

2004 (2)

K. P. Prokopidis, E. P. Kosmidou, and T. D. Tsiboukis, "An FDTD algorithm for wave propagation in dispersive media using higher-order schemes," J. Electromagn. Waves Appl. 18, 1171-1194 (2004).
[CrossRef]

C. R. Simovski and P. A. Belov, "Low-frequency spatial dispersion in wire media," Phys. Rev. E 70, 046616 (2004).
[CrossRef]

2003 (1)

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silverinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B 67, 113103 (2003).
[CrossRef]

2002 (1)

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, "Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires," J. Electromagn. Waves Applic. 16, 1153-1170 (2002).
[CrossRef]

2000 (1)

J. Pendry, "Negative refraction index makes perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1996 (1)

J. Pendry, A. Holden, W. Steward, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

1994 (1)

J. R. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computat. Phys. 114, 185-200 (1994).
[CrossRef]

1968 (1)

V. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1966 (1)

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propgat. 14, 302-307 (1966).
[CrossRef]

1962 (1)

W. Rotman, "Plasma simulations by artificial dielectrics and parallel-plate media," IRE Trans. Ant. Propag. 10, 82-95 (1962).
[CrossRef]

Belov, P. A.

P. Ikonen, P. A. Belov, C. R. Simovski, and S. I. Maslovski, "Experimental demonstration of subwavelength field channeling at microwave frequencies using a capacitively loaded wire medium," Phys. Rev. B 73, 073102 (2006).
[CrossRef]

P. A. Belov, Y. Hao, and S. Sudhakaran, "Subwavelength microwave imaging using an array of parallel conducting wires as a lens," Phys. Rev. B 73, 033108 (2006).
[CrossRef]

P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113110 (2006).
[CrossRef]

P. A. Belov, C. R. Simovski, and P. Ikonen, "Canalization of sub-wavelength images by electromagnetic crystals," Phys. Rev. B. 71, 193105 (2005).
[CrossRef]

C. R. Simovski and P. A. Belov, "Low-frequency spatial dispersion in wire media," Phys. Rev. E 70, 046616 (2004).
[CrossRef]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silverinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B 67, 113103 (2003).
[CrossRef]

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, "Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires," J. Electromagn. Waves Applic. 16, 1153-1170 (2002).
[CrossRef]

Berenger, J. R.

J. R. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computat. Phys. 114, 185-200 (1994).
[CrossRef]

Fernandes, C.

M. Silveirinha and C. Fernandes, "Homogenization of metamaterial surfaces and slabs: the crossed wire mesh canonical problem," IEEE Trans. Antennas Propgat. 53, 59-69 (2005).
[CrossRef]

M. Silveirinha and C. Fernandes, "Homogenization of 3D connected and non-connected wire metamaterials," IEEE Trans. Microwave Theory Tech. 54, 1418-1430 (2005).
[CrossRef]

Hao, Y.

P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113110 (2006).
[CrossRef]

P. A. Belov, Y. Hao, and S. Sudhakaran, "Subwavelength microwave imaging using an array of parallel conducting wires as a lens," Phys. Rev. B 73, 033108 (2006).
[CrossRef]

Holden, A.

J. Pendry, A. Holden, W. Steward, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Ikonen, P.

P. Ikonen, P. A. Belov, C. R. Simovski, and S. I. Maslovski, "Experimental demonstration of subwavelength field channeling at microwave frequencies using a capacitively loaded wire medium," Phys. Rev. B 73, 073102 (2006).
[CrossRef]

P. A. Belov, C. R. Simovski, and P. Ikonen, "Canalization of sub-wavelength images by electromagnetic crystals," Phys. Rev. B. 71, 193105 (2005).
[CrossRef]

Kosmidou, E. P.

K. P. Prokopidis, E. P. Kosmidou, and T. D. Tsiboukis, "An FDTD algorithm for wave propagation in dispersive media using higher-order schemes," J. Electromagn. Waves Appl. 18, 1171-1194 (2004).
[CrossRef]

Marques, R.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silverinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Maslovski, S. I.

P. Ikonen, P. A. Belov, C. R. Simovski, and S. I. Maslovski, "Experimental demonstration of subwavelength field channeling at microwave frequencies using a capacitively loaded wire medium," Phys. Rev. B 73, 073102 (2006).
[CrossRef]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silverinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Nefedov, I. S.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silverinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Pendry, J.

J. Pendry, "Negative refraction index makes perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

J. Pendry, A. Holden, W. Steward, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Prokopidis, K. P.

K. P. Prokopidis, E. P. Kosmidou, and T. D. Tsiboukis, "An FDTD algorithm for wave propagation in dispersive media using higher-order schemes," J. Electromagn. Waves Appl. 18, 1171-1194 (2004).
[CrossRef]

Rotman, W.

W. Rotman, "Plasma simulations by artificial dielectrics and parallel-plate media," IRE Trans. Ant. Propag. 10, 82-95 (1962).
[CrossRef]

Silveirinha, M.

M. Silveirinha and C. Fernandes, "Homogenization of metamaterial surfaces and slabs: the crossed wire mesh canonical problem," IEEE Trans. Antennas Propgat. 53, 59-69 (2005).
[CrossRef]

M. Silveirinha and C. Fernandes, "Homogenization of 3D connected and non-connected wire metamaterials," IEEE Trans. Microwave Theory Tech. 54, 1418-1430 (2005).
[CrossRef]

Silverinha, M.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silverinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Simovski, C. R.

P. Ikonen, P. A. Belov, C. R. Simovski, and S. I. Maslovski, "Experimental demonstration of subwavelength field channeling at microwave frequencies using a capacitively loaded wire medium," Phys. Rev. B 73, 073102 (2006).
[CrossRef]

P. A. Belov, C. R. Simovski, and P. Ikonen, "Canalization of sub-wavelength images by electromagnetic crystals," Phys. Rev. B. 71, 193105 (2005).
[CrossRef]

C. R. Simovski and P. A. Belov, "Low-frequency spatial dispersion in wire media," Phys. Rev. E 70, 046616 (2004).
[CrossRef]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silverinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Steward, W.

J. Pendry, A. Holden, W. Steward, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Sudhakaran, S.

P. A. Belov, Y. Hao, and S. Sudhakaran, "Subwavelength microwave imaging using an array of parallel conducting wires as a lens," Phys. Rev. B 73, 033108 (2006).
[CrossRef]

Tretyakov, S. A.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silverinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B 67, 113103 (2003).
[CrossRef]

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, "Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires," J. Electromagn. Waves Applic. 16, 1153-1170 (2002).
[CrossRef]

Tsiboukis, T. D.

K. P. Prokopidis, E. P. Kosmidou, and T. D. Tsiboukis, "An FDTD algorithm for wave propagation in dispersive media using higher-order schemes," J. Electromagn. Waves Appl. 18, 1171-1194 (2004).
[CrossRef]

Veselago, V.

V. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Viitanen, A. J.

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, "Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires," J. Electromagn. Waves Applic. 16, 1153-1170 (2002).
[CrossRef]

Yee, K. S.

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propgat. 14, 302-307 (1966).
[CrossRef]

Youngs, I.

J. Pendry, A. Holden, W. Steward, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propgat. (2)

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propgat. 14, 302-307 (1966).
[CrossRef]

M. Silveirinha and C. Fernandes, "Homogenization of metamaterial surfaces and slabs: the crossed wire mesh canonical problem," IEEE Trans. Antennas Propgat. 53, 59-69 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

M. Silveirinha and C. Fernandes, "Homogenization of 3D connected and non-connected wire metamaterials," IEEE Trans. Microwave Theory Tech. 54, 1418-1430 (2005).
[CrossRef]

IRE Trans. Ant. Propag. (1)

W. Rotman, "Plasma simulations by artificial dielectrics and parallel-plate media," IRE Trans. Ant. Propag. 10, 82-95 (1962).
[CrossRef]

J. Computat. Phys. (1)

J. R. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computat. Phys. 114, 185-200 (1994).
[CrossRef]

J. Electromagn. Waves Appl. (1)

K. P. Prokopidis, E. P. Kosmidou, and T. D. Tsiboukis, "An FDTD algorithm for wave propagation in dispersive media using higher-order schemes," J. Electromagn. Waves Appl. 18, 1171-1194 (2004).
[CrossRef]

J. Electromagn. Waves Applic. (1)

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, "Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires," J. Electromagn. Waves Applic. 16, 1153-1170 (2002).
[CrossRef]

Phys. Rev. B (4)

P. Ikonen, P. A. Belov, C. R. Simovski, and S. I. Maslovski, "Experimental demonstration of subwavelength field channeling at microwave frequencies using a capacitively loaded wire medium," Phys. Rev. B 73, 073102 (2006).
[CrossRef]

P. A. Belov, Y. Hao, and S. Sudhakaran, "Subwavelength microwave imaging using an array of parallel conducting wires as a lens," Phys. Rev. B 73, 033108 (2006).
[CrossRef]

P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113110 (2006).
[CrossRef]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silverinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Phys. Rev. B. (1)

P. A. Belov, C. R. Simovski, and P. Ikonen, "Canalization of sub-wavelength images by electromagnetic crystals," Phys. Rev. B. 71, 193105 (2005).
[CrossRef]

Phys. Rev. E (1)

C. R. Simovski and P. A. Belov, "Low-frequency spatial dispersion in wire media," Phys. Rev. E 70, 046616 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

J. Pendry, A. Holden, W. Steward, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

J. Pendry, "Negative refraction index makes perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (6)

J. Brown, "Artificial Dielectrics," Progress in dielectrics 2, 195-225 (1960).

M. G. Silveirinha, "Nonlocal homogenization model for a periodic array of epsilon-negative rods," accepted to Phys. Rev. E (arXiv: cond-mat/0602471) (2006).

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Norwood, MA: Artech House, 1995).

F. B. Hildebrand, Introduction to Numerical Analysis (New York: Mc-Graw-Hill, 1956).

Y. Zhao, P. A. Belov, and Y. Hao, "Modelling of wave propagation in wire media using spatially dispersive finite-difference time-domain method: numerical aspects," submitted to IEEE Trans. Antennas Propagat. (arXiv: cond-mat/0604012) (2006).

P. A. Belov and M. G. Silveirinha, "Resolution of sub-wavelength lenses formed by the wire medium," accepted to Phys. Rev. E (arXiv: physics/0511139) (2006).

Supplementary Material (4)

» Media 1: MOV (3635 KB)     
» Media 2: MOV (3282 KB)     
» Media 3: MOV (4606 KB)     
» Media 4: MOV (3233 KB)     

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 (13)

Fig. 1.
Fig. 1.

The wire medium: a rectangular lattice of parallel ideally conducting thin wires.

Fig. 2.
Fig. 2.

The layout of the computation domain for two-dimensional FDTD simulations

Fig. 3.
Fig. 3.

Animation (3.54 Mb): Transient propagation of the wave excited by a point sinusoidal magnetic source located at the λ/200 distance from the front interface of 1λ×2λ slab of the wire medium. Figure: Snapshots of magnetic field Hz at the different time steps: (a) t=175Δt, (b) t=400Δ t , (c) t=530Δt.

Fig. 4.
Fig. 4.

Power flow diagram in the steady state for the 0.5λ×1λ slab of the wire medium excited by a point magnetic source located at the λ/10 distance from the front interface.

Fig. 5.
Fig. 5.

Animation (3.20 Mb): Distributions of electric and magnetic fields for a 0.5λ×2λ slab of the wire medium excited by a point source located at λ/10 from the front interface.

Fig. 6.
Fig. 6.

Absolute values of the fields plotted in Fig. 5

Fig. 7.
Fig. 7.

Animation (4.49 Mb): Distributions of electric and magnetic fields for a 2λ×λ slab of the wire medium excited by a point source located at λ/10 from the front interface.

Fig. 8.
Fig. 8.

Distributions of electric and magnetic field in the steady state for a 0.5λ×2λ slab of the uniaxial Drude material (14) with kp/k=4 excited by a point source located at λ/10 distance from the front interface.

Fig. 9.
Fig. 9.

Distributions of electric and magnetic fields in the steady state for a slab of the uniaxial material with infinite permittivity along anisotropy axis (15) excited by a point source located at λ/10 distance from the front interface.

Fig. 10.
Fig. 10.

Absolute values of magnetic field in the source and image planes of the transmission devices formed by three different materials: a) wire medium (Fig. 6), uniaxial material with infinite permittivity along anisotropy axis (Fig. 9); b) uniaxial Drude material (Fig. 8).

Fig. 11.
Fig. 11.

Absolute values of magnetic field at the source and image planes for a 0.5λ×2λ slab of the wire medium excited by three equally spaced magnetic sources with the phase differences equal to 180° located at λ/20 distance from the front interface.

Fig. 12.
Fig. 12.

Animation (3.15 Mb): Distributions of electric and magnetic fields in the steady state for a 0.5λ×2λ slab of the wire medium excited by three equally spaced magnetic sources with the phase differences equal to 180° located at λ/20 from the front interface.

Fig. 13.
Fig. 13.

Absolute values of the fields plotted in Fig. 12.

Equations (21)

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

ε ̳ ̳ ( ω , q ) = ε ( ω , qx ) xx + yy + zz , ε ( ω , qx ) = 1 k p 2 k 2 q x 2 ,
k p 2 = 2 π ( ab ) log ab 2 π r + F ( a b ) , F ( ξ ) = 1 2 log ξ + n = 1 + ( coth ( π n ξ ) 1 n ) + π 6 ξ .
k p 2 = 2 π a 2 ln a 2 π r + 0.5275 .
D ( ω , q ) = ε 0 ε ̳ ̳ ( ω , q ) E ( ω , q ) ,
( k 2 q x 2 ) D x ( ω , q ) + ( q x 2 k 2 + k p 2 ) ε 0 E x ( ω , q ) = 0 ,
D y ( ω , q ) = ε 0 E y ( ω , q ) , D z ( ω , q ) = ε 0 E z ( ω , q ) .
( 2 x 2 1 c 2 2 t 2 ) D x ( t , r ) + ( 1 c 2 2 x 2 2 x 2 + k p 2 ) ε 0 E x ( t , r ) = 0 ,
D y ( t , x ) = ε 0 E y ( t , r ) , D z ( t , x ) = ε 0 E z ( t , r ) .
2 t 2 δ t 2 Δ t 2 , δ t 2 F m x , m y , m z n F m x , m y , m z n + 1 2 F m x , m y , m z n + F m x , m y , m z n 1 ;
2 x 2 δ x 2 Δ x 2 , δ x 2 F m x , m y , m z n F m x + 1 , m y , m z n 2 F m x , m y , m z n + F m x 1 , m y , m z n ;
( δ x 2 Δ x 2 1 c 2 δ t 2 Δ t 2 ) D x + ( 1 c 2 δ t 2 Δ t 2 δ x 2 Δ x 2 + k p 2 ) ε 0 E x = 0 ,
( D x m x + 1 , m y , m z n 2 D x m x , m y , m z n + D x m x 1 , m y , m z n Δ x 2 1 c 2 D x m x , m y , m z n + 1 2 D x m x , m y , m z n + D x m x , m y , m z n 1 ; Δ t 2 )
+ ε 0 ( 1 c 2 E x m x , m y , m z n + 1 2 E x m x , m y , m z n + E x m x , m y , m z n 1 Δ t 2 E x m x + 1 , m y , m z n 2 E x m x , m y , m z n + E x m x 1 , m y , m z n Δ x 2
+ k p 2 E x m x , m y , m z n ) = 0 .
E x m x , m y , m z n + 1 = c 2 Δ t 2 Δ x 2 ( E x m x + 1, m y , m z n + E x m x 1 , m y , m z n ) + ( 2 2 c 2 Δ t 2 Δ x 2 c 2 Δ t 2 k p 2 ) E x m x , m y , m z n
E x m x , m y , m z n 1 + ε 0 1 [ D x m x , m y , m z n + 1 + D x m x , m y , m z n 1 2 ( 1 c 2 Δ t 2 Δ x 2 ) D x m x , m y , m z n
c 2 Δ t 2 Δ x 2 ( D x m x + 1 , m y , m z n + D x m x 1 , m y , m z n ) ] .
E x m x , m y , m z n + 1 = ( 2 c 2 Δ t 2 k p 2 ) E x m x , m y , m z n E x m x , m y , m z n 1
+ ε 0 1 [ D x m x , m y , m z n + 1 2 D x m x , m y , m z n + D x m x , m y , m z n 1 ] .
ε ̳ ̳ = ε ( ω ) xx + yy + zz , ε ( ω ) = 1 k p 2 k 2 .
ε ̳ ̳ = xx + yy + zz .

Metrics