Abstract

The wire medium consisting of an array of parallel thin metallic wires was previously studied by using an effective medium with spatial dispersion. In this paper, the validity of conventional effective model was examined analytically and numerically by studying a canonical structure of the wire medium. It is noted that the conventional model fails for high transversal spatial harmonics, which consequently results in discrepancy in the scattering between the effective model and the physical structure. In this study, we propose a new effective model to include higher order spatial dispersions: instead of the second-order expansion, the proposed dispersion equation is based on the fourth–order expansion of the dispersion equation of the photonic states. Compared with the 3D full-wave simulation results of the wire medium, the proposed model has demonstrated significant improvement in numerical accuracy in characterizing the EM behavior in this type of metamaterials.

© 2013 Optical Society of America

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  1. J. Brown, “Artificial dielectrics,” Progress in Dielectrics 2, 195–225 (1960).
  2. W. Rotman, “Plasma simulations by artificial dielectrics and parallel-plate media,” IRE Trans. Antennas Propag. 10(1), 82–95 (1962).
    [Crossref]
  3. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
    [Crossref] [PubMed]
  4. 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 Appl. 16(8), 1153–1170 (2002).
    [Crossref]
  5. P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
    [Crossref]
  6. M. G. Silveirinha, “Additional boundary condition for the wire medium,” IEEE Trans. Antenn. Propag. 54(6), 1766–1780 (2006).
    [Crossref]
  7. P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056607 (2006).
    [Crossref] [PubMed]
  8. P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105 (2005).
    [Crossref]
  9. 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(3), 033108 (2006).
    [Crossref]
  10. M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Ultimate limit of resolution of subwavelength imaging devices formed by metallic rods,” Opt. Lett. 33(15), 1726–1728 (2008).
    [Crossref] [PubMed]
  11. Y. Zhao, P. A. Belov, and Y. Hao, “Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs,” Opt. Express 14(12), 5154–5167 (2006).
    [Crossref] [PubMed]
  12. 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,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
    [Crossref]
  13. P. A. Belov, Y. Zhao, A. Alomainy, and Y. Hao, “Experimental study of the subwavelength imaging by a wire medium slab,” in Antenna Technology: Small and Smart Antennas Metamaterials and Applications, 2007. IWAT '07. International Workshop on, 459–462, (2007).
  14. P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
    [Crossref]
  15. A. Rahman, P. A. Belov, and Y. Hao, “Tailoring silver nanorod arrays for subwavelength imaging of arbitrary coherent sources,” Phys. Rev. B 82(11), 113408 (2010).
    [Crossref]
  16. A. Rahman, S. Y. Kosulnikov, Y. Hao, C. Parini, and P. A. Belov, “Subwavelength optical imaging with an array of silver nanorods,” J. Nanophotonics 5(1), 051601 (2011).
    [Crossref]
  17. P. Ikonen, C. Simovski, S. Tretyakov, P. Belov, and Y. Hao, “Magnification of subwavelength field distributions at microwave frequencies using a wire medium slab operating in the canalization regime,” Appl. Phys. Lett. 91(10), 104102 (2007).
    [Crossref]
  18. Y. Zhao, “Investigation of image magnification properties of hyperlenses formed by a tapered array of metallic wires using a spatially dispersive Finite-Difference Time-Domain method in cylindrical coordinates,” J. Opt. A, Pure Appl. Opt. 14(3), 035102 (2012).
  19. A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35(2), 142–144 (2010).
    [Crossref] [PubMed]
  20. A. Rahman, Y. Hao, and C. Parini, “Subwavelength image splitter with a metallic wire array,” Phys. Rev. B 82(15), 153102 (2010).
    [Crossref]
  21. R. M. Mäkinen, J. S. Juntunen, and M. A. Kivikoski, “An improved thin-wire model for FDTD,” IEEE Trans. Microw. Theory Tech. 50(5), 1245–1255 (2002).
    [Crossref]

2012 (1)

Y. Zhao, “Investigation of image magnification properties of hyperlenses formed by a tapered array of metallic wires using a spatially dispersive Finite-Difference Time-Domain method in cylindrical coordinates,” J. Opt. A, Pure Appl. Opt. 14(3), 035102 (2012).

2011 (1)

A. Rahman, S. Y. Kosulnikov, Y. Hao, C. Parini, and P. A. Belov, “Subwavelength optical imaging with an array of silver nanorods,” J. Nanophotonics 5(1), 051601 (2011).
[Crossref]

2010 (3)

A. Rahman, P. A. Belov, and Y. Hao, “Tailoring silver nanorod arrays for subwavelength imaging of arbitrary coherent sources,” Phys. Rev. B 82(11), 113408 (2010).
[Crossref]

A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35(2), 142–144 (2010).
[Crossref] [PubMed]

A. Rahman, Y. Hao, and C. Parini, “Subwavelength image splitter with a metallic wire array,” Phys. Rev. B 82(15), 153102 (2010).
[Crossref]

2008 (2)

M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Ultimate limit of resolution of subwavelength imaging devices formed by metallic rods,” Opt. Lett. 33(15), 1726–1728 (2008).
[Crossref] [PubMed]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

2007 (2)

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,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
[Crossref]

P. Ikonen, C. Simovski, S. Tretyakov, P. Belov, and Y. Hao, “Magnification of subwavelength field distributions at microwave frequencies using a wire medium slab operating in the canalization regime,” Appl. Phys. Lett. 91(10), 104102 (2007).
[Crossref]

2006 (4)

Y. Zhao, P. A. Belov, and Y. Hao, “Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs,” Opt. Express 14(12), 5154–5167 (2006).
[Crossref] [PubMed]

M. G. Silveirinha, “Additional boundary condition for the wire medium,” IEEE Trans. Antenn. Propag. 54(6), 1766–1780 (2006).
[Crossref]

P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056607 (2006).
[Crossref] [PubMed]

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(3), 033108 (2006).
[Crossref]

2005 (1)

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105 (2005).
[Crossref]

2003 (1)

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

2002 (2)

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 Appl. 16(8), 1153–1170 (2002).
[Crossref]

R. M. Mäkinen, J. S. Juntunen, and M. A. Kivikoski, “An improved thin-wire model for FDTD,” IEEE Trans. Microw. Theory Tech. 50(5), 1245–1255 (2002).
[Crossref]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[Crossref] [PubMed]

1962 (1)

W. Rotman, “Plasma simulations by artificial dielectrics and parallel-plate media,” IRE Trans. Antennas Propag. 10(1), 82–95 (1962).
[Crossref]

1960 (1)

J. Brown, “Artificial dielectrics,” Progress in Dielectrics 2, 195–225 (1960).

Belov, P.

P. Ikonen, C. Simovski, S. Tretyakov, P. Belov, and Y. Hao, “Magnification of subwavelength field distributions at microwave frequencies using a wire medium slab operating in the canalization regime,” Appl. Phys. Lett. 91(10), 104102 (2007).
[Crossref]

Belov, P. A.

A. Rahman, S. Y. Kosulnikov, Y. Hao, C. Parini, and P. A. Belov, “Subwavelength optical imaging with an array of silver nanorods,” J. Nanophotonics 5(1), 051601 (2011).
[Crossref]

A. Rahman, P. A. Belov, and Y. Hao, “Tailoring silver nanorod arrays for subwavelength imaging of arbitrary coherent sources,” Phys. Rev. B 82(11), 113408 (2010).
[Crossref]

A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35(2), 142–144 (2010).
[Crossref] [PubMed]

M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Ultimate limit of resolution of subwavelength imaging devices formed by metallic rods,” Opt. Lett. 33(15), 1726–1728 (2008).
[Crossref] [PubMed]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

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,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
[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(3), 033108 (2006).
[Crossref]

P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056607 (2006).
[Crossref] [PubMed]

Y. Zhao, P. A. Belov, and Y. Hao, “Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs,” Opt. Express 14(12), 5154–5167 (2006).
[Crossref] [PubMed]

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105 (2005).
[Crossref]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 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 Appl. 16(8), 1153–1170 (2002).
[Crossref]

Brown, J.

J. Brown, “Artificial dielectrics,” Progress in Dielectrics 2, 195–225 (1960).

Hao, Y.

A. Rahman, S. Y. Kosulnikov, Y. Hao, C. Parini, and P. A. Belov, “Subwavelength optical imaging with an array of silver nanorods,” J. Nanophotonics 5(1), 051601 (2011).
[Crossref]

A. Rahman, P. A. Belov, and Y. Hao, “Tailoring silver nanorod arrays for subwavelength imaging of arbitrary coherent sources,” Phys. Rev. B 82(11), 113408 (2010).
[Crossref]

A. Rahman, Y. Hao, and C. Parini, “Subwavelength image splitter with a metallic wire array,” Phys. Rev. B 82(15), 153102 (2010).
[Crossref]

A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35(2), 142–144 (2010).
[Crossref] [PubMed]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

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,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
[Crossref]

P. Ikonen, C. Simovski, S. Tretyakov, P. Belov, and Y. Hao, “Magnification of subwavelength field distributions at microwave frequencies using a wire medium slab operating in the canalization regime,” Appl. Phys. Lett. 91(10), 104102 (2007).
[Crossref]

Y. Zhao, P. A. Belov, and Y. Hao, “Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs,” Opt. Express 14(12), 5154–5167 (2006).
[Crossref] [PubMed]

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(3), 033108 (2006).
[Crossref]

Holden, A. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[Crossref] [PubMed]

Ikonen, P.

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

P. Ikonen, C. Simovski, S. Tretyakov, P. Belov, and Y. Hao, “Magnification of subwavelength field distributions at microwave frequencies using a wire medium slab operating in the canalization regime,” Appl. Phys. Lett. 91(10), 104102 (2007).
[Crossref]

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105 (2005).
[Crossref]

Juntunen, J. S.

R. M. Mäkinen, J. S. Juntunen, and M. A. Kivikoski, “An improved thin-wire model for FDTD,” IEEE Trans. Microw. Theory Tech. 50(5), 1245–1255 (2002).
[Crossref]

Kivikoski, M. A.

R. M. Mäkinen, J. S. Juntunen, and M. A. Kivikoski, “An improved thin-wire model for FDTD,” IEEE Trans. Microw. Theory Tech. 50(5), 1245–1255 (2002).
[Crossref]

Kosulnikov, S. Y.

A. Rahman, S. Y. Kosulnikov, Y. Hao, C. Parini, and P. A. Belov, “Subwavelength optical imaging with an array of silver nanorods,” J. Nanophotonics 5(1), 051601 (2011).
[Crossref]

Mäkinen, R. M.

R. M. Mäkinen, J. S. Juntunen, and M. A. Kivikoski, “An improved thin-wire model for FDTD,” IEEE Trans. Microw. Theory Tech. 50(5), 1245–1255 (2002).
[Crossref]

Marques, R.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Maslovski, S. I.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Nefedov, I. S.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Parini, C.

A. Rahman, S. Y. Kosulnikov, Y. Hao, C. Parini, and P. A. Belov, “Subwavelength optical imaging with an array of silver nanorods,” J. Nanophotonics 5(1), 051601 (2011).
[Crossref]

A. Rahman, Y. Hao, and C. Parini, “Subwavelength image splitter with a metallic wire array,” Phys. Rev. B 82(15), 153102 (2010).
[Crossref]

A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35(2), 142–144 (2010).
[Crossref] [PubMed]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

Pendry, J. B.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[Crossref] [PubMed]

Rahman, A.

A. Rahman, S. Y. Kosulnikov, Y. Hao, C. Parini, and P. A. Belov, “Subwavelength optical imaging with an array of silver nanorods,” J. Nanophotonics 5(1), 051601 (2011).
[Crossref]

A. Rahman, Y. Hao, and C. Parini, “Subwavelength image splitter with a metallic wire array,” Phys. Rev. B 82(15), 153102 (2010).
[Crossref]

A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35(2), 142–144 (2010).
[Crossref] [PubMed]

A. Rahman, P. A. Belov, and Y. Hao, “Tailoring silver nanorod arrays for subwavelength imaging of arbitrary coherent sources,” Phys. Rev. B 82(11), 113408 (2010).
[Crossref]

Rotman, W.

W. Rotman, “Plasma simulations by artificial dielectrics and parallel-plate media,” IRE Trans. Antennas Propag. 10(1), 82–95 (1962).
[Crossref]

Silveirinha, M.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Silveirinha, M. G.

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Ultimate limit of resolution of subwavelength imaging devices formed by metallic rods,” Opt. Lett. 33(15), 1726–1728 (2008).
[Crossref] [PubMed]

M. G. Silveirinha, “Additional boundary condition for the wire medium,” IEEE Trans. Antenn. Propag. 54(6), 1766–1780 (2006).
[Crossref]

P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056607 (2006).
[Crossref] [PubMed]

Simovski, C.

P. Ikonen, C. Simovski, S. Tretyakov, P. Belov, and Y. Hao, “Magnification of subwavelength field distributions at microwave frequencies using a wire medium slab operating in the canalization regime,” Appl. Phys. Lett. 91(10), 104102 (2007).
[Crossref]

Simovski, C. R.

M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Ultimate limit of resolution of subwavelength imaging devices formed by metallic rods,” Opt. Lett. 33(15), 1726–1728 (2008).
[Crossref] [PubMed]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105 (2005).
[Crossref]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 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(3), 033108 (2006).
[Crossref]

Tretyakov, S.

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

P. Ikonen, C. Simovski, S. Tretyakov, P. Belov, and Y. Hao, “Magnification of subwavelength field distributions at microwave frequencies using a wire medium slab operating in the canalization regime,” Appl. Phys. Lett. 91(10), 104102 (2007).
[Crossref]

Tretyakov, S. A.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 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 Appl. 16(8), 1153–1170 (2002).
[Crossref]

Tse, S.

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[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 Appl. 16(8), 1153–1170 (2002).
[Crossref]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[Crossref] [PubMed]

Zhao, Y.

Y. Zhao, “Investigation of image magnification properties of hyperlenses formed by a tapered array of metallic wires using a spatially dispersive Finite-Difference Time-Domain method in cylindrical coordinates,” J. Opt. A, Pure Appl. Opt. 14(3), 035102 (2012).

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

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,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
[Crossref]

Y. Zhao, P. A. Belov, and Y. Hao, “Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs,” Opt. Express 14(12), 5154–5167 (2006).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

P. Ikonen, C. Simovski, S. Tretyakov, P. Belov, and Y. Hao, “Magnification of subwavelength field distributions at microwave frequencies using a wire medium slab operating in the canalization regime,” Appl. Phys. Lett. 91(10), 104102 (2007).
[Crossref]

IEEE Trans. Antenn. Propag. (2)

M. G. Silveirinha, “Additional boundary condition for the wire medium,” IEEE Trans. Antenn. Propag. 54(6), 1766–1780 (2006).
[Crossref]

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,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

R. M. Mäkinen, J. S. Juntunen, and M. A. Kivikoski, “An improved thin-wire model for FDTD,” IEEE Trans. Microw. Theory Tech. 50(5), 1245–1255 (2002).
[Crossref]

IRE Trans. Antennas Propag. (1)

W. Rotman, “Plasma simulations by artificial dielectrics and parallel-plate media,” IRE Trans. Antennas Propag. 10(1), 82–95 (1962).
[Crossref]

J. Electromagn. Waves Appl. (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 Appl. 16(8), 1153–1170 (2002).
[Crossref]

J. Nanophotonics (1)

A. Rahman, S. Y. Kosulnikov, Y. Hao, C. Parini, and P. A. Belov, “Subwavelength optical imaging with an array of silver nanorods,” J. Nanophotonics 5(1), 051601 (2011).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

Y. Zhao, “Investigation of image magnification properties of hyperlenses formed by a tapered array of metallic wires using a spatially dispersive Finite-Difference Time-Domain method in cylindrical coordinates,” J. Opt. A, Pure Appl. Opt. 14(3), 035102 (2012).

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (6)

A. Rahman, Y. Hao, and C. Parini, “Subwavelength image splitter with a metallic wire array,” Phys. Rev. B 82(15), 153102 (2010).
[Crossref]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

A. Rahman, P. A. Belov, and Y. Hao, “Tailoring silver nanorod arrays for subwavelength imaging of arbitrary coherent sources,” Phys. Rev. B 82(11), 113408 (2010).
[Crossref]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105 (2005).
[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(3), 033108 (2006).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056607 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[Crossref] [PubMed]

Progress in Dielectrics (1)

J. Brown, “Artificial dielectrics,” Progress in Dielectrics 2, 195–225 (1960).

Other (1)

P. A. Belov, Y. Zhao, A. Alomainy, and Y. Hao, “Experimental study of the subwavelength imaging by a wire medium slab,” in Antenna Technology: Small and Smart Antennas Metamaterials and Applications, 2007. IWAT '07. International Workshop on, 459–462, (2007).

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Figures (10)

Fig. 1
Fig. 1

Physical wire medium formed by an array of thin wires periodically arranged in rectangular lattice. a and b denote the lattice constants in y- and z- directions respectively. The thin wires are aligned in x-direction, and are uniform, with radii r and length d.

Fig. 2
Fig. 2

The transmission coefficient as a function of the transverse component of wave component k y d /π for   k 0 =π/d calculated by using FDTD and analytical method. (a)  k p =4.8415 k 0 ; (b) k p =9.683 k 0 .

Fig. 3
Fig. 3

The condition where the conventional effective model is sufficiently accurate for   k 0 =π/d .

Fig. 4
Fig. 4

The coupling between the TE and TM waves in a physical thin wire array as a function of ky.

Fig. 5
Fig. 5

Comparison of the fitted surface γ TM and the source data for the surface fitting γ TM_FDTD obtained through FDTD simulation of physical thin wire array.

Fig. 6
Fig. 6

The analytical results of the proposed effective media, referenced by the transmission of the thin wire array calculated by FDTD. (a) k p =4.8415 k 0 ; (b) k p =9.683 k 0 .

Fig. 7
Fig. 7

Comparison of the conditions where the effective models become inaccurate.

Fig. 8
Fig. 8

The analytical transmission of the conventional and the proposed effective media, referenced by the FDTD result. The wire array is illuminated by a plane wave with k y = k z 0 . (a) k p =4.8415 k 0 ; (b) k p =9.683 k 0 .

Fig. 9
Fig. 9

The analytical results of the conventional and the proposed effective media, referenced by the FDTD result of the thin wire array. The wire array is with filling ratio of (a) 0.0005101 and (b) 0.0015623.

Fig. 10
Fig. 10

The analytical results of the conventional and the proposed effective media, referenced by the FDTD result of the thin wire array, which is in a rectangular lattice ab .

Equations (17)

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1 π ln b 2πr + 1 b p y (0) sin p y (0) a cos p y (0) acos q y a + n0 ( 1 b p y (n) sin p y (n) a cos p y (n) acos q y a 1 2π| n | ) =0,
p y (n) =j ( q z + 2πn b ) 2 + q x 2 k 2 , Re{ ( ) }>0 ,
q x 2 + q y 2 + q z 2 = k 2 k p 2 .
ε ¯ ¯ =ε( k, q x )xx+yy+zz ,
ε( k, q x )= ε 0 ( 1 k p 2 k 2 q x 2 ) ,
k p 2 = 2π/( ab ) log ab 2πr +F(a/b ) ,
F(ξ)= 1 2 logξ+ n=1 + ( coth( πnξ )1 n ) + π 6 ξ .
T thin wire array = | H z_imageplane | | H z_sourceplane | .
DR= | T thin wire array T effective | T thin wire array ×100% ,
q x =j γ TM ,
γ TM = k p 2 + k y 2 k 2 ,
T effective = 1 1+ γ TM k y 2 γ x ( γ TM 2 + k 2 ) ctanh( γ TM d /2 ) .
γ TM = k p 2 + k y 2 k 2 +( k y 2 + k p 2 )( A k y 2 k p 2 +B k y 2 k 2 ) ,
γ TM = k p 2 + k y 2 + k z 2 k 2 +( k y 2 + k z 2 + k p 2 )( A k y 2 + k z 2 k p 2 +B k y 2 + k z 2 k 2 ) ,
q x 2 +( q y 2 + q z 2 + k p 2 )( A q y 2 + q z 2 k p 2 +B q y 2 + q z 2 k 2 +1 )= k 2 .
ε 0 ( q y 2 + q z 2 )=ε( k 2 q x 2 ) ,
ε( k, q x , q y , q z )= ε 0 ( 1 A q y 2 + q z 2 k p 2 +B q y 2 + q z 2 k 2 +1 k p 2 k 2 q x 2 ) .

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