Abstract

We study the guided modes in a wire medium (WM) slab, taking into account the nonlocality and losses in the structure. We show that due to the fact that the WM is an extremely spatially dispersive metamaterial, the effect of nonlocality plays a critical role, since it results in coupling between the otherwise orthogonal guided modes. We observe the effects of strong and weak coupling, depending on the level of losses in the system.

© 2014 Optical Society of America

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  1. C. R. Simovsky, P. A. Belov, A. V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4221–4342 (2012).
    [CrossRef]
  2. M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Subwavelength imaging at infrared frequencies using an array of metallic nanorods,” Phys. Rev. B 75, 035108 (2007).
    [CrossRef]
  3. P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
    [CrossRef]
  4. P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010).
    [CrossRef]
  5. J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
    [CrossRef]
  6. P. Ginzburg, F. Rodríguez Fortuño, G. A. Wurtz, W. Dickson, A. Murphy, F. Morgan, R. J. Pollard, I. Iorsh, A. Atrashchenko, P. A. Belov, Yu. S. Kivshar, A. Nevet, G. Ankonina, M. Orenstein, and A. V. Zayats, “Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials,” Opt. Express 21, 14907–14917 (2013).
    [CrossRef]
  7. P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E 73, 056607 (2006).
    [CrossRef]
  8. Y. Zhao, G. Palikaras, P. A. Belov, R. F. Dubrovka, C. R. Simovski, Y. Hao, and C. G. Parini, “Magnification of subwavelength field distributions using a tapered array of metallic wires with planar interfaces and an embedded dielectric phase compensator,” New J. Phys. 12, 103045 (2010).
    [CrossRef]
  9. S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
    [CrossRef]
  10. M. Navarro-Cia, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17, 18184–18195 (2009).
    [CrossRef]
  11. E. K. Stone and E. Hendry, “Dispersion of spoof surface plasmons in open-ended metallic hole arrays,” Phys. Rev. B 84, 035418 (2011).
    [CrossRef]
  12. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
    [CrossRef]
  13. F. Lemoult, G. Lerosey, J. Rosny, and M. Fink, “Resonant metalenses for breaking the diffraction barrier,” Phys. Rev. Lett. 104, 203901 (2010).
    [CrossRef]
  14. F. Lemoult, M. Fink, and G. Lerosey, “A polychromatic approach to far-field superlensing at visible wavelengths,” Nat. Commun. 3, 889 (2012).
    [CrossRef]
  15. F. Lemoult, N. Kaina, M. Fink, and G. Lerosey, “Wave propagation control at the deep subwavelength scale in metamaterials,” Nat. Phys. 9, 55–60 (2012).
    [CrossRef]
  16. F. Lemoult, M. Fink, and G. Lerosey, “Revisiting the wire medium: an ideal resonant metalens,” Waves Random Complex Media 21, 591–613 (2011).
    [CrossRef]
  17. 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, 113103 (2003).
    [CrossRef]
  18. S. I. Maslovski and M. G. Silveirinha, “Nonlocal permittivity from a quasistatic model for a class of wire media,” Phys. Rev. B 80, 245101 (2009).
    [CrossRef]
  19. O. Luukkonen, C. R. Simovski, A. V. Raisanen, and S. A. Tretyakov, “An efficient and simple analytical model for analysis of propagation properties in impedance waveguides,” IEEE Trans. Microwave Theor. Tech. 56, 1624–1632 (2008).
    [CrossRef]
  20. A. F. Alexandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Springer-Verlag, 1984).
  21. P. A. Belov, R. Dubrovka, I. Iorsh, I. Yagupov, and Y. S. Kivshar, “Single-mode subwavelength waveguides with wire metamaterials,” Appl. Phys. Lett. 103, 161103 (2013).
    [CrossRef]
  22. M. Silveirinha, C. A. Fernandes, and J. R. Costa, “Superlens made of a metamaterial with extreme effective parameters,” Phys. Rev. B 78, 195121 (2008).
    [CrossRef]
  23. A. N. Kondratenko, Plasma Waveguides (Atomizdat, 1976).
  24. M. Silveirinha, “Additional boundary condition for the wire medium,” IEEE Trans. Antennas Propag. 54, 1766–1780 (2006).
    [CrossRef]
  25. A. E. Ageyskiy, S. Y. Kosulnikov, and P. A. Belov, “Resonant excitation of evanescent spatial harmonics in medium formed by parallel metallic nanorods,” Opt. Spectrosc. 110, 572–585 (2011).
    [CrossRef]
  26. A. E. Ageyskiy, S. Y. Kosulnikov, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Quarter-wavelength nanorod lens based on internal imaging,” Phys. Rev. B 85, 033105 (2012).
    [CrossRef]

2013

2012

A. E. Ageyskiy, S. Y. Kosulnikov, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Quarter-wavelength nanorod lens based on internal imaging,” Phys. Rev. B 85, 033105 (2012).
[CrossRef]

C. R. Simovsky, P. A. Belov, A. V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4221–4342 (2012).
[CrossRef]

F. Lemoult, M. Fink, and G. Lerosey, “A polychromatic approach to far-field superlensing at visible wavelengths,” Nat. Commun. 3, 889 (2012).
[CrossRef]

F. Lemoult, N. Kaina, M. Fink, and G. Lerosey, “Wave propagation control at the deep subwavelength scale in metamaterials,” Nat. Phys. 9, 55–60 (2012).
[CrossRef]

2011

F. Lemoult, M. Fink, and G. Lerosey, “Revisiting the wire medium: an ideal resonant metalens,” Waves Random Complex Media 21, 591–613 (2011).
[CrossRef]

E. K. Stone and E. Hendry, “Dispersion of spoof surface plasmons in open-ended metallic hole arrays,” Phys. Rev. B 84, 035418 (2011).
[CrossRef]

A. E. Ageyskiy, S. Y. Kosulnikov, and P. A. Belov, “Resonant excitation of evanescent spatial harmonics in medium formed by parallel metallic nanorods,” Opt. Spectrosc. 110, 572–585 (2011).
[CrossRef]

2010

Y. Zhao, G. Palikaras, P. A. Belov, R. F. Dubrovka, C. R. Simovski, Y. Hao, and C. G. Parini, “Magnification of subwavelength field distributions using a tapered array of metallic wires with planar interfaces and an embedded dielectric phase compensator,” New J. Phys. 12, 103045 (2010).
[CrossRef]

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010).
[CrossRef]

F. Lemoult, G. Lerosey, J. Rosny, and M. Fink, “Resonant metalenses for breaking the diffraction barrier,” Phys. Rev. Lett. 104, 203901 (2010).
[CrossRef]

2009

2008

M. Silveirinha, C. A. Fernandes, and J. R. Costa, “Superlens made of a metamaterial with extreme effective parameters,” Phys. Rev. B 78, 195121 (2008).
[CrossRef]

O. Luukkonen, C. R. Simovski, A. V. Raisanen, and S. A. Tretyakov, “An efficient and simple analytical model for analysis of propagation properties in impedance waveguides,” IEEE Trans. Microwave Theor. Tech. 56, 1624–1632 (2008).
[CrossRef]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

2007

M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Subwavelength imaging at infrared frequencies using an array of metallic nanorods,” Phys. Rev. B 75, 035108 (2007).
[CrossRef]

2006

P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E 73, 056607 (2006).
[CrossRef]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef]

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

2005

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef]

2003

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, 113103 (2003).
[CrossRef]

Ageyskiy, A. E.

A. E. Ageyskiy, S. Y. Kosulnikov, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Quarter-wavelength nanorod lens based on internal imaging,” Phys. Rev. B 85, 033105 (2012).
[CrossRef]

A. E. Ageyskiy, S. Y. Kosulnikov, and P. A. Belov, “Resonant excitation of evanescent spatial harmonics in medium formed by parallel metallic nanorods,” Opt. Spectrosc. 110, 572–585 (2011).
[CrossRef]

Agrafiotis, S.

Alexandrov, A. F.

A. F. Alexandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Springer-Verlag, 1984).

Andrews, S. R.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef]

Ankonina, G.

Atrashchenko, A.

Atrashenko, A. V.

C. R. Simovsky, P. A. Belov, A. V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4221–4342 (2012).
[CrossRef]

Bartal, G.

J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Belov, P. A.

P. Ginzburg, F. Rodríguez Fortuño, G. A. Wurtz, W. Dickson, A. Murphy, F. Morgan, R. J. Pollard, I. Iorsh, A. Atrashchenko, P. A. Belov, Yu. S. Kivshar, A. Nevet, G. Ankonina, M. Orenstein, and A. V. Zayats, “Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials,” Opt. Express 21, 14907–14917 (2013).
[CrossRef]

P. A. Belov, R. Dubrovka, I. Iorsh, I. Yagupov, and Y. S. Kivshar, “Single-mode subwavelength waveguides with wire metamaterials,” Appl. Phys. Lett. 103, 161103 (2013).
[CrossRef]

C. R. Simovsky, P. A. Belov, A. V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4221–4342 (2012).
[CrossRef]

A. E. Ageyskiy, S. Y. Kosulnikov, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Quarter-wavelength nanorod lens based on internal imaging,” Phys. Rev. B 85, 033105 (2012).
[CrossRef]

A. E. Ageyskiy, S. Y. Kosulnikov, and P. A. Belov, “Resonant excitation of evanescent spatial harmonics in medium formed by parallel metallic nanorods,” Opt. Spectrosc. 110, 572–585 (2011).
[CrossRef]

Y. Zhao, G. Palikaras, P. A. Belov, R. F. Dubrovka, C. R. Simovski, Y. Hao, and C. G. Parini, “Magnification of subwavelength field distributions using a tapered array of metallic wires with planar interfaces and an embedded dielectric phase compensator,” New J. Phys. 12, 103045 (2010).
[CrossRef]

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010).
[CrossRef]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Subwavelength imaging at infrared frequencies using an array of metallic nanorods,” Phys. Rev. B 75, 035108 (2007).
[CrossRef]

P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E 73, 056607 (2006).
[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, 113103 (2003).
[CrossRef]

Beruete, M.

Bogdankevich, L. S.

A. F. Alexandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Springer-Verlag, 1984).

Catrysse, P. B.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef]

Costa, J. R.

M. Silveirinha, C. A. Fernandes, and J. R. Costa, “Superlens made of a metamaterial with extreme effective parameters,” Phys. Rev. B 78, 195121 (2008).
[CrossRef]

Dickson, W.

Dubrovka, R.

P. A. Belov, R. Dubrovka, I. Iorsh, I. Yagupov, and Y. S. Kivshar, “Single-mode subwavelength waveguides with wire metamaterials,” Appl. Phys. Lett. 103, 161103 (2013).
[CrossRef]

Dubrovka, R. F.

Y. Zhao, G. Palikaras, P. A. Belov, R. F. Dubrovka, C. R. Simovski, Y. Hao, and C. G. Parini, “Magnification of subwavelength field distributions using a tapered array of metallic wires with planar interfaces and an embedded dielectric phase compensator,” New J. Phys. 12, 103045 (2010).
[CrossRef]

Falcone, F.

Fan, S.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef]

Fernandes, C. A.

M. Silveirinha, C. A. Fernandes, and J. R. Costa, “Superlens made of a metamaterial with extreme effective parameters,” Phys. Rev. B 78, 195121 (2008).
[CrossRef]

Fink, M.

F. Lemoult, M. Fink, and G. Lerosey, “A polychromatic approach to far-field superlensing at visible wavelengths,” Nat. Commun. 3, 889 (2012).
[CrossRef]

F. Lemoult, N. Kaina, M. Fink, and G. Lerosey, “Wave propagation control at the deep subwavelength scale in metamaterials,” Nat. Phys. 9, 55–60 (2012).
[CrossRef]

F. Lemoult, M. Fink, and G. Lerosey, “Revisiting the wire medium: an ideal resonant metalens,” Waves Random Complex Media 21, 591–613 (2011).
[CrossRef]

F. Lemoult, G. Lerosey, J. Rosny, and M. Fink, “Resonant metalenses for breaking the diffraction barrier,” Phys. Rev. Lett. 104, 203901 (2010).
[CrossRef]

Garcia-Vidal, F. J.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef]

Ginzburg, P.

Hao, Y.

Y. Zhao, G. Palikaras, P. A. Belov, R. F. Dubrovka, C. R. Simovski, Y. Hao, and C. G. Parini, “Magnification of subwavelength field distributions using a tapered array of metallic wires with planar interfaces and an embedded dielectric phase compensator,” New J. Phys. 12, 103045 (2010).
[CrossRef]

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010).
[CrossRef]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

Hendry, E.

E. K. Stone and E. Hendry, “Dispersion of spoof surface plasmons in open-ended metallic hole arrays,” Phys. Rev. B 84, 035418 (2011).
[CrossRef]

Ikonen, P.

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

Iorsh, I.

Kaina, N.

F. Lemoult, N. Kaina, M. Fink, and G. Lerosey, “Wave propagation control at the deep subwavelength scale in metamaterials,” Nat. Phys. 9, 55–60 (2012).
[CrossRef]

Kivshar, Y. S.

P. A. Belov, R. Dubrovka, I. Iorsh, I. Yagupov, and Y. S. Kivshar, “Single-mode subwavelength waveguides with wire metamaterials,” Appl. Phys. Lett. 103, 161103 (2013).
[CrossRef]

A. E. Ageyskiy, S. Y. Kosulnikov, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Quarter-wavelength nanorod lens based on internal imaging,” Phys. Rev. B 85, 033105 (2012).
[CrossRef]

Kivshar, Yu. S.

Kondratenko, A. N.

A. N. Kondratenko, Plasma Waveguides (Atomizdat, 1976).

Kosulnikov, S. Y.

A. E. Ageyskiy, S. Y. Kosulnikov, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Quarter-wavelength nanorod lens based on internal imaging,” Phys. Rev. B 85, 033105 (2012).
[CrossRef]

A. E. Ageyskiy, S. Y. Kosulnikov, and P. A. Belov, “Resonant excitation of evanescent spatial harmonics in medium formed by parallel metallic nanorods,” Opt. Spectrosc. 110, 572–585 (2011).
[CrossRef]

Lemoult, F.

F. Lemoult, M. Fink, and G. Lerosey, “A polychromatic approach to far-field superlensing at visible wavelengths,” Nat. Commun. 3, 889 (2012).
[CrossRef]

F. Lemoult, N. Kaina, M. Fink, and G. Lerosey, “Wave propagation control at the deep subwavelength scale in metamaterials,” Nat. Phys. 9, 55–60 (2012).
[CrossRef]

F. Lemoult, M. Fink, and G. Lerosey, “Revisiting the wire medium: an ideal resonant metalens,” Waves Random Complex Media 21, 591–613 (2011).
[CrossRef]

F. Lemoult, G. Lerosey, J. Rosny, and M. Fink, “Resonant metalenses for breaking the diffraction barrier,” Phys. Rev. Lett. 104, 203901 (2010).
[CrossRef]

Lerosey, G.

F. Lemoult, M. Fink, and G. Lerosey, “A polychromatic approach to far-field superlensing at visible wavelengths,” Nat. Commun. 3, 889 (2012).
[CrossRef]

F. Lemoult, N. Kaina, M. Fink, and G. Lerosey, “Wave propagation control at the deep subwavelength scale in metamaterials,” Nat. Phys. 9, 55–60 (2012).
[CrossRef]

F. Lemoult, M. Fink, and G. Lerosey, “Revisiting the wire medium: an ideal resonant metalens,” Waves Random Complex Media 21, 591–613 (2011).
[CrossRef]

F. Lemoult, G. Lerosey, J. Rosny, and M. Fink, “Resonant metalenses for breaking the diffraction barrier,” Phys. Rev. Lett. 104, 203901 (2010).
[CrossRef]

Liu, Yo.

J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Liu, Zh.

J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Luukkonen, O.

O. Luukkonen, C. R. Simovski, A. V. Raisanen, and S. A. Tretyakov, “An efficient and simple analytical model for analysis of propagation properties in impedance waveguides,” IEEE Trans. Microwave Theor. Tech. 56, 1624–1632 (2008).
[CrossRef]

Maier, S. A.

M. Navarro-Cia, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17, 18184–18195 (2009).
[CrossRef]

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[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, 113103 (2003).
[CrossRef]

Martin-Moreno, L.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef]

Maslovski, S. I.

A. E. Ageyskiy, S. Y. Kosulnikov, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Quarter-wavelength nanorod lens based on internal imaging,” Phys. Rev. B 85, 033105 (2012).
[CrossRef]

S. I. Maslovski and M. G. Silveirinha, “Nonlocal permittivity from a quasistatic model for a class of wire media,” Phys. Rev. B 80, 245101 (2009).
[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, 113103 (2003).
[CrossRef]

Morgan, F.

Murphy, A.

Navarro-Cia, M.

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, 113103 (2003).
[CrossRef]

Nevet, A.

Orenstein, M.

Palikaras, G.

Y. Zhao, G. Palikaras, P. A. Belov, R. F. Dubrovka, C. R. Simovski, Y. Hao, and C. G. Parini, “Magnification of subwavelength field distributions using a tapered array of metallic wires with planar interfaces and an embedded dielectric phase compensator,” New J. Phys. 12, 103045 (2010).
[CrossRef]

Palikaras, G. K.

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010).
[CrossRef]

Parini, C.

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010).
[CrossRef]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

Parini, C. G.

Y. Zhao, G. Palikaras, P. A. Belov, R. F. Dubrovka, C. R. Simovski, Y. Hao, and C. G. Parini, “Magnification of subwavelength field distributions using a tapered array of metallic wires with planar interfaces and an embedded dielectric phase compensator,” New J. Phys. 12, 103045 (2010).
[CrossRef]

Pollard, R. J.

Rahman, A.

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010).
[CrossRef]

Raisanen, A. V.

O. Luukkonen, C. R. Simovski, A. V. Raisanen, and S. A. Tretyakov, “An efficient and simple analytical model for analysis of propagation properties in impedance waveguides,” IEEE Trans. Microwave Theor. Tech. 56, 1624–1632 (2008).
[CrossRef]

Rodríguez Fortuño, F.

Rosny, J.

F. Lemoult, G. Lerosey, J. Rosny, and M. Fink, “Resonant metalenses for breaking the diffraction barrier,” Phys. Rev. Lett. 104, 203901 (2010).
[CrossRef]

Rukhadze, A. A.

A. F. Alexandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Springer-Verlag, 1984).

Shen, J. T.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef]

Silveirinha, M.

M. Silveirinha, C. A. Fernandes, and J. R. Costa, “Superlens made of a metamaterial with extreme effective parameters,” Phys. Rev. B 78, 195121 (2008).
[CrossRef]

M. Silveirinha, “Additional boundary condition for the wire medium,” IEEE Trans. Antennas Propag. 54, 1766–1780 (2006).
[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, 113103 (2003).
[CrossRef]

Silveirinha, M. G.

S. I. Maslovski and M. G. Silveirinha, “Nonlocal permittivity from a quasistatic model for a class of wire media,” Phys. Rev. B 80, 245101 (2009).
[CrossRef]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Subwavelength imaging at infrared frequencies using an array of metallic nanorods,” Phys. Rev. B 75, 035108 (2007).
[CrossRef]

P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E 73, 056607 (2006).
[CrossRef]

Simovski, C. R.

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010).
[CrossRef]

Y. Zhao, G. Palikaras, P. A. Belov, R. F. Dubrovka, C. R. Simovski, Y. Hao, and C. G. Parini, “Magnification of subwavelength field distributions using a tapered array of metallic wires with planar interfaces and an embedded dielectric phase compensator,” New J. Phys. 12, 103045 (2010).
[CrossRef]

O. Luukkonen, C. R. Simovski, A. V. Raisanen, and S. A. Tretyakov, “An efficient and simple analytical model for analysis of propagation properties in impedance waveguides,” IEEE Trans. Microwave Theor. Tech. 56, 1624–1632 (2008).
[CrossRef]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Subwavelength imaging at infrared frequencies using an array of metallic nanorods,” Phys. Rev. B 75, 035108 (2007).
[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, 113103 (2003).
[CrossRef]

Simovsky, C. R.

C. R. Simovsky, P. A. Belov, A. V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4221–4342 (2012).
[CrossRef]

Sorolla, M.

Stacy, A. M.

J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Stone, E. K.

E. K. Stone and E. Hendry, “Dispersion of spoof surface plasmons in open-ended metallic hole arrays,” Phys. Rev. B 84, 035418 (2011).
[CrossRef]

Sun, C.

J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Tretyakov, S. A.

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

O. Luukkonen, C. R. Simovski, A. V. Raisanen, and S. A. Tretyakov, “An efficient and simple analytical model for analysis of propagation properties in impedance waveguides,” IEEE Trans. Microwave Theor. Tech. 56, 1624–1632 (2008).
[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, 113103 (2003).
[CrossRef]

Tse, S.

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

Wang, Yu.

J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Wurtz, G. A.

Yagupov, I.

P. A. Belov, R. Dubrovka, I. Iorsh, I. Yagupov, and Y. S. Kivshar, “Single-mode subwavelength waveguides with wire metamaterials,” Appl. Phys. Lett. 103, 161103 (2013).
[CrossRef]

Yao, J.

J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Zayats, A. V.

Zhang, X.

J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Zhao, Y.

Y. Zhao, G. Palikaras, P. A. Belov, R. F. Dubrovka, C. R. Simovski, Y. Hao, and C. G. Parini, “Magnification of subwavelength field distributions using a tapered array of metallic wires with planar interfaces and an embedded dielectric phase compensator,” New J. Phys. 12, 103045 (2010).
[CrossRef]

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010).
[CrossRef]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

Adv. Mater.

C. R. Simovsky, P. A. Belov, A. V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4221–4342 (2012).
[CrossRef]

Appl. Phys. Lett.

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010).
[CrossRef]

P. A. Belov, R. Dubrovka, I. Iorsh, I. Yagupov, and Y. S. Kivshar, “Single-mode subwavelength waveguides with wire metamaterials,” Appl. Phys. Lett. 103, 161103 (2013).
[CrossRef]

IEEE Trans. Antennas Propag.

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

IEEE Trans. Microwave Theor. Tech.

O. Luukkonen, C. R. Simovski, A. V. Raisanen, and S. A. Tretyakov, “An efficient and simple analytical model for analysis of propagation properties in impedance waveguides,” IEEE Trans. Microwave Theor. Tech. 56, 1624–1632 (2008).
[CrossRef]

Nat. Commun.

F. Lemoult, M. Fink, and G. Lerosey, “A polychromatic approach to far-field superlensing at visible wavelengths,” Nat. Commun. 3, 889 (2012).
[CrossRef]

Nat. Phys.

F. Lemoult, N. Kaina, M. Fink, and G. Lerosey, “Wave propagation control at the deep subwavelength scale in metamaterials,” Nat. Phys. 9, 55–60 (2012).
[CrossRef]

New J. Phys.

Y. Zhao, G. Palikaras, P. A. Belov, R. F. Dubrovka, C. R. Simovski, Y. Hao, and C. G. Parini, “Magnification of subwavelength field distributions using a tapered array of metallic wires with planar interfaces and an embedded dielectric phase compensator,” New J. Phys. 12, 103045 (2010).
[CrossRef]

Opt. Express

Opt. Spectrosc.

A. E. Ageyskiy, S. Y. Kosulnikov, and P. A. Belov, “Resonant excitation of evanescent spatial harmonics in medium formed by parallel metallic nanorods,” Opt. Spectrosc. 110, 572–585 (2011).
[CrossRef]

Phys. Rev. B

A. E. Ageyskiy, S. Y. Kosulnikov, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Quarter-wavelength nanorod lens based on internal imaging,” Phys. Rev. B 85, 033105 (2012).
[CrossRef]

M. Silveirinha, C. A. Fernandes, and J. R. Costa, “Superlens made of a metamaterial with extreme effective parameters,” Phys. Rev. B 78, 195121 (2008).
[CrossRef]

M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Subwavelength imaging at infrared frequencies using an array of metallic nanorods,” Phys. Rev. B 75, 035108 (2007).
[CrossRef]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. A. 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, 193108 (2008).
[CrossRef]

E. K. Stone and E. Hendry, “Dispersion of spoof surface plasmons in open-ended metallic hole arrays,” Phys. Rev. B 84, 035418 (2011).
[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, 113103 (2003).
[CrossRef]

S. I. Maslovski and M. G. Silveirinha, “Nonlocal permittivity from a quasistatic model for a class of wire media,” Phys. Rev. B 80, 245101 (2009).
[CrossRef]

Phys. Rev. E

P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E 73, 056607 (2006).
[CrossRef]

Phys. Rev. Lett.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef]

F. Lemoult, G. Lerosey, J. Rosny, and M. Fink, “Resonant metalenses for breaking the diffraction barrier,” Phys. Rev. Lett. 104, 203901 (2010).
[CrossRef]

Science

J. Yao, Zh. Liu, Yo. Liu, Yu. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Waves Random Complex Media

F. Lemoult, M. Fink, and G. Lerosey, “Revisiting the wire medium: an ideal resonant metalens,” Waves Random Complex Media 21, 591–613 (2011).
[CrossRef]

Other

A. F. Alexandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Springer-Verlag, 1984).

A. N. Kondratenko, Plasma Waveguides (Atomizdat, 1976).

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Figures (4)

Fig. 1.
Fig. 1.

Waveguiding structure: a planar slab of WM of thickness a, cladded on both sides by a uniform dielectric with a constant permittivity εd. The WM consists of parallel perfectly conducting wires embedded into a uniform host medium with a dielectric permittivity εh.

Fig. 2.
Fig. 2.

Band structure of symmetric and antisymmetric guided TM modes in nonlocal [(a) (b) black curves for symmetric; red curves for antisymmetric modes] and local [(c) (d) black curves for symmetric; green curves for antisymmetric modes] WM slab models with εh=3, εd=1, for different slab thicknesses a˜=(ωh0/c)a: (a) (c) a˜=3 and (b) (d) a˜=7. The gray area corresponds to the leaky modes, Ω>Kz/εd. The dashed line Ω=1+Kz2/εh separates “fast” and “slow” guided modes, and the horizontal dotted line marks the lower boundary of the mode band gap Ω=1 in the local WM slab model.

Fig. 3.
Fig. 3.

Spatial structure of Ez(ω,kz)(x) of symmetric guided TM modes with Kz=2.0 in nonlocal WM slab model with εh=3 and εd=1 for slab thickness a˜=7. The upper (a) (b) and lower (c) (d) rows show the spatial structure of the two consecutive “slow” modes (with Ω<1+Kz2/εh) and the two consecutive “fast” modes (with Ω>1+Kz2/εh), respectively (see Fig. 2 for their band structure at Kz=2.0).

Fig. 4.
Fig. 4.

Band structure of the real (a) (b) and negative imaginary (c) (d) part of the eigenfrequencies for the case of low Im(εh)=0.1 (a) (c) and high Im(εh)=1.0 (b) (d) losses, for nonlocal WM slab with a˜=3, εd=1, Re(εh)=3.

Equations (47)

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εWM=ε0εh(εxx(ω,kx)x^x^+y^y^+z^z^)
εxx(ω,kx)=1ωh02ω2ch2kx2,
{E,B}={E(x),B(x)}ei(ωtkzz).
iωBx(ω,kz)=ikzEy(ω,kz),iωBy(ω,kz)=ikzEx(ω,kz)Ez(ω,kz)x,iωBz(ω,kz)=Ey(ω,kz)x,c2ε0ikzBy(ω,kz)=iωε0Ex(ω,kz)+jx(ω,kz),c2ε0ikzBx(ω,kz)c2ε0Bz(ω,kz)x=iωε0Ey(ω,kz)+jy(ω,kz),c2ε0By(ω,kz)x=iωε0Ez(ω,kz)+jz(ω,kz),
ikzEx(ω,kz)Ez(ω,kz)xiωBy(ω,kz)=0,c2ε0ikzBy(ω,kz)iωε0Ex(ω,kz)+jx(ω,kz)=0,c2ε0By(ω,kz)x+iωε0Ez(ω,kz)jz(ω,kz)=0.
Ez(ω,kz)(0)=iS1By(ω,kz)(0)+iS2By(ω,kz)(a),
Ez(ω,kz)(a)=iS2By(ω,kz)(0)+iS1By(ω,kz)(a),
S1=2c2ωεhan=0c2kz2ω2εhεxx(n)c2kz2ω2εhεxx(n)+c2αn2εxx(n),
S2=2c2ωεhan=0(1)n(c2kz2ω2εhεxx(n))c2kz2ω2εhεxx(n)+c2αn2εxx(n),
S1nl=cεhΩ1Kz2+εh[εh3/2Ωtan(a˜εh1/2Ω)+Kz2κxtanh(a˜κx)],
S2nl=cεhΩ1Kz2+εh[εh3/2Ωsin(a˜εh1/2Ω)+Kz2κxsinh(a˜κx)],
εxxl=1ωh02ω2.
S1l=cεhΩ21κxtanh(ΩΩ21a˜κx),
S2l=cεhΩ21κxsinh(ΩΩ21a˜κx),
Ezω,kz(0)=Ezω,kz(a);Byω,kz(0)=Byω,kz(a).
Ezω,kz(0)=Ezω,kz(a);Byω,kz(0)=Byω,kz(a).
ZWMs,as=ε0c2Ezω,kz(0)Byω,kz(0)=iε0c2(S1±S2),
Zd=iε0εdc3ΩKz2Ω2εd.
ZWMs,as+Zd=0,
symmetric:Kz2εdΩ2+εdεh1Kz2+εh[εh3/2Ωcot(εh1/2Ωa˜/2)+Kz2κxcoth(κxa˜/2)]=0,
antisymmetric:Kz2εdΩ2+εdεh1Kz2+εh[εh3/2Ωtan(εh1/2Ωa˜/2)+Kz2κxtanh(κxa˜/2)]=0.
symmetric:Kz=Ωεhcot2(εhΩa˜/2)+εh,
antisymmetric:Kz=Ωεhtan2(εhΩa˜/2)+εh.
symmetric:Kz2εdΩ2+εdεhΩΩ21κxcoth[κxa˜2ΩΩ21]=0,
antisymmetric:Kz2εdΩ2+εdεhΩΩ21κxtanh[κxa˜2ΩΩ21]=0.
Ω<Kz/εd
ωh02+c2kz2εh<ω<ckzεd
E1(n)=c2ωεhkzαnc2kz2ω2εhεxx(n)+c2αn2εxx(n)2c2a[By(ω,kz)(0)(1)nBy(ω,kz)(a)],
E3(n)=ic2ωεhc2kz2ω2εhεxx(n)c2kz2ω2εhεxx(n)+c2αn2εxx(n)2a[By(ω,kz)(0)(1)nBy(ω,kz)(a)],
B2(n)=αnεxx(n)c2kz2ω2εhεxx(n)+c2αn2εxx(n)2c2a[By(ω,kz)(0)(1)nBy(ω,kz)(a)],
Ex(ω,kz)(x)=Ex(ω,kz)(x)(odd),jx(ω,kz)(x)=jx(ω,kz)(x)(odd),Ez(ω,kz)(x)=Ez(ω,kz)(x)(even),jz(ω,kz)(x)=jz(ω,kz)(x)(even),By(ω,kz)(x)=By(ω,kz)(x)(odd),
Ex(ω,kz)(x)=n=0E1(n)sin(αnx),jx(ω,kz)(x)=n=0j1(n)sin(αnx),Ez(ω,kz)(x)=n=0E3(n)cos(αnx),jz(ω,kz)(x)=n=0j3(n)cos(αnx),By(ω,kz)(x)=n=0B2(n)sin(αnx),
ji(n)=k=13σik(n)Ek(n),
σik(n)=iωε0[δikεik(n)],
ikzE1(n)+αnE3(n)iωB2(n)=0,iωεhεxx(n)E1(n)+c2ikzB2(n)=0,iωεhE3(n)+c2αnB2(n)=2c2a[By(ω,kz)(0)(1)nBy(ω,kz)(a)].
E3(n)=ic2ωεh[c2kz2ω2εhεxx(n)]c2kz2ω2εhεxx(n)+c2αn2εxx(n)×2a[By(ω,kz)(0)(1)nBy(ω,kz)(a)].
[2Hzx2+εh(ωc)2Hz]x=0,a=0,
H(x)Hinc={eikxx+Reikxx,x<0ATMekpκxεh(xa/2)+A+TMe+kpκxεh(xa/2),0xa+ATEMeikpΩ(xa/2)+A+TEMeikpΩ(xa/2),Teikx(xa),x>a,
(1ekpκxεha/2ekpκxεha/2eikpaΩ/2eikpaΩ/20ikxkpκxεh3/2ekpκxεha/2kpκxεh3/2ekpκxεha/2ikpΩεheikpaΩ/2ikpΩεheikpaΩ/20kx2(ωc)2qekpκxεha/2qekpκxεha/20000ekpκxεha/2ekpκxεha/2eikpaΩ/2eikpaΩ/210kpκxεh3/2ekpκxεha/2kpκxεh3/2ekpκxεha/2ikpΩεheikpaΩ/2ikpΩεheikpaΩ/2ikx0qekpκxεha/2qekpκxεha/200kx2(ωc)2)×(RATMA+TMATEMA+TEMT)=(1ikxkx2+(ωc)2000),
T=d11d21,
R=d11+d211,
ATM=12(1+εhKz2)(sech(κxa˜/2)d1+csch(κxa˜/2)d2),
A+TM=12(1+εhKz2)(sech(κxa˜/2)d1csch(κxa˜/2)d2),
ATEM=d2sec(εh1/2Ωa˜/2)+id1cosec(εh1/2Ωa˜/2)2d1d2(1+Kz2εh),
A+TEM=d2sec(εh1/2Ωa˜/2)id1cosec(εh1/2Ωa˜/2)2d1d2(1+Kz2εh),
d1=1+1εh(Kz2+εh)Kz2Ω2×(εh3/2Ωtan(εh1/2Ωa˜/2)+Kz2κxtanh(κxa˜/2)),
d2=1+1εh(Kz2+εh)Kz2Ω2×(εh3/2Ωcot(εh1/2Ωa˜/2)+Kz2κxcoth(κxa˜/2)).

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