Abstract

Metallic photonic crystals have gaps starting from the null frequency. They can be used as antenna substrates. Using two computer codes based on rigorous scattering theories, we investigate the properties of nondoped and doped two-dimensional metallic photonic crystals. We show numerically that such a structure can simulate a material that has a plasmon frequency in the microwave domain. Below this frequency the crystal is opaque and acts as a good reflector. These calculations confirm both a conjecture made by specialists in solid-state physics and mathematical considerations developed by specialists in limit analysis.

© 1998 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [Crossref] [PubMed]
  3. J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  4. J. Rarity and C. Weisbuch, eds., Microcavities and Photonic Bandgaps: Physics and Applications, Vol. 324 of NATO Advanced Study Institute Series E (Kluwer, Dordrecht, The Netherlands, 1996).
  5. D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994).
    [Crossref]
  6. C. Soukoulis, Photonic Band Gaps and Localization (Plenum, New York, 1993).
  7. G. Kurizki and J. W. Haus, eds., special issue on photonic band structures, J. Mod. Opt.41, 173–404 (1994).
    [Crossref]
  8. P. R. Bunker and T. J. Sears, feature on development and applications of materials exhibiting photonic band gaps, J. Opt. Soc. Am. B 10, 171–413 (1993).
    [Crossref]
  9. G. Tayeb and D. Maystre, “Rigorous theoretical study of finite size two-dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A 14, 3323–3332 (1997).
    [Crossref]
  10. E. Ozbay, B. Temelkuran, M. Sigalas, G. Tuttle, C. Soukoulis, and K. Ho, “Defect structures in metallic photonic crystals,” Appl. Phys. Lett. 69, 3797–3799 (1996).
    [Crossref]
  11. S. Cheng, R. Biswas, E. Ozbay, J. McCalmont, G. Tuttle, and K. Ho, “Optimized dipole antennas on photonic band gap crystal,” Appl. Phys. Lett. 67, 3399–3401 (1995).
    [Crossref]
  12. E. Brown and O. McMahon, “High zenithal directivity from a dipole antenna on a photonic crystal,” Appl. Phys. Lett. 68, 1300–1302 (1996).
    [Crossref]
  13. C. Maggiore, A. Clogston, G. Spalek, W. Sailor, and F. Mueller, “Low-loss microwave cavity using layered-dielectric materials,” Appl. Phys. Lett. 64, 1451–1453 (1994).
    [Crossref]
  14. D. Smith, S. Schultz, N. Kroll, M. Sigalas, K. Ho, and C. Soukoulis, “Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity,” Appl. Phys. Lett. 65, 645–647 (1994).
    [Crossref]
  15. E. Brown and O. McMahon, “Large electromagnetic stop bands in metallodielectric photonic crystal,” Appl. Phys. Lett. 67, 2138–2140 (1995).
    [Crossref]
  16. D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526–2538 (1994).
    [Crossref]
  17. J. B. Pendry, “Calculating photonic band structure,” J. Phys. Condens. Matter 8, 1085–1108 (1996).
    [Crossref]
  18. D. Felbacq, “Etude théorique et numérique de la diffraction de la lumierè par des ensembles de tiges parallèles,” Ph.D. dissertation (Faculté St Jérôme, Marseille, France, 1994).
  19. D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibers,” Waves Random Media 7, 245–256 (1997).
    [Crossref]
  20. D. Maystre and R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196–200 (1976).
    [Crossref]
  21. M. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
    [Crossref]
  22. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
    [Crossref] [PubMed]

1997 (2)

1996 (4)

J. B. Pendry, “Calculating photonic band structure,” J. Phys. Condens. Matter 8, 1085–1108 (1996).
[Crossref]

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

E. Ozbay, B. Temelkuran, M. Sigalas, G. Tuttle, C. Soukoulis, and K. Ho, “Defect structures in metallic photonic crystals,” Appl. Phys. Lett. 69, 3797–3799 (1996).
[Crossref]

E. Brown and O. McMahon, “High zenithal directivity from a dipole antenna on a photonic crystal,” Appl. Phys. Lett. 68, 1300–1302 (1996).
[Crossref]

1995 (2)

S. Cheng, R. Biswas, E. Ozbay, J. McCalmont, G. Tuttle, and K. Ho, “Optimized dipole antennas on photonic band gap crystal,” Appl. Phys. Lett. 67, 3399–3401 (1995).
[Crossref]

E. Brown and O. McMahon, “Large electromagnetic stop bands in metallodielectric photonic crystal,” Appl. Phys. Lett. 67, 2138–2140 (1995).
[Crossref]

1994 (4)

D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526–2538 (1994).
[Crossref]

C. Maggiore, A. Clogston, G. Spalek, W. Sailor, and F. Mueller, “Low-loss microwave cavity using layered-dielectric materials,” Appl. Phys. Lett. 64, 1451–1453 (1994).
[Crossref]

D. Smith, S. Schultz, N. Kroll, M. Sigalas, K. Ho, and C. Soukoulis, “Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity,” Appl. Phys. Lett. 65, 645–647 (1994).
[Crossref]

D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994).
[Crossref]

1993 (1)

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

1976 (2)

D. Maystre and R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196–200 (1976).
[Crossref]

M. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[Crossref]

Biswas, R.

S. Cheng, R. Biswas, E. Ozbay, J. McCalmont, G. Tuttle, and K. Ho, “Optimized dipole antennas on photonic band gap crystal,” Appl. Phys. Lett. 67, 3399–3401 (1995).
[Crossref]

Bouchitté, G.

D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibers,” Waves Random Media 7, 245–256 (1997).
[Crossref]

Brown, E.

E. Brown and O. McMahon, “High zenithal directivity from a dipole antenna on a photonic crystal,” Appl. Phys. Lett. 68, 1300–1302 (1996).
[Crossref]

E. Brown and O. McMahon, “Large electromagnetic stop bands in metallodielectric photonic crystal,” Appl. Phys. Lett. 67, 2138–2140 (1995).
[Crossref]

Bunker, P. R.

Cheng, S.

S. Cheng, R. Biswas, E. Ozbay, J. McCalmont, G. Tuttle, and K. Ho, “Optimized dipole antennas on photonic band gap crystal,” Appl. Phys. Lett. 67, 3399–3401 (1995).
[Crossref]

Clogston, A.

C. Maggiore, A. Clogston, G. Spalek, W. Sailor, and F. Mueller, “Low-loss microwave cavity using layered-dielectric materials,” Appl. Phys. Lett. 64, 1451–1453 (1994).
[Crossref]

Felbacq, D.

D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibers,” Waves Random Media 7, 245–256 (1997).
[Crossref]

D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526–2538 (1994).
[Crossref]

D. Felbacq, “Etude théorique et numérique de la diffraction de la lumierè par des ensembles de tiges parallèles,” Ph.D. dissertation (Faculté St Jérôme, Marseille, France, 1994).

Ho, K.

E. Ozbay, B. Temelkuran, M. Sigalas, G. Tuttle, C. Soukoulis, and K. Ho, “Defect structures in metallic photonic crystals,” Appl. Phys. Lett. 69, 3797–3799 (1996).
[Crossref]

S. Cheng, R. Biswas, E. Ozbay, J. McCalmont, G. Tuttle, and K. Ho, “Optimized dipole antennas on photonic band gap crystal,” Appl. Phys. Lett. 67, 3399–3401 (1995).
[Crossref]

D. Smith, S. Schultz, N. Kroll, M. Sigalas, K. Ho, and C. Soukoulis, “Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity,” Appl. Phys. Lett. 65, 645–647 (1994).
[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, 4773–4776 (1996).
[Crossref] [PubMed]

Hutley, M.

M. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[Crossref]

Joannopoulos, J.

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

Kroll, N.

D. Smith, S. Schultz, N. Kroll, M. Sigalas, K. Ho, and C. Soukoulis, “Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity,” Appl. Phys. Lett. 65, 645–647 (1994).
[Crossref]

Maggiore, C.

C. Maggiore, A. Clogston, G. Spalek, W. Sailor, and F. Mueller, “Low-loss microwave cavity using layered-dielectric materials,” Appl. Phys. Lett. 64, 1451–1453 (1994).
[Crossref]

Maystre, D.

G. Tayeb and D. Maystre, “Rigorous theoretical study of finite size two-dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A 14, 3323–3332 (1997).
[Crossref]

D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526–2538 (1994).
[Crossref]

D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994).
[Crossref]

M. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[Crossref]

D. Maystre and R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196–200 (1976).
[Crossref]

McCalmont, J.

S. Cheng, R. Biswas, E. Ozbay, J. McCalmont, G. Tuttle, and K. Ho, “Optimized dipole antennas on photonic band gap crystal,” Appl. Phys. Lett. 67, 3399–3401 (1995).
[Crossref]

McMahon, O.

E. Brown and O. McMahon, “High zenithal directivity from a dipole antenna on a photonic crystal,” Appl. Phys. Lett. 68, 1300–1302 (1996).
[Crossref]

E. Brown and O. McMahon, “Large electromagnetic stop bands in metallodielectric photonic crystal,” Appl. Phys. Lett. 67, 2138–2140 (1995).
[Crossref]

Meade, R.

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Mueller, F.

C. Maggiore, A. Clogston, G. Spalek, W. Sailor, and F. Mueller, “Low-loss microwave cavity using layered-dielectric materials,” Appl. Phys. Lett. 64, 1451–1453 (1994).
[Crossref]

Ozbay, E.

E. Ozbay, B. Temelkuran, M. Sigalas, G. Tuttle, C. Soukoulis, and K. Ho, “Defect structures in metallic photonic crystals,” Appl. Phys. Lett. 69, 3797–3799 (1996).
[Crossref]

S. Cheng, R. Biswas, E. Ozbay, J. McCalmont, G. Tuttle, and K. Ho, “Optimized dipole antennas on photonic band gap crystal,” Appl. Phys. Lett. 67, 3399–3401 (1995).
[Crossref]

Pendry, J. B.

J. B. Pendry, “Calculating photonic band structure,” J. Phys. Condens. Matter 8, 1085–1108 (1996).
[Crossref]

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

Petit, R.

D. Maystre and R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196–200 (1976).
[Crossref]

Sailor, W.

C. Maggiore, A. Clogston, G. Spalek, W. Sailor, and F. Mueller, “Low-loss microwave cavity using layered-dielectric materials,” Appl. Phys. Lett. 64, 1451–1453 (1994).
[Crossref]

Schultz, S.

D. Smith, S. Schultz, N. Kroll, M. Sigalas, K. Ho, and C. Soukoulis, “Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity,” Appl. Phys. Lett. 65, 645–647 (1994).
[Crossref]

Sears, T. J.

Sigalas, M.

E. Ozbay, B. Temelkuran, M. Sigalas, G. Tuttle, C. Soukoulis, and K. Ho, “Defect structures in metallic photonic crystals,” Appl. Phys. Lett. 69, 3797–3799 (1996).
[Crossref]

D. Smith, S. Schultz, N. Kroll, M. Sigalas, K. Ho, and C. Soukoulis, “Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity,” Appl. Phys. Lett. 65, 645–647 (1994).
[Crossref]

Smith, D.

D. Smith, S. Schultz, N. Kroll, M. Sigalas, K. Ho, and C. Soukoulis, “Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity,” Appl. Phys. Lett. 65, 645–647 (1994).
[Crossref]

Soukoulis, C.

E. Ozbay, B. Temelkuran, M. Sigalas, G. Tuttle, C. Soukoulis, and K. Ho, “Defect structures in metallic photonic crystals,” Appl. Phys. Lett. 69, 3797–3799 (1996).
[Crossref]

D. Smith, S. Schultz, N. Kroll, M. Sigalas, K. Ho, and C. Soukoulis, “Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity,” Appl. Phys. Lett. 65, 645–647 (1994).
[Crossref]

C. Soukoulis, Photonic Band Gaps and Localization (Plenum, New York, 1993).

Spalek, G.

C. Maggiore, A. Clogston, G. Spalek, W. Sailor, and F. Mueller, “Low-loss microwave cavity using layered-dielectric materials,” Appl. Phys. Lett. 64, 1451–1453 (1994).
[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, 4773–4776 (1996).
[Crossref] [PubMed]

Tayeb, G.

Temelkuran, B.

E. Ozbay, B. Temelkuran, M. Sigalas, G. Tuttle, C. Soukoulis, and K. Ho, “Defect structures in metallic photonic crystals,” Appl. Phys. Lett. 69, 3797–3799 (1996).
[Crossref]

Tuttle, G.

E. Ozbay, B. Temelkuran, M. Sigalas, G. Tuttle, C. Soukoulis, and K. Ho, “Defect structures in metallic photonic crystals,” Appl. Phys. Lett. 69, 3797–3799 (1996).
[Crossref]

S. Cheng, R. Biswas, E. Ozbay, J. McCalmont, G. Tuttle, and K. Ho, “Optimized dipole antennas on photonic band gap crystal,” Appl. Phys. Lett. 67, 3399–3401 (1995).
[Crossref]

Winn, J.

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

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, 4773–4776 (1996).
[Crossref] [PubMed]

Appl. Phys. Lett. (6)

E. Ozbay, B. Temelkuran, M. Sigalas, G. Tuttle, C. Soukoulis, and K. Ho, “Defect structures in metallic photonic crystals,” Appl. Phys. Lett. 69, 3797–3799 (1996).
[Crossref]

S. Cheng, R. Biswas, E. Ozbay, J. McCalmont, G. Tuttle, and K. Ho, “Optimized dipole antennas on photonic band gap crystal,” Appl. Phys. Lett. 67, 3399–3401 (1995).
[Crossref]

E. Brown and O. McMahon, “High zenithal directivity from a dipole antenna on a photonic crystal,” Appl. Phys. Lett. 68, 1300–1302 (1996).
[Crossref]

C. Maggiore, A. Clogston, G. Spalek, W. Sailor, and F. Mueller, “Low-loss microwave cavity using layered-dielectric materials,” Appl. Phys. Lett. 64, 1451–1453 (1994).
[Crossref]

D. Smith, S. Schultz, N. Kroll, M. Sigalas, K. Ho, and C. Soukoulis, “Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity,” Appl. Phys. Lett. 65, 645–647 (1994).
[Crossref]

E. Brown and O. McMahon, “Large electromagnetic stop bands in metallodielectric photonic crystal,” Appl. Phys. Lett. 67, 2138–2140 (1995).
[Crossref]

J. Opt. Soc. Am. A (2)

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

J. Phys. Condens. Matter (1)

J. B. Pendry, “Calculating photonic band structure,” J. Phys. Condens. Matter 8, 1085–1108 (1996).
[Crossref]

Opt. Commun. (2)

D. Maystre and R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196–200 (1976).
[Crossref]

M. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[Crossref]

Phys. Rev. Lett. (3)

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

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

Pure Appl. Opt. (1)

D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994).
[Crossref]

Waves Random Media (1)

D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibers,” Waves Random Media 7, 245–256 (1997).
[Crossref]

Other (5)

C. Soukoulis, Photonic Band Gaps and Localization (Plenum, New York, 1993).

G. Kurizki and J. W. Haus, eds., special issue on photonic band structures, J. Mod. Opt.41, 173–404 (1994).
[Crossref]

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

J. Rarity and C. Weisbuch, eds., Microcavities and Photonic Bandgaps: Physics and Applications, Vol. 324 of NATO Advanced Study Institute Series E (Kluwer, Dordrecht, The Netherlands, 1996).

D. Felbacq, “Etude théorique et numérique de la diffraction de la lumierè par des ensembles de tiges parallèles,” Ph.D. dissertation (Faculté St Jérôme, Marseille, France, 1994).

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Figures (19)

Fig. 1
Fig. 1

2D metallic photonic crystal represented by a grating model with Ng=3. The grids are infinite along the x and z directions.

Fig. 2
Fig. 2

Transmission factor of a metallic photonic crystal made by perfectly conducting wires of radius r=0.01d illuminated in normal incidence.

Fig. 3
Fig. 3

Same as Fig. 2 but for r=0.001d.

Fig. 4
Fig. 4

Layout of the photonic crystal and the equivalent homogeneous layer.

Fig. 5
Fig. 5

Permittivity of the homogeneous material equivalent to a metallic photonic crystal with rods of radius r=10-2 illuminated with normal incidence. Solid curves, numerical result; dashed curves, theoretical result of Eq. (1).

Fig. 6
Fig. 6

Same as Fig. 5 but for interface shifts su (solid curves) and sl (dashed curves).

Fig. 7
Fig. 7

Permittivity of the homogeneous material equivalent to a metallic photonic crystal with radius r=0.01 made with Ng=3 grids, for three values of incidence angle α (in degrees). Solid curves, numerical result, dashed curves, theoretical result obtained from Eqs. (1) and (2).

Fig. 8
Fig. 8

Same as Fig. 7 but for interfaces su (solid curves) and sl (dashed curves).

Fig. 9
Fig. 9

Same parameters as in Fig. 5 but with r=0.001.

Fig. 10
Fig. 10

Same parameters as in Fig. 6 but with r=0.001. The solid and dashed curves are superposable.

Fig. 11
Fig. 11

Same parameters as in Fig. 7 but with r=0.001.

Fig. 12
Fig. 12

Same parameters as in Fig. 8 but with r=0.001.

Fig. 13
Fig. 13

2D crystal with 9×9 wires (d=1, r=0.01). Here five central wires have been removed. The line below the crystal is the one used for the computation of the transmission factor.

Fig. 14
Fig. 14

Transmission factor versus wavelength for the crystal of Fig. 13. Solid curve, no defect; dotted and dashed curves, central wires removed as shown.

Fig. 15
Fig. 15

Maps of the modulus of the total field for the crystal of Fig. 13 (nine central wires have been removed) illuminated with a plane wave at λ=6.7 (upper map) and λ=4.45 (lower map).

Fig. 16
Fig. 16

Positions of the 37 wires used to illustrate the homogenization of a 2D finite crystal. The crystal is illuminated by a plane wave coming from the top. Wire spacing, d=1; wire radius, r=10-2.

Fig. 17
Fig. 17

Permittivity of a homogeneous rod equivalent to the 37 wires of Fig. 16. Solid curve, numerical result; dashed curve, the theoretical permittivity given by Eqs. (1) and (2).

Fig. 18
Fig. 18

Maps of the modulus of the total field for the set of 37 wires (upper map) and the homogenized rod (lower map) illuminated by a plane wave with λ=4 coming from the top. White circle, actual dimension of the homogenized rod.

Fig. 19
Fig. 19

Same as Fig. 18 but for λ=10.

Equations (6)

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

h=1-ωp2ω2=1-λ2λp2,
ωp=cd 2πln(d/2r)1/2,
λp=2πcωp=d[2π ln(d/2r)]1/2.
|r|2+|t|2=1,
su=yu,
sl=-(Ng-1)d-yl.

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