Abstract

The characteristics of the guided electromagnetic wave propagation through a subwavelength hole surrounded by a doubly dispersive metamaterial are investigated. Characteristic equations are derived for the surface polariton modes related to the subwavelength hole and mode classifications established. The surface polariton modes for two different hole-radii are numerically obtained and their electromagnetic dispersion curves and power flux characteristics analyzed and compared with each other. In particular, it was found that the border of the counter-propagation between the forward and backward Poynting vectors was located within the metamaterial, rather than at the interface between the metamaterial and the free space.

© 2005 Optical Society of America

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IEEE Ant. Wireless Prop. Lett. (1)

P. Baccarelli, P. Burghignoli, G. Lovat, and S. Paulotto, �??Surface-wave suppression in a double-negative metamaterial grounded slab,�?? IEEE Ant. Wireless Prop. Lett. 2, 269-272 (2003).
[CrossRef]

IEEE Trans. Ant. Prop. (1)

V. L .Granatstein, S. P. Schlesinger, and A. Vigants, �??The open plasmaguide in extreme of magnetic field,�?? IEEE Trans. Ant. Prop. 11, 489-496 (1963).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

T. Tamir and S. Palócz, �??Surface waves on plasma-clad metal rods,�?? IEEE Trans. Microwave Theory Tech. 12, 189-196 (1964).
[CrossRef]

J. Appl. Phys. (2)

A. A. Oliner and T. Tamir, �??Backward waves on isotropic plasma slabs,�?? J. Appl. Phys. 33, 231-233 (1962)
[CrossRef]

B. �??I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, �??Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability,�?? J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

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

A. V. Novitsky and L. M. Barkovsky, �??Guided modes in negative-refractive-index fibres,�?? J. Opt. A: Pure Appl. Opt 7, S51-S56 (2005).
[CrossRef]

J. Phys.: Condens. Matter (1)

R. Ruppin, �??Surface polaritons of a left-handed material slab,�?? J. Phys.: Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

Microwave Opt. Tech. Lett. (4)

H. Dong and T. X. Wu, �??Analysis of discontinuities in double-negative (DNG) slab waveguides,�?? Microwave Opt. Tech. Lett. 39, 483-488 (2003).
[CrossRef]

H. Cory and A. Barger, �??Surface-wave propagation along a metamaterial slab,�?? Microwave Opt. Tech. Lett. 38, 392-395 (2003).
[CrossRef]

H. Cory and T. Blum, "Surface-wave propagation along a metamaterial cylindrical guide", Microwave Opt. Tech. Lett. 44, 31-35 (2005).
[CrossRef]

M. M. B. Suwailiam, Z. Chen, �??Surface waves on a grounded double-negative (DNG) slab waveguide,�?? Microwave Opt. Tech. Lett. 44, 494-498 (2005).
[CrossRef]

Opt. Commun. (2)

A. Degiron, H. J. Lezec, N. Yammamoto, and T. W. Ebbesen, �??Optical transmission properties of a single subwavelnegth aperture in a real metal,�?? Opt. Commun. 239, 61-64 (2004).
[CrossRef]

N. Bonod, E. Popov, and M. Nevière, �??Light transmission through a subwavelength microstructured aperture: electromagnetic theory and applications,�?? Opt. Commun. 245, 355-361 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys Rev E (1)

J. Schelleng, C. Monzon, P. F. Loschialpo, D. W. Forester, and L. N. Medgye-Mitschang, �??Characteristics of waves guided by a grounded �??left-handed�?? material slab of finite extent,�?? Phys Rev E 70, 066606 (2004).
[CrossRef]

Phys. Lett. A (1)

R. Ruppin, �??Surface polaritons of a left-handed medium,�?? Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

Phys. Rev. E (2)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, �??Guided modes in negative-refractive-index waveguides,�?? Phys. Rev. E 67, 057602 (2003).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, �??Nonlinear surface waves in left-handed materials,�?? Phys. Rev. E 69, 016617 (2004)
[CrossRef]

Phys. Rev. Lett. (4)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, �??Composite medium with simultaneously negative permeability and permittivity,�?? Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, �??Terahertz response of a microfabricated rodsplit- ring-resonator electromagnetic metamaterial,�?? Phys. Rev. Lett. 94, 063901 (2005).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, �??Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,�?? Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, �??Multiple paths to enhance optical transmission through a single subwavelength slit,�?? Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

Phys. Solid State (1)

A. V. Klyuchnik, S. Y. Kurganov, and Y. E. Lozovik, �??Plasma optics of nanostructures,�?? Phys. Solid State 45, 1327-1331 (2003).
[CrossRef]

Radio Sci. (1)

A. Safaai-Jazi and G. L .Yip, �??Classification of hybrid modes in cylindrical dielectric optical waveguides,�?? Radio Sci. 12, 603-609 (1977).
[CrossRef]

Science (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, �??Beaming light from a subwavelength aperture,�?? Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

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

Other (2)

K. Y. Kim, "Guided and Leaky Modes of Circular Open Electromagnetic Waveguides: Dielectric, Plasma, and Metamaterial Columns", Ph.D. Thesis, Kyungpook National University, (2004), <a href="http://palgong.knu.ac.kr/~doors/PDFs/PhDThesis.pdf">http://palgong.knu.ac.kr/~doors/PDFs/PhDThesis.pdf</a>

H. Raether, "Surface Plasmons on Smooth and Rough Surfaces and on Gratings", (Springer-Verlag, 1988).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic view of subwavelength DDMTM hole with diameter D=2a in cylindrical coordinate system. The inner and outer regions are the free space (region 1) and DDMTM (region 2), respectively.

Fig. 2.
Fig. 2.

Material constants of DDMTM. The DNG and ENG regions are from 4 to 6 GHz and 6 to 10 GHz, respectively.

Fig. 3.
Fig. 3.

Allowed SP mode region of DDMTM hole for DNG and SNG cases. (a) DNG with μ r 2 ε r 2 > μ r 1 ε r 1 , (b) DNG with μ r 1 ε r 1 > μ r 2 ε r 2 , and (c) SNG (ENG or MNG).

Fig. 4.
Fig. 4.

TE-like modes of DDMTM hole with D=20.0 mm. (a) Dispersion curves and (b) normalized power flux. Corresponding operating wave numbers are also shown.

Fig. 5.
Fig. 5.

TE-like modes of DDMTM hole with D=2.0 mm. (a) Dispersion curves and (b) normalized power flux. Insets are enlarged scales. Corresponding operating wave numbers are also shown.

Fig. 6.
Fig. 6.

TM-like modes of DDMTM hole with D=20.0 mm. (a) Dispersion curves and (b) normalized power flux. Corresponding operating wave numbers are also shown.

Fig. 7.
Fig. 7.

TM-like modes of DDMTM hole with D=2.0 mm. (a) Dispersion curves and (b) normalized power flux. The inset in (b) is an enlarged scale of the normalized power flux for the HE11 mode. At 7.32 GHz (point b), η=0. Points a, b, c, d, e, and f indicate the positions of the plots of the Ponyting vectors S z1 and S z2 in Fig. 8.

Fig. 8.
Fig. 8.

Spatial power distributions of Poynting vectors Sz1 and Sz2. Amplitude is an arbitrary unit.

Equations (9)

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ε r 2 ( ω ) = 1 ω p 2 ω 2
μ r 2 ( ω ) = 1 F ω 2 ω 2 ω 0 2
[ ε r 1 k 1 I m ( k 1 a ) I m ( k 1 a ) ε r 2 k 2 K m ( k 2 a ) K m ( k 2 a ) ] [ μ r 1 k 1 I m ( k 1 a ) I m ( k 1 a ) μ r 2 k 2 K m ( k 2 a ) K m ( k 2 a ) ] = [ m β k 0 a ( 1 k 1 2 1 k 2 2 ) ] 2 .
ε r 1 k 1 I 1 ( k 1 a ) I 0 ( k 1 a ) + ε r 2 k 2 K 1 ( k 2 a ) K 0 ( k 2 a ) = 0
μ r 1 k 1 I 1 ( k 1 a ) I 0 ( k 1 a ) + μ r 2 k 2 K 1 ( k 2 a ) K 0 ( k 2 a ) = 0 .
( μ r 2 μ r 1 + ε r 2 ε r 1 ) Q 2 ± { ( μ r 2 μ r 1 + ε r 2 ε r 1 ) Q 2 } 2 + R μ r 1 ε r 1 P = 0
P = 1 k 1 a ( I m 1 ( k 1 a ) I m ( k 1 a ) m k 1 a )
Q = 1 k 2 a ( K m 1 ( k 2 a ) K m ( k 2 a ) + m k 2 a )
R = { m β k 0 a 2 ( 1 k 1 2 1 k 2 2 ) } 2 .

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