Abstract

The transmission through periodic arrays of subwavelength H-fractal apertures in a gold film at infrared wavelengths is investigated numerically. H-fractal apertures support subwavelength cut-off resonances that are hybridized with surface plasmons along the sidewalls of the aperture. Enhanced transmission occurs at wavelengths that are about ten times the aperture side length. The highly subwavelength size scale of the H-fractal enables an effective medium parameter description for the aperture array, which reveals a lossy plasma permittivity and a diamagnetic permeability.

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2009 (2)

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 1–25 (2009) (DOI ).
[CrossRef]

L. Lin, L. B. Hande, and A. Roberts, “Resonant nanometric cross-shaped apertures: Single apertures versus periodic arrays,” Appl. Phys. Lett. 95(20), 201116 (2009).
[CrossRef]

2008 (1)

2007 (5)

Y. Poujet, J. Salvi, and F. I. Baida, “90% Extraordinary optical transmission in the visible range through annular aperture metallic arrays,” Opt. Lett. 32(20), 2942–2944 (2007).
[CrossRef] [PubMed]

S. Collin, F. Pardo, and J. L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15(7), 4310–4320 (2007).
[CrossRef] [PubMed]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

C. Huang, Q. Wang, and Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
[CrossRef]

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76(19), 195414 (2007).
[CrossRef]

2006 (2)

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006).
[CrossRef] [PubMed]

L. Sun and L. Hesselink, “Low-loss subwavelength metal C-aperture waveguide,” Opt. Lett. 31(24), 3606–3608 (2006).
[CrossRef] [PubMed]

2005 (5)

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13(6), 1933–1938 (2005).
[CrossRef] [PubMed]

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72(8), 085436 (2005).
[CrossRef]

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwave through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[CrossRef]

K. J. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuiperts, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

2004 (2)

H. Cao and A. Nahata, “Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures,” Opt. Express 12(16), 3664–3672 (2004).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

2003 (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. 68, 065602 (2003).

2002 (1)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Agrawal, A.

Baida, F. I.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Brolo, A. G.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 1–25 (2009) (DOI ).
[CrossRef]

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13(6), 1933–1938 (2005).
[CrossRef] [PubMed]

Cao, H.

Catrysse, P. B.

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72(8), 085436 (2005).
[CrossRef]

Chan, C. T.

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwave through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[CrossRef]

Collin, S.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Enoch, S.

K. J. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuiperts, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005).
[CrossRef]

Fan, S.

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72(8), 085436 (2005).
[CrossRef]

Garcia-Vidal, F. J.

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76(19), 195414 (2007).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Gordon, R.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 1–25 (2009) (DOI ).
[CrossRef]

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13(6), 1933–1938 (2005).
[CrossRef] [PubMed]

Hande, L. B.

L. Lin, L. B. Hande, and A. Roberts, “Resonant nanometric cross-shaped apertures: Single apertures versus periodic arrays,” Appl. Phys. Lett. 95(20), 201116 (2009).
[CrossRef]

Hesselink, L.

Hou, B.

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwave through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[CrossRef]

Huang, C.

C. Huang, Q. Wang, and Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
[CrossRef]

Kavanagh, K. L.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 1–25 (2009) (DOI ).
[CrossRef]

Klein Koerkamp, K. J.

K. J. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuiperts, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005).
[CrossRef]

Koschny, T.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. 68, 065602 (2003).

Kuiperts, L.

K. J. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuiperts, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Lin, L.

L. Lin, L. B. Hande, and A. Roberts, “Resonant nanometric cross-shaped apertures: Single apertures versus periodic arrays,” Appl. Phys. Lett. 95(20), 201116 (2009).
[CrossRef]

Markos, P.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. 68, 065602 (2003).

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Martin-Moreno, L.

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76(19), 195414 (2007).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Mary, A.

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76(19), 195414 (2007).
[CrossRef]

Nahata, A.

Pardo, F.

Pelouard, J. L.

Pendry, J. B.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Poujet, Y.

Qiu, M.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006).
[CrossRef] [PubMed]

Roberts, A.

L. Lin, L. B. Hande, and A. Roberts, “Resonant nanometric cross-shaped apertures: Single apertures versus periodic arrays,” Appl. Phys. Lett. 95(20), 201116 (2009).
[CrossRef]

Rodrigo, S. G.

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76(19), 195414 (2007).
[CrossRef]

Ruan, Z.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006).
[CrossRef] [PubMed]

Salvi, J.

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Segerink, F. B.

K. J. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuiperts, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005).
[CrossRef]

Sheng, P.

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwave through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[CrossRef]

Shin, H.

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72(8), 085436 (2005).
[CrossRef]

Sinton, D.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 1–25 (2009) (DOI ).
[CrossRef]

Smith, D. R.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. 68, 065602 (2003).

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Soukoulis, C. M.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. 68, 065602 (2003).

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Sun, L.

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

van der Molen, K. J.

K. J. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuiperts, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005).
[CrossRef]

van Hulst, N. F.

K. J. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuiperts, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005).
[CrossRef]

Vardeny, Z. V.

Wang, Q.

C. Huang, Q. Wang, and Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
[CrossRef]

Wen, W.

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwave through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Zhou, L.

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwave through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[CrossRef]

Zhu, Y.

C. Huang, Q. Wang, and Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

L. Lin, L. B. Hande, and A. Roberts, “Resonant nanometric cross-shaped apertures: Single apertures versus periodic arrays,” Appl. Phys. Lett. 95(20), 201116 (2009).
[CrossRef]

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

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

Laser Photon. Rev. (1)

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole-arrays in metal films: physics and applications,” Laser Photon. Rev. 1–25 (2009) (DOI ).
[CrossRef]

Nature (3)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. (1)

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. 68, 065602 (2003).

Phys. Rev. B (6)

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72(8), 085436 (2005).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

K. J. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuiperts, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005).
[CrossRef]

W. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng, “Resonant transmission of microwave through subwavelength fractal slits in a metallic plate,” Phys. Rev. B 72(15), 153406 (2005).
[CrossRef]

C. Huang, Q. Wang, and Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
[CrossRef]

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76(19), 195414 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006).
[CrossRef] [PubMed]

Science (1)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Other (2)

E. D. Palik, Handbook of optical constants of solids (Academic Press, Orlando, FL, 1985).

D. H. Werner, and R. Mittra, Frontiers in Electromagnetics (IEEE Press, Piscataway, NJ, 2000), Chap. 2.

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Figures (5)

Fig. 1
Fig. 1

Schematic of a unit cell in a square lattice of H-fractal apertures. For our simulations, the central line length is d = 300 nm, the line width is w = 30 nm, and the lattice constant is a. For the fractal aperture of two orders, the side length is s = 480 nm.

Fig. 2
Fig. 2

(a) The transmission spectrum (solid line) of a 100 nm thick gold film with the H-fractal apertures (two scaling orders) with a = 600 nm at normal incidence and the transmission spectrum (dash line) of H-apertures without the second fractal order. (b) The magnitude of the normalized time-averaged Poynting vector at the transmission peak wavelength of 4.13 μm in the middle of the gold film. (c) The normalized magnitude of the electric field in the y-z plane through the center slit of the fractal aperture, where the normalization is taken with respect to the incident E-field.

Fig. 3
Fig. 3

The transmission of the gold film with the H-fractal apertures at normal incidence for (a) varying lattice constants, a=600, 800, 1000 nm, and (b) film thicknesses, h=100, 300, 600 nm.

Fig. 4
Fig. 4

(a) The ω-β relation for the aperture waveguide. The frequency is f = ω/2π, and β is the propagation constant along z and is normalized to the vacuum wavenumber k0 . The black solid and red dash lines are the real and the imaginary parts of β, respectively. The blue thick line is the real part of β for the PEC case. The inset is the ω-β relation for an EM wave in gold. (b) The magnitude of the normalized time-averaged Poynting vector of the waveguide mode at f = 64.5 THz for the real metal. (c) The normalized magnitude of Ez of the waveguide mode for the real metal. (d) The normalized magnitude of Ez of the waveguide mode for the PEC case.

Fig. 5
Fig. 5

(a) The complex reflection and transmission coefficients of the 600 nm thick metallic film with the fractal apertures at normal incidence. (b) The effective permittivity and permeability retrieved from the reflection and transmission coefficients. The black and red open squares are, respectively, the real and imaginary parts of the effective permittivity calculated from Eq. (2). The wavelength is normalized to the lattice constant a = 600nm.

Equations (2)

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ε m ( ω ) = ε b ω p 2 / ( ω 2 + i γ ω ) ,
ε x e f f = A [ 1 ( ω p e f f ) 2 / ( ω 2 + i γ e f f ω ) ] ,

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