Abstract

Photonic band structures of surface modes on structured metal surfaces with periodic holes in them are obtained using the full-vectorial finite-difference time-domain method. Surface modes do exist for almost all investigated lattice types with any hole size, shape and depth. The results for a square lattice of wax-filled box holes in brass are also in very good agreement with the experimental results. We also show that, for structured surfaces with holes of finite depth, the holes might act as cavities. Thus there exist propagating coupled cavity modes with low group velocity, confined at the surface and decaying exponentially into the dielectric above.

© 2005 Optical Society of America

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References

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Can. J. Phys. (1)

R. A. Hurd, �??The propagation of an Electromagnetic Wave along an Infinite Corrugated Surface,�?? Can. J. Phys. 32, 727�??734 (1954).
[CrossRef]

IRE Trans AP (1)

R. S. Elliott, �??On the theory of corrugated plane surfaces,�?? IRE Trans AP-2, 71�??81 (1954).

J. Appl. Phys. (1)

M. Qiu and S. He, �??A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,�?? J. Appl. Phys. 87, 8268�??8275 (2000).
[CrossRef]

J. Comput. Physics (1)

J. P. Berenger, �??Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves,�?? J. Comput. Physics 127, 363�??379 (1996).
[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, S97�??S101 (2005).
[CrossRef]

Nature (1)

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

Opt. Lett. (2)

Phys. Rev. B (2)

C. T. Chan, Q. L. Yu, and K. M. Ho, �??Order-N spectral method for electromagnetic waves,�?? Phys. Rev. B 51, 16635�??16642 (1995).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, �??Guided modes in photonic crystal slabs,�?? Phys. Rev. B 60, 5751�??5758 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

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] [PubMed]

Proc. IRE (1)

W. Rotman, �??A study of single surface corrugated guides,�?? Proc. IRE 39, 952�??959 (1951).
[CrossRef]

Science (2)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, �??Mimiching Surface Plasmons with Structured Surfaces,�?? Science 305, 847�??848 (2004).
[CrossRef] [PubMed]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, �??Experimental Verification of Designer Surface Plasmons,�?? Science 308, 670�??672 (2005).
[CrossRef] [PubMed]

Other (1)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House INC, Norwood, 2000).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic pictures of structured surfaces. The lattice constant (the distance between two neighboring holes) is d and the depth of the holes in the conductor is h. (a) A square lattice of square holes. The edge size of the square holes is a. (b) A square lattice of cylinder holes with a radius of R. (c) A triangular lattice of cylinder holes.

Fig. 2.
Fig. 2.

Photonic band structures for surface modes of a square lattice of square air holes in a perfect electric conductor (See Fig. 1(a)). The edge size of the square air holes is a = 0.875d. (a) Depth of the air holes is h = 1.0d. (b) Depth of the air holes is h = 4.0d. The red dashed line is the cut-off frequency of waveguide modes of air holes. The shaded grey region indicates the radiation modes in the air background, while the magenta region indicates the modes decay exponentially into air but are coupled to air-hole waveguide modes. The solid dots are obtained by the surface plasmon dispersion relation of Eq. 2.

Fig. 3.
Fig. 3.

The field cross sections of the surface mode at the X point (Fig. 2(a)) for (a) Ez at the PEC/air interface in the x - y plane, (b) Ez through the hole center in the x - z plane, and (c) Ex through the hole center in the x - z plane. Outlines of the holes are shown in black lines.

Fig. 4.
Fig. 4.

The Ex field cross sections of the modes at the M point in Fig. 1(b) through the hole center in the x - z plane. Outlines of the holes are shown in black lines. Only one of the degenerated modes is shown here. (a) (ωcd/2πc)=0.550. (b) (ωcd/2πc)=0.577. (c) (ωcd/2πc)=0.621. (d) (ωcd/2πc)=0.679.

Fig. 5.
Fig. 5.

The dispersion of the surface modes on the wax-filled brass tube array for light propagating along (a) the x-direction (ΓX) and (b) the y-direction (ΓX′). The red dashed line is the cut-off frequency. The circles are experimental results in Ref. [7]. At the X point, kx = π/d. At the Δ point, kx = π/2d. At the X′ point, ky = π/d. The shaded grey region indicates the radiation modes which can couple to modes in air.

Fig. 6.
Fig. 6.

Photonic band structures for surface modes of structured surfaces with air holes of (a) a square lattice and (b) a triangular lattice. The holes have a radius of R = 0.475d. The depth of the holes in the conductor is h = 1.0d.

Equations (2)

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ω c = πc a ε h μ h ,
k x 2 c 2 = ω 2 + 1 ω pl 2 ω 2 64 a 4 ω 4 π 4 d 4 ,

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