Abstract

Based on a modal expansion of electromagnetic fields, a rigorous method for analyzing surface plasmon polaritons (SPPs) on a periodically corrugated metal surface has been formulated in this paper. This method takes into account the finite conductivity of the metal as well as higher-order modes within the grooves of the surface structure, thus is able to accurately calculate the loss of these spoof SPPs propagating along the structured surface. In the terahertz (THz) frequency range, the properties of the dispersion and loss of spoof SPPs on corrugated Al surfaces are analyzed. For spoof SPPs at THz frequencies, the strong confinement of the fields is often accompanied with considerable absorption loss, but the performance of both low-loss propagation and subwavelength field confinement for spoof SPPs can be achieved by the optimum design of surface structure.

© 2008 Optical Society of America

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References

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  1. H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).
  2. H. E. Ponath and G. I. Stegeman eds., Nonlinear Surface Electromagnetic Phenomena (North-Holland, Amsterdam, 1991).
  3. V. M. Agranovich and D. L. Mills eds., Surface Polaritons (North-Holland, Amsterdam, 1982).
  4. A. V. Zayats and I. I. Smolyaninov, "Near-field photonics: surface plasmon polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
    [CrossRef]
  5. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  6. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Reports 408, 131-314 (2005).
    [CrossRef]
  7. S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M.W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
    [CrossRef] [PubMed]
  8. J. F. OHara, R. D. Averitt, and A. J. Taylor, "Terahertz surface plasmon polariton coupling on metallic gratings," Opt. Express 12, 6397-6402 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. 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, 176805-1-4 (2006).
    [CrossRef] [PubMed]
  13. Y. Chen, Z. Song, Y. Li, M. Hu, Q. Xing, Z. Zhang, L. Chai, and C. Y. Wang, "Effective surface plasmon polaritons on the metal wire with arrays of subwavelength grooves," Opt. Express 14, 13021-13029 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  16. D. R. Lide, CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, 2004).
  17. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976).
  18. M. Nagel, A. Marchewka, and H. Kurz, "Low-index discontinuity terahertz waveguides," Opt. Express 14, 9944-9954 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]

2006

2005

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]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Reports 408, 131-314 (2005).
[CrossRef]

2004

J. F. OHara, R. D. Averitt, and A. J. Taylor, "Terahertz surface plasmon polariton coupling on metallic gratings," Opt. Express 12, 6397-6402 (2004).
[CrossRef]

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

2003

A. V. Zayats and I. I. Smolyaninov, "Near-field photonics: surface plasmon polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[CrossRef]

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

2001

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M.W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Barnes, W. L.

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

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M.W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Chai, L.

Chen, Y.

Dereux, A.

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

Ebbesen, T. W.

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

Erland, J.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M.W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

Fang, H.

S. Q. Lou, T. Y. Guo, H. Fang, H. L. Li, and S. S. Jian, "A new type of terahertz waveguides," Chin. Phys. Lett. 23, 235-238 (2006).
[CrossRef]

Garcia-Vidal, F. J.

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]

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

Guo, T. Y.

S. Q. Lou, T. Y. Guo, H. Fang, H. L. Li, and S. S. Jian, "A new type of terahertz waveguides," Chin. Phys. Lett. 23, 235-238 (2006).
[CrossRef]

Hibbins, A. P.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

Hu, M.

Hvam, J. M.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M.W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Jian, S. S.

S. Q. Lou, T. Y. Guo, H. Fang, H. L. Li, and S. S. Jian, "A new type of terahertz waveguides," Chin. Phys. Lett. 23, 235-238 (2006).
[CrossRef]

Kurz, H.

Leosson, K.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M.W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Li, H. L.

S. Q. Lou, T. Y. Guo, H. Fang, H. L. Li, and S. S. Jian, "A new type of terahertz waveguides," Chin. Phys. Lett. 23, 235-238 (2006).
[CrossRef]

Li, Y.

Lou, S. Q.

S. Q. Lou, T. Y. Guo, H. Fang, H. L. Li, and S. S. Jian, "A new type of terahertz waveguides," Chin. Phys. Lett. 23, 235-238 (2006).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Reports 408, 131-314 (2005).
[CrossRef]

Marchewka, A.

Martin-Moreno, L.

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]

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

Nagel, M.

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, S97-S101 (2005).
[CrossRef]

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

Sambles, J. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

Skovgaard, P. M.W.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M.W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Reports 408, 131-314 (2005).
[CrossRef]

A. V. Zayats and I. I. Smolyaninov, "Near-field photonics: surface plasmon polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[CrossRef]

Song, Z.

Wang, C. Y.

Xing, Q.

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Reports 408, 131-314 (2005).
[CrossRef]

A. V. Zayats and I. I. Smolyaninov, "Near-field photonics: surface plasmon polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[CrossRef]

Zhang, Z.

Chin. Phys. Lett.

S. Q. Lou, T. Y. Guo, H. Fang, H. L. Li, and S. S. Jian, "A new type of terahertz waveguides," Chin. Phys. Lett. 23, 235-238 (2006).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

A. V. Zayats and I. I. Smolyaninov, "Near-field photonics: surface plasmon polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[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, S97-S101 (2005).
[CrossRef]

Nature

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

Opt. Express

Phys. Reports

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Reports 408, 131-314 (2005).
[CrossRef]

Phys. Rev. Lett.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M.W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Science

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

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

Other

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, 176805-1-4 (2006).
[CrossRef] [PubMed]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

D. R. Lide, CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, 2004).

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976).

J. Saxler, J. Gomez Rivas, C. Janke, H. P. M. Pellemans, P. Haring Bolivar, and H. Kurz, "Time-domain measurements of surface plasmon polaritons in the terahertz frequency range," Phys. Rev. B 69, 155427-1-4 (2004).
[CrossRef]

H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).

H. E. Ponath and G. I. Stegeman eds., Nonlinear Surface Electromagnetic Phenomena (North-Holland, Amsterdam, 1991).

V. M. Agranovich and D. L. Mills eds., Surface Polaritons (North-Holland, Amsterdam, 1982).

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Figures (5)

Fig. 1.
Fig. 1.

Convergence of the real (a) and imaginary (b) parts of the propagation constant β calculated from Eq. (12) for d=50 µm, h=50 µm, and f=0.8 THz. The corresponding results obtained within the PEC approximation are included as triangles for comparison. The inset shows the geometry of structured surface.

Fig. 2.
Fig. 2.

(a) Dispersion curves for spoof SPPs. (b) Attenuation coefficients of spoof SPPs. The lattice constant is d=50 µm. The solid and dashed lines correspond to the groove depths h=d and h=0.5d, respectively.

Fig. 3.
Fig. 3.

Spatial variation of the amplitude of the H field in a unit cell of the surface structure with d=50 µm, a=0.2d, and h=d. For clarity, different length scales are used in the z direction for z≤0 and z>0.

Fig. 4.
Fig. 4.

Dispersion relations (a) and attenuation coefficients (b) of spoof SPPs for different lattice constants d=35, 50, and 75 µm. The parameters of the groove geometry are a=10 µm and h=50 µm. Dotted lines indicate the asymptotic frequencies for three cases.

Fig. 5.
Fig. 5.

(a) Groove depth versus the groove width. (b) Parameter D versus the groove width for f=0.6 THz. Note that for each groove case in (a), the attenuation coefficient of spoof SPPs at f=0.6 THz is always equal to Im(β)=0.045 cm-1. (c)-(d) Spatial variation of the amplitude of the H field at f=0.6 THz for the cases with a=0.2d (h=d) and a=0.6d (h=0.6d), respectively. The lattice constant is d=50 µm.

Equations (12)

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H y I ( x , z ) = n A n ( 1 ) e q n ( 1 ) z e i β n x ,
H y III ( x , z ) = n A n ( 3 ) e q n ( 3 ) ( z + h ) e i β n x ,
H y II ( x , z ) = m [ A m ( 2 ) e gm ( z + h 2 ) + B m ( 2 ) e g m ( z + h 2 ) ] ψ m ( x ) ,
1 a d 2 d 2 1 ε ( x ) ψ m ψ n d x 1 a 1 ε ( x ) ψ m ψ n dx = N m δ mn ,
A m ( 2 ) e i g m h 2 B m ( 2 ) e i g m h 2 = i k 0 q 0 ( 1 ) m U mm [ A m ( 2 ) e i g m h 2 + B m ( 2 ) e i g m h 2 ] ,
A m ( 2 ) e i g m h 2 B m ( 2 ) e i g m h 2 = i ε m m V mm [ A m ( 2 ) e i g m h 2 + B m ( 2 ) e i g m h 2 ] ,
ζ m cot ( g m h 2 ) + i η m tan ( g m h 2 ) = k 0 q 0 ( 1 ) m U mm ( ζ m i η m ) ,
ζ m cot ( g m h 2 ) i η m tan ( g m h 2 ) = ε m m V mm ( ζ m + i η m ) ,
K 1 [ ζ ] + iK [ η ] = k 0 q 0 ( 1 ) U ( [ ζ ] i [ η ] ) ,
K 1 [ ζ ] iK [ η ] = ε m V ( [ ζ ] + i [ η ] ) ,
[ ζ ] + i [ η ] = 1 ε m V 1 ( K + K 1 ) [ ζ ] .
det { Q q 0 ( 1 ) k 0 I } = 0 ,

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