Abstract

A detailed study of guided modes in a nanoscale metallic rectangular waveguide is presented by using the effective dielectric constant approach. The guided modes, including both traditional waveguide mode and surface plasmon mode, are investigated for the silver rectangular waveguide. The mode evolution in narrow waveguide is also discussed with the emphasis on the dependence of mode dispersion with waveguide height. Finally, the red-shift of the cutoff wavelength of the fundamental mode is observed when the waveguide height decreases, contrary to the behavior of regular metallic waveguide with PEC boundary. The comprehensive analysis can provide some guideline in the design of subwavelength optical devices based on the dispersion characteristics of metallic rectangular bore.

© 2007 Optical Society of America

Full Article  |  PDF Article
Related Articles
Light transmission along dispersive plasmonic gap and its subwavelength guidance characteristics

Ki Young Kim, Young Ki Cho, Heung-Sik Tae, and Jeong-Hae Lee
Opt. Express 14(1) 320-330 (2006)

Waveguiding in nanoscale metallic apertures

Stéphane Collin, Fabrice Pardo, and Jean-Luc Pelouard
Opt. Express 15(7) 4310-4320 (2007)

Feasibility study of nanoscaled optical waveguide based on near-resonant surface plasmon polariton

Min Yan, Lars Thylén, Min Qiu, and Devang Parekh
Opt. Express 16(10) 7499-7507 (2008)

References

  • View by:
  • |
  • |
  • |

  1. P. N. Prasad, Nanophotonics (Wiley-Interscience, New Jersey, 2004).
    [Crossref]
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [Crossref] [PubMed]
  3. T. Rindzevicius, Y. Alaverdyan, and B. Sepulveda. “Nanohole plasmons in optically thin gold films,” J. Phys. Chem. C 111, 1207–1212(2007).
    [Crossref]
  4. F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
    [Crossref]
  5. C. K. Chang, D. Z. Lin, and C. S. Yeh, et. al., “Experimental analysis of surface plasmon behavior in metallic circular slits,” Appl. Phys. Lett. 90, 061113 (2007).
    [Crossref]
  6. K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
    [Crossref]
  7. A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
    [Crossref]
  8. R. Gordon, L. K. S. Kumar, and A. G. Brolo, “Resonant light transmission through a nanohole in a metal film,” IEEE Nanotechnology 5, 291–294 (2006).
    [Crossref]
  9. F. M. Kong, K. Li, and B. I. Wu, et. al., “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromagn. Res. 76, 449–466 (2007)
    [Crossref]
  10. E. X. Jin and X. Xu, “Finite-difference time-domain studies on optical transmission through planar nano-apertures in a metal Film,” Jpn. J. Appl. Phys. 43, 407–417(2004).
    [Crossref]
  11. K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis (Wiley, Chichester, 2001).
    [Crossref]
  12. S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon polaritons,” Opt. Express 14, 9467–9476 (2006).
    [Crossref] [PubMed]
  13. S. Collin, F. Pardo, and J. L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15, 4310–4320(2007).
    [Crossref] [PubMed]
  14. Y. Satuby and M. Orenstein, “Surface-plasmon-polariton modes in deep metallic trenches-measurement and analysis,” Opt. Express 15, 4247–4252 (2007).
    [Crossref] [PubMed]
  15. 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 (2003).
    [Crossref]
  16. C. Sönnichsen, “Plasmons in metal nanostructures,” PhD Thesis (Ludwig-Maximilians-Universtät München, München, 2001).
  17. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379, (1972).
    [Crossref]

2007 (5)

T. Rindzevicius, Y. Alaverdyan, and B. Sepulveda. “Nanohole plasmons in optically thin gold films,” J. Phys. Chem. C 111, 1207–1212(2007).
[Crossref]

C. K. Chang, D. Z. Lin, and C. S. Yeh, et. al., “Experimental analysis of surface plasmon behavior in metallic circular slits,” Appl. Phys. Lett. 90, 061113 (2007).
[Crossref]

F. M. Kong, K. Li, and B. I. Wu, et. al., “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromagn. Res. 76, 449–466 (2007)
[Crossref]

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

Y. Satuby and M. Orenstein, “Surface-plasmon-polariton modes in deep metallic trenches-measurement and analysis,” Opt. Express 15, 4247–4252 (2007).
[Crossref] [PubMed]

2006 (4)

S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon polaritons,” Opt. Express 14, 9467–9476 (2006).
[Crossref] [PubMed]

R. Gordon, L. K. S. Kumar, and A. G. Brolo, “Resonant light transmission through a nanohole in a metal film,” IEEE Nanotechnology 5, 291–294 (2006).
[Crossref]

K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
[Crossref]

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[Crossref]

2004 (2)

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[Crossref]

E. X. Jin and X. Xu, “Finite-difference time-domain studies on optical transmission through planar nano-apertures in a metal Film,” Jpn. J. Appl. Phys. 43, 407–417(2004).
[Crossref]

2003 (2)

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

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 (2003).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379, (1972).
[Crossref]

Alaverdyan, Y.

T. Rindzevicius, Y. Alaverdyan, and B. Sepulveda. “Nanohole plasmons in optically thin gold films,” J. Phys. Chem. C 111, 1207–1212(2007).
[Crossref]

Baida, F. I.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[Crossref]

Barnes, W. L.

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

Belkhir, A.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[Crossref]

Bozhevolnyi, S. I.

Brolo, A. G.

R. Gordon, L. K. S. Kumar, and A. G. Brolo, “Resonant light transmission through a nanohole in a metal film,” IEEE Nanotechnology 5, 291–294 (2006).
[Crossref]

Chang, C. K.

C. K. Chang, D. Z. Lin, and C. S. Yeh, et. al., “Experimental analysis of surface plasmon behavior in metallic circular slits,” Appl. Phys. Lett. 90, 061113 (2007).
[Crossref]

Cho, Y. K.

K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379, (1972).
[Crossref]

Collin, S.

Degiron, A.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[Crossref]

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.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[Crossref]

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

Gordon, R.

R. Gordon, L. K. S. Kumar, and A. G. Brolo, “Resonant light transmission through a nanohole in a metal film,” IEEE Nanotechnology 5, 291–294 (2006).
[Crossref]

Grzegorczyk, T. M.

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 (2003).
[Crossref]

Jin, E. X.

E. X. Jin and X. Xu, “Finite-difference time-domain studies on optical transmission through planar nano-apertures in a metal Film,” Jpn. J. Appl. Phys. 43, 407–417(2004).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379, (1972).
[Crossref]

Kawano, K.

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis (Wiley, Chichester, 2001).
[Crossref]

Kim, K. Y.

K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
[Crossref]

Kitoh, T.

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis (Wiley, Chichester, 2001).
[Crossref]

Kong, F. M.

F. M. Kong, K. Li, and B. I. Wu, et. al., “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromagn. Res. 76, 449–466 (2007)
[Crossref]

Kong, J. A.

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 (2003).
[Crossref]

Kumar, L. K. S.

R. Gordon, L. K. S. Kumar, and A. G. Brolo, “Resonant light transmission through a nanohole in a metal film,” IEEE Nanotechnology 5, 291–294 (2006).
[Crossref]

Lamrous, O.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[Crossref]

Lee, J. H.

K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
[Crossref]

Lezec, H. J.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[Crossref]

Li, K.

F. M. Kong, K. Li, and B. I. Wu, et. al., “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromagn. Res. 76, 449–466 (2007)
[Crossref]

Lin, D. Z.

C. K. Chang, D. Z. Lin, and C. S. Yeh, et. al., “Experimental analysis of surface plasmon behavior in metallic circular slits,” Appl. Phys. Lett. 90, 061113 (2007).
[Crossref]

Orenstein, M.

Pardo, F.

Pelouard, J. L.

Prasad, P. N.

P. N. Prasad, Nanophotonics (Wiley-Interscience, New Jersey, 2004).
[Crossref]

Rindzevicius, T.

T. Rindzevicius, Y. Alaverdyan, and B. Sepulveda. “Nanohole plasmons in optically thin gold films,” J. Phys. Chem. C 111, 1207–1212(2007).
[Crossref]

Satuby, Y.

Sepulveda, B.

T. Rindzevicius, Y. Alaverdyan, and B. Sepulveda. “Nanohole plasmons in optically thin gold films,” J. Phys. Chem. C 111, 1207–1212(2007).
[Crossref]

Sönnichsen, C.

C. Sönnichsen, “Plasmons in metal nanostructures,” PhD Thesis (Ludwig-Maximilians-Universtät München, München, 2001).

Tae, H. S.

K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
[Crossref]

Van Labeke, D.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[Crossref]

Wu, B. I.

F. M. Kong, K. Li, and B. I. Wu, et. al., “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromagn. Res. 76, 449–466 (2007)
[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 (2003).
[Crossref]

Xu, X.

E. X. Jin and X. Xu, “Finite-difference time-domain studies on optical transmission through planar nano-apertures in a metal Film,” Jpn. J. Appl. Phys. 43, 407–417(2004).
[Crossref]

Yamamoto, N.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[Crossref]

Yeh, C. S.

C. K. Chang, D. Z. Lin, and C. S. Yeh, et. al., “Experimental analysis of surface plasmon behavior in metallic circular slits,” Appl. Phys. Lett. 90, 061113 (2007).
[Crossref]

Zhang, Y.

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 (2003).
[Crossref]

Appl. Phys. Lett. (1)

C. K. Chang, D. Z. Lin, and C. S. Yeh, et. al., “Experimental analysis of surface plasmon behavior in metallic circular slits,” Appl. Phys. Lett. 90, 061113 (2007).
[Crossref]

IEEE Nanotechnology (1)

R. Gordon, L. K. S. Kumar, and A. G. Brolo, “Resonant light transmission through a nanohole in a metal film,” IEEE Nanotechnology 5, 291–294 (2006).
[Crossref]

J. Appl. Phys. (1)

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 (2003).
[Crossref]

J. Phys. Chem. C (1)

T. Rindzevicius, Y. Alaverdyan, and B. Sepulveda. “Nanohole plasmons in optically thin gold films,” J. Phys. Chem. C 111, 1207–1212(2007).
[Crossref]

Jpn. J. Appl. Phys. (1)

E. X. Jin and X. Xu, “Finite-difference time-domain studies on optical transmission through planar nano-apertures in a metal Film,” Jpn. J. Appl. Phys. 43, 407–417(2004).
[Crossref]

Nature (1)

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

Opt. Commun. (1)

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[Crossref]

Opt. Express (3)

Opto-Electron. Rev. (1)

K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
[Crossref]

Phys. Rev. B (2)

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[Crossref]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379, (1972).
[Crossref]

Prog. Electromagn. Res. (1)

F. M. Kong, K. Li, and B. I. Wu, et. al., “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromagn. Res. 76, 449–466 (2007)
[Crossref]

Other (3)

P. N. Prasad, Nanophotonics (Wiley-Interscience, New Jersey, 2004).
[Crossref]

C. Sönnichsen, “Plasmons in metal nanostructures,” PhD Thesis (Ludwig-Maximilians-Universtät München, München, 2001).

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis (Wiley, Chichester, 2001).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Cross section of metallic rectangular waveguide (a) and the use of effective dielectric constant method in the x-direction (b) and y-direction (c)

Fig. 2.
Fig. 2.

Dispersion characteristics of TWG modes and SPPs modes in silver waveguide, the insets show the E field distributions of several modes in the air-core.

Fig. 3.
Fig. 3.

Dispersion evolution for SPPs mode in silver waveguide with different height

Fig. 4.
Fig. 4.

Calculated cutoff wavelength for the primary SPPs modes in a silver rectangular waveguide with different aspect ratio

Equations (21)

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

ε r 2 ( ω ) = ε r 2 ( 1 ω p 2 ω ( ω + i ω τ ) )
ϕ h x ( y ) = { B 1 e γ y ( y b ) ( y b ) A 1 e i k y y + A 2 e i k y y ( b < y < b ) B 2 e γ y ( y + b ) ( y b )
i k y ε r 1 ( A 1 e i k y b A 2 e i k y b ) = B 1 γ y ε r 2 ( ω )
A 1 e i k y b + A 2 e i k y b = B 1
i k y ε r 1 ( A 1 e i k y b A 2 e i k y b ) = B 2 γ y ε r 2 ( ω )
A 1 e i k y b + A 2 e i k y b = B 2
( 1 i ρ y 1 + i ρ y ) e i 2 k y b = e i ( n 1 ) π ( n = 1 , 2 , 3 , )
tan ( k y b ( n 1 ) π 2 ) = ρ y ( n = 1 , 2 , 3 , )
tanh ( k y b ) = ρ y ( Even solution )
coth ( k y b ) = ρ y ( Odd solution )
ϕ E y ( x ) = { D 1 e γ x ( x a ) ( x a ) C 1 e i k x x + C 2 e i k x x ( a < x < a ) D 2 e γ x ( x + b ) ( x a )
i k x ( C 1 e i k x a C 2 e i k x a ) = D 1 γ x
C 1 e i k x a + C 2 e i k x a = D 1
i k x ( C 1 e i k x a C 2 e i k x a ) = D 2 γ x
C 1 e i k x a + C 2 e i k x a = D 2
( 1 i ρ x 1 + i ρ x ) e i 2 k y b = e i ( m 1 ) π ( m = 1 , 2 , 3 , )
tan ( k x a ( m 1 ) π 2 ) = ρ x ( m = 1 , 2 , 3 , )
TWG modes E mn x : tan ( k x a ( m 1 ) π 2 ) = ε r 1 ε r 2 ( ω ) γ x k x , tan ( k y b ( n 1 ) π 2 ) = γ y k y
SPP modes E en x : tanh ( k x a ) = ε r 1 ε r 2 ( ω ) γ x k x , tan ( k y b ( n 1 ) π 2 ) = γ y k y
SPP modes E on x : coth ( k x a ) = ε r 1 ε r 2 ( ω ) γ x k x , tan ( k y b ( n 1 ) π 2 ) = γ y k y
β = { k 0 2 ε r 1 k x 2 k y 2 E mn x , E mn y k 0 2 ε r 1 + k x 2 k y 2 E en x , E on x k 0 2 ε r 1 k x 2 + k y 2 E me y , E mo y

Metrics