Abstract

Plasmonic modes in rectangular metallic waveguides are analyzed in depth and are demonstrated to possess attractive properties for different applications. Their dispersion characteristics allow for wide range of applications including slow and fast light, metamaterial, low loss energy transmission, and opportunities for sensing devices. The sensitivity of this waveguide configuration is higher than its counterparts and can reach four times the sensitivity of the MIM structures. The characteristics of the TM10 mode are demonstrated. Its applications for sensing, low propagation loss with relaxed practical dimension are also highlighted. A high effective index of more than 30 is also obtainable for the TE01 mode for slow light operation. A non resonant negative index material with isotropic polarization in the visible region is also proposed using this waveguide structure.

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References

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  1. S. A. Maier, Plasmonics: Fundamentals and Applications, (Springer, 2007).
  2. G. Veronis and S. Fan, “Modes of Subwavelength Plasmonic Slot Waveguides,” J. Lightwave Technol. 25(9), 2511–2521 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
  4. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
    [CrossRef]
  5. R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995).
    [CrossRef]
  6. J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003).
    [CrossRef] [PubMed]
  7. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
    [CrossRef]
  8. H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  12. A. Alù, N. Engheta, and A. Alu’, “Light squeezing through arbitrarily shaped plasmonic channels and sharp bends,” Phys. Rev. B 78(3), 035440 (2008).
    [CrossRef]
  13. F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. Kumar, and R. Gordon, “Transmission of light through single rectangular hole in a real metal,” Phys. Rev. B 74(15), 153411 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  22. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
    [CrossRef]
  23. H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]

2010 (1)

2009 (2)

2008 (2)

2007 (3)

2006 (4)

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
[CrossRef] [PubMed]

A. Alù, N. Engheta, and A. Alu’, “Optical nanotransmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes,” J. Opt. Soc. Am. B 23(3), 571–583 (2006).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. Kumar, and R. Gordon, “Transmission of light through single rectangular hole in a real metal,” Phys. Rev. B 74(15), 153411 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

2005 (2)

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

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

2003 (2)

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003).
[CrossRef] [PubMed]

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

2002 (1)

R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘Fast’ Light,” Prog. Opt. 43, 497–530 (2002).
[CrossRef]

1999 (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

1998 (1)

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

1995 (1)

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Alù, A.

A. Alù, N. Engheta, and A. Alu’, “Light squeezing through arbitrarily shaped plasmonic channels and sharp bends,” Phys. Rev. B 78(3), 035440 (2008).
[CrossRef]

A. Alù, N. Engheta, and A. Alu’, “Optical nanotransmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes,” J. Opt. Soc. Am. B 23(3), 571–583 (2006).
[CrossRef]

Alu’, A.

A. Alù, N. Engheta, and A. Alu’, “Light squeezing through arbitrarily shaped plasmonic channels and sharp bends,” Phys. Rev. B 78(3), 035440 (2008).
[CrossRef]

A. Alù, N. Engheta, and A. Alu’, “Optical nanotransmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes,” J. Opt. Soc. Am. B 23(3), 571–583 (2006).
[CrossRef]

Atwater, H. A.

J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express 16(23), 19001–19017 (2008).
[CrossRef]

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Bakr, M. H.

Barnes, W. L.

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

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘Fast’ Light,” Prog. Opt. 43, 497–530 (2002).
[CrossRef]

Brolo, A.

Crozier, K. B.

Dereux, A.

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

Dionne, J. A.

J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express 16(23), 19001–19017 (2008).
[CrossRef]

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Ebbesen, T. W.

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 sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Engheta, N.

A. Alù, N. Engheta, and A. Alu’, “Light squeezing through arbitrarily shaped plasmonic channels and sharp bends,” Phys. Rev. B 78(3), 035440 (2008).
[CrossRef]

A. Alù, N. Engheta, and A. Alu’, “Optical nanotransmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes,” J. Opt. Soc. Am. B 23(3), 571–583 (2006).
[CrossRef]

Fan, S.

G. Veronis and S. Fan, “Modes of Subwavelength Plasmonic Slot Waveguides,” J. Lightwave Technol. 25(9), 2511–2521 (2007).
[CrossRef]

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
[CrossRef] [PubMed]

Feigenbaum, E.

García-Vidal, F. J.

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. Kumar, and R. Gordon, “Transmission of light through single rectangular hole in a real metal,” Phys. Rev. B 74(15), 153411 (2006).
[CrossRef]

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘Fast’ Light,” Prog. Opt. 43, 497–530 (2002).
[CrossRef]

Ghaemi, H. F.

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

Gordon, R.

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. Kumar, and R. Gordon, “Transmission of light through single rectangular hole in a real metal,” Phys. Rev. B 74(15), 153411 (2006).
[CrossRef]

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

Harris, R. D.

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995).
[CrossRef]

Homola, J.

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003).
[CrossRef] [PubMed]

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

Ibanescu, M.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

Joannopoulos, J. D.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

Kaminski, N.

Karalis, A.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

Kumar, L.

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. Kumar, and R. Gordon, “Transmission of light through single rectangular hole in a real metal,” Phys. Rev. B 74(15), 153411 (2006).
[CrossRef]

Lezec, H. J.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

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

Li, X.

Lidorikis, E.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

Martín-Moreno, L.

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. Kumar, and R. Gordon, “Transmission of light through single rectangular hole in a real metal,” Phys. Rev. B 74(15), 153411 (2006).
[CrossRef]

Moreno, E.

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. Kumar, and R. Gordon, “Transmission of light through single rectangular hole in a real metal,” Phys. Rev. B 74(15), 153411 (2006).
[CrossRef]

Orenstein, M.

Polman, A.

J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express 16(23), 19001–19017 (2008).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Shin, H.

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
[CrossRef] [PubMed]

Soljacic, M.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Swillam, M. A.

Thio, T.

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

Verhagen, E.

Veronis, G.

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Wilkinson, J. S.

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995).
[CrossRef]

Wolff, P. A.

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

Yang, T.

Yee, S. S.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

Anal. Bioanal. Chem. (1)

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003).
[CrossRef] [PubMed]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (1)

Nature (2)

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 sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Opt. Express (4)

Phys. Rev. B (3)

A. Alù, N. Engheta, and A. Alu’, “Light squeezing through arbitrarily shaped plasmonic channels and sharp bends,” Phys. Rev. B 78(3), 035440 (2008).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. Kumar, and R. Gordon, “Transmission of light through single rectangular hole in a real metal,” Phys. Rev. B 74(15), 153411 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[CrossRef] [PubMed]

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
[CrossRef] [PubMed]

Prog. Opt. (1)

R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘Fast’ Light,” Prog. Opt. 43, 497–530 (2002).
[CrossRef]

Science (1)

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

Sens. Actuators B Chem. (2)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Other (4)

Electromagnetics Module User’s Guide (Comsol, 2007), Sweden. http://www.comsol.com .

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

FDTD Solutions Reference Guide, (Lumerical Solutions, 2009).

S. A. Maier, Plasmonics: Fundamentals and Applications, (Springer, 2007).

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Figures (14)

Fig. 1
Fig. 1

The dispersion characteristics of the fundamental y-polarized mode of rectangular waveguide 20x40 nm with silver metal walls and filed dielectric of refractive index 3.5 using finite difference frequency domain solver (-) and using Comsol (o).

Fig. 2
Fig. 2

The dispersion characteristics of the fundamental x-polarized mode of rectangular waveguide 20x40 nm with silver metal walls and filed dielectric of refractive index 3.5.

Fig. 3
Fig. 3

The propagation loss of the fundamental x-polarized and y-polarized mode of rectangular waveguide 20x40 nm with silver metal walls and filed dielectric of refractive index 3.5.

Fig. 4
Fig. 4

The sensitivity of the propagation constant with respect to the refractive index of the filled material for both MIM and rectangular waveguide 360x600 nm TM10

Fig. 5
Fig. 5

The transmission characteristics through rectangular channel waveguide of length 1 microns in using the TM10 mode.

Fig. 6
Fig. 6

The transmission characteristics through rectangular channel waveguide with different length L using the TM10 mode. a) the transmission for different wavelengths, and b) the transmission peak for different channel length.

Fig. 7
Fig. 7

The normalized dispersion characteristics of rectangular waveguide with 80x50 nm

Fig. 8
Fig. 8

a) The dispersion characteristics of gold metallic waveguide filled with n d = 3.5 with for different waveguide heights. b) The change of the bandwidth of negative dispersion with the change of the heights for the same width of 70 nm.

Fig. 9
Fig. 9

The dispersion characteristics of gold metallic waveguide filled with Si3Ni4 with for different waveguide heights.

Fig. 10
Fig. 10

The spectrum of the imaginary part of the effective index, k which defines the backward wave region in a rectangular waveguide with width of 100 nm and silver walls and filled with n = 3.5.

Fig. 11
Fig. 11

, The maximum effective index of rectangular waveguide with gold metal and filled with nd = 3.5 for fixed height, Wy , of 10 nm.

Fig. 12
Fig. 12

The maximum effective index of rectangular waveguide with gold metal and filled with nd = 3.5 for fixed width of 70 nm at wavelength of 633 nm.

Fig. 13
Fig. 13

The normalized values of the maximum effective index for different filled material for rectangular waveguide with 10x70 nm.

Fig. 14
Fig. 14

The wavelengths at which the maximum values of the effective index occur for different filled material for rectangular waveguide with 10x70 nm.

Equations (3)

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k s p p = ω c ε d ε m ε d + ε m
λ p < λ < λ s p p
λ s p p λ p 1 + ε d

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