Abstract

A fully-analytic expression is derived for the phase of reflection of surface plasmons at a semi-infinite boundary. We apply this phase of reflection result in the geometric optics method to calculate the properties of surface plasmon stripe waveguides. Comprehensive vectorial numerical computations are compared with the analytic method to show that it is accurate. The loss of the surface plasmon stripe waveguide is calculated using the geometric optics approach, which is also found to be in close agreement with numerical computations. The geometric optics approach may be used to obtain accurate results for other surface plasmon structures, such as microdisk or ring resonators, with greater efficiency and physical intuition than numerical computations.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2007

H. A. Atwater, "The Promise of Plasmonics," Sci. Am. 62, 7 (2007).

Y. Satuby and M. Orenstein, "Surface plasmon polariton waveguiding: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
[CrossRef]

2006

I. Breukelaar, R. Charbonneau, and P. Berini, "Long-range surface plasmon-polariton mode cutoff and radiation in embedded stripe waveguides," J. Appl. Phys. 100, 043104 (2006).
[CrossRef]

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, "Channel plasmon-polaritons: modal shape, dispersion, and losses," Opt. Lett. 31, 3447 (2006).
[CrossRef] [PubMed]

R. Gordon, "Vectorial method for calculating the Fresnel reflection of surface plasmon polaritons," Phys. Rev. B 75, 039901 (2006).
[CrossRef]

R. Zia, J. Schuller, and M. Brongersma, "Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides," Phys. Rev. B 74, 165415 (2006).
[CrossRef]

2005

2004

2003

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

2002

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, "Non-diffraction-limited light transport by gold nanowires," Europhys. Lett. 60, 663 (2002).
[CrossRef]

2001

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076 (2001).
[CrossRef]

J.-C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, "Near-field observation of surface plasmon polariton propagation on thin metal stripes," Phys. Rev. B 64, 045411 (2001).
[CrossRef]

1999

J. Homola, S. S. Yee, and G. Gauglitz, "Surface Plasmon Resonance Sensors: Review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

1976

1972

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Y. Satuby and M. Orenstein, "Surface plasmon polariton waveguiding: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076 (2001).
[CrossRef]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Europhys. Lett.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, "Non-diffraction-limited light transport by gold nanowires," Europhys. Lett. 60, 663 (2002).
[CrossRef]

J. Appl. Phys.

I. Breukelaar, R. Charbonneau, and P. Berini, "Long-range surface plasmon-polariton mode cutoff and radiation in embedded stripe waveguides," J. Appl. Phys. 100, 043104 (2006).
[CrossRef]

Nature

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

Opt. Lett.

Phys. Rev. B

J.-C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, "Near-field observation of surface plasmon polariton propagation on thin metal stripes," Phys. Rev. B 64, 045411 (2001).
[CrossRef]

R. Gordon, "Vectorial method for calculating the Fresnel reflection of surface plasmon polaritons," Phys. Rev. B 75, 039901 (2006).
[CrossRef]

R. Zia, J. Schuller, and M. Brongersma, "Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides," Phys. Rev. B 74, 165415 (2006).
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Sci. Am.

H. A. Atwater, "The Promise of Plasmonics," Sci. Am. 62, 7 (2007).

Sens. Actuators B

J. Homola, S. S. Yee, and G. Gauglitz, "Surface Plasmon Resonance Sensors: Review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Other

H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, 1988).

B. E. A. Saleh, Fundamentals of Photonics, (Wiley-Interscience, 1991).
[CrossRef]

M. Sandtke, H. Schoenmaker, and I. Attema, "Visualizing surface plasmon polariton wavepackets in space and time," CLEO, QMC5 (2006).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of surface plasmon stripe waveguide (SPSW) propagation

Fig. 2.
Fig. 2.

Effective index as a function of stripe width for SPSW modes (solid line), TE modes of a dielectric waveguide with the same refractive index as the SPP (dashed line), and numerical values (points).

Fig. 3.
Fig. 3.

Dispersion of effective index for SPSW fundamental mode for various waveguide widths.

Fig. 4.
Fig. 4.

Dependence of the group velocity of SPSW on wavelength for various waveguide widths, including material dispersion

Fig. 5.
Fig. 5.

Dependence of the loss of SPSW on the stripe width at the wavelength of 800 nm.

Equations (7)

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

r = I cos ( θ ) ε p 2 ( 1 ε m ε d ) π ε d ε m I cos ( θ ) ε p 2 ( 1 ε m ε d ) + π ε d ε m
I = ( ε d u 2 ) du ε d u 2 ε p sin 2 ( θ ) ( u 2 ε p ε d ε m ) ( u 2 ε p ε m ε d )
tan ( φ 2 ) = s 2 π 2 ε m 2 arctanh ( cos θ p ) + 2 p q ( ε m 2 ε m ε d ε d 2 ) cos ( θ ) arctanh ( q )
tan ( π n p w λ cos θ m π 2 ) = tan ( φ 2 )
n effective = n p sin θ m
γ = ξ l z l + s
S = λ 0 2 π n p cos ( θ ) φ θ

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