Abstract

We investigate the properties of plasmon polaritons guided by 2D monoangular metal corners with a vector finite-element method. Such corner waveguides in general include both V-channel- and Λ-wedge-type waveguides. The influences of both geometric parameters (i.e., corner angle, tip sharpness, etc.) and operating wavelength to the mode properties, such as effective mode index, loss, and mode field size, are inspected. It is noticed that both a smaller corner angle and a sharper corner tip help to better confine the mode field. The confinement of the V-channel waveguide is found to be especially sensitive to its angle, while the confinement of the Λ-wedge waveguide is affected about equally by its angle and tip sharpness. Almost all superior mode field confinement is realized at the expense of higher propagation loss for such waveguides. The chromatic dispersion of such waveguides is found to be adequate for applications in integrated optical circuits. The mode behaviors of realistic corner waveguides with finite sidewalls are also studied.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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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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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. J. Andersen and V. Solodukhov, "Field behavior near a dielectric wedge," IEEE Trans. Antennas Propag. 26, 598-602 (1978).
    [CrossRef]
  25. A. S. Sudbø, "Why are accurate computations of mode fields in rectangular dielectric waveguides difficult?" J. Lightwave Technol. 10, 418-419 (1992).
    [CrossRef]
  26. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985), Part II, Subpart 1.
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    [CrossRef]
  28. For example, the Corning SMF-28e+ optical fiber has dispersion ≤18 ps/nm/km at 1550 nm wavelength. http://www.corning.com.

2006

2005

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Express 13, 977-984 (2005).
[CrossRef] [PubMed]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, "Integrated optical components utilizing long-range surface plasmon polaritons," J. Lightwave Technol. 23, 413-422 (2005).
[CrossRef]

L. Liu, Z. Han, and S. He, "Novel surface plasmon waveguide for high integration," Opt. Express 13, 6645-6650 (2005).
[CrossRef] [PubMed]

G. Veronis and S. Fan, "Guided subwavelength plasmonic mode supported by a slot in a thin metal film," Opt. Lett. 30, 3359-3361 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. OKamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

2004

D. K. Gramotnev and D. F. P. Pile, "Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
[CrossRef]

2002

I. V. Novikov and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
[CrossRef]

2001

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures," Phys. Rev. B 63, 125417 (2001).
[CrossRef]

2000

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures," Phys. Rev. B 61, 10484-10503 (2000).
[CrossRef]

1995

H. E. Hernández-Figueroa, F. A. Fernández, Y. Lu, and J. B. Davies, "Vectorial finite element modelling of 2D leaky waveguides," IEEE Trans. Magn. 31, 1710-1713 (1995).
[CrossRef]

1992

A. S. Sudbø, "Why are accurate computations of mode fields in rectangular dielectric waveguides difficult?" J. Lightwave Technol. 10, 418-419 (1992).
[CrossRef]

1991

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
[CrossRef]

1986

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

1978

J. Andersen and V. Solodukhov, "Field behavior near a dielectric wedge," IEEE Trans. Antennas Propag. 26, 598-602 (1978).
[CrossRef]

1975

P. McIsaac, "Symmetry-induced modal characteristics of uniform waveguides--I: Summary of results," IEEE Trans. Microwave Theory Tech. 23, 421-429 (1975).
[CrossRef]

1972

J. Meixner, "The behavior of electromagnetic fields at edges," IEEE Trans. Antennas Propag. 20, 442-446 (1972).
[CrossRef]

1946

C. J. Bouwkamp, "A note on singularities occurring at sharp edges in electromagnetic diffraction theory," Physica (The Hague) 12, 467-474 (1946).
[CrossRef]

Appl. Phys. Lett.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

D. K. Gramotnev and D. F. P. Pile, "Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface," Appl. Phys. Lett. 85, 6323-6325 (2004).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. OKamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

IEEE Trans. Antennas Propag.

J. Meixner, "The behavior of electromagnetic fields at edges," IEEE Trans. Antennas Propag. 20, 442-446 (1972).
[CrossRef]

J. Andersen and V. Solodukhov, "Field behavior near a dielectric wedge," IEEE Trans. Antennas Propag. 26, 598-602 (1978).
[CrossRef]

IEEE Trans. Magn.

H. E. Hernández-Figueroa, F. A. Fernández, Y. Lu, and J. B. Davies, "Vectorial finite element modelling of 2D leaky waveguides," IEEE Trans. Magn. 31, 1710-1713 (1995).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

P. McIsaac, "Symmetry-induced modal characteristics of uniform waveguides--I: Summary of results," IEEE Trans. Microwave Theory Tech. 23, 421-429 (1975).
[CrossRef]

J. Lightwave Technol.

Nature

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
[CrossRef]

I. V. Novikov and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
[CrossRef]

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures," Phys. Rev. B 61, 10484-10503 (2000).
[CrossRef]

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures," Phys. Rev. B 63, 125417 (2001).
[CrossRef]

Phys. Rev. Lett.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Physica (The Hague)

C. J. Bouwkamp, "A note on singularities occurring at sharp edges in electromagnetic diffraction theory," Physica (The Hague) 12, 467-474 (1946).
[CrossRef]

Other

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985), Part II, Subpart 1.

M. Yan and M. Qiu, "Analysis of surface plasmon polariton using anisotropic finite elements," IEEE Photon. Technol. Lett. (to be published).

Gmsh, http://www.geuz.org/gmsh/.

For example, the Corning SMF-28e+ optical fiber has dispersion ≤18 ps/nm/km at 1550 nm wavelength. http://www.corning.com.

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Figures (11)

Fig. 1
Fig. 1

(a)–(c) show diagrams of V-channel, 1D surface, and Λ-wedge metal waveguides, respectively. The hatched region is metal, and the white region is dielectric material. (d) Geometric parameters for a generalized metal-corner waveguide. (e) Sample mesh of a circular region with a 200 nm diameter. The corner has a 30° angle, and is rounded with an arc of 10 nm in radius.

Fig. 2
Fig. 2

Schematic mode field patterns suggested by symmetry analysis. Only transverse electric (solid lines with arrow heads) and magnetic (dashed lines with arrow heads) fields in the air region are shown. The domain below the thick solid line is metal. (a) Mode in a V-channel waveguide with PEC symmetry. (b) Mode on a flat surface with PEC symmetry. (c) Mode on a Λ wedge with PEC symmetry. (d) Mode in a V-channel waveguide with PMC symmetry. (e) Mode on a flat surface with PMC symmetry. (f) Mode on a Λ wedge with PMC symmetry.

Fig. 3
Fig. 3

Fundamental mode guided by two types of corner waveguides. (a) V-channel waveguide; (b) Λ-wedge waveguide. Colormap is for H t 2 , and quiver is for H t . Wavelength is at 0.633 μ m . Corner angle is 30°. Corner tip is rounded with an arc with 10 nm in radius. Axis unit, micrometers.

Fig. 4
Fig. 4

(a) Dispersion, (b) mode field size, and (c) loss curves of the guided CPP mode as the corner angle changes. Gray (forward-line-shaded) region in (a) is the mode continuum region of an Ag–air interface at λ = 0.633 μ m ( 1.55 μ m ) .

Fig. 5
Fig. 5

(a) Dispersion, (b) mode field size, and (c) loss curves of the guided CPP mode as the curvature of the corner tip increases. All waveguides have a corner angle at 30°. The bottom-left (blue) set of axes is for λ = 0.633 μ m , and the top-right (red) set of axes is for λ = 1.55 μ m .

Fig. 6
Fig. 6

(a) Dispersion, (b) mode field size, and (c) loss curves of the guided CPP mode in both V-channel and Λ-wedge waveguides as the size of the flat section at the corner tip increases.

Fig. 7
Fig. 7

Chromatic properties of the corner waveguides. The corner angle is at 20°, and the tip is rounded with an arc of 10 nm in radius. (a) Effective mode index; (b) loss; (c) mode field size; and (d) GVD. The gray region below the black curve in (a) denotes the mode continuum region of a flat Ag–air interface.

Fig. 8
Fig. 8

Variations of n eff values of two supermodes supported by a realistic V-channel waveguide.

Fig. 9
Fig. 9

H t 2 (colormap) and H t (quiver) plots of two supermodes guided by a realistic V-channel waveguide at λ = 1.4 μ m . (a) Mode with PEC symmetry; (b) mode with PMC symmetry. Axis unit, micrometers.

Fig. 10
Fig. 10

Variation of n eff value of the mode guided by a realistic Λ-wedge waveguide.

Fig. 11
Fig. 11

H t (colormap) and H t (quiver) of the mode guided by a realistic Λ-wedge waveguide at λ = 2 μ m . Axis unit, micrometers.

Equations (5)

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ϵ = ϵ ( ϵ 0 ϵ ) ω p 2 ω 2 + i ω γ ,
k t s = k 0 n eff 2 n SPP 2 ,
k t a = k 0 n eff 2 n air 2 ,
MFS = 1 k t s ,
GVD = λ c d 2 n eff d λ 2 .

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