Abstract

The scattering of a surface plasmon polariton (SPP) by a rectangular dielectric channel discontinuity is analyzed through a rigorous magnetic field integral equation method. The scattering phenomenon is formulated by means of the magnetic-type scalar integral equation, which is subsequently treated through an entire-domain Galerkin method of moments (MoM), based on a Fourier-series plane wave expansion of the magnetic field inside the discontinuity. The use of Green’s function Fourier transform allows all integrations over the area and along the boundary of the discontinuity to be performed analytically, resulting in a MoM matrix with entries that are expressed as spectral integrals of closed-form expressions. Complex analysis techniques, such as Cauchy’s residue theorem and the saddle-point method, are applied to obtain the amplitudes of the transmitted and reflected SPP modes and the radiated field pattern. Through numerical results, we examine the wavelength selectivity of transmission and reflection against the channel dimensions as well as the sensitivity to changes in the refractive index of the discontinuity, which is useful for sensing applications.

© 2009 Optical Society of America

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A. Y. Nikitin, F. Lopez-Tejeira, and L. Martin-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007).
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[CrossRef]

2006 (3)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189-193 (2006).
[CrossRef] [PubMed]

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).
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S. Xiao, L. Liu, and M. Qiu, “Resonator channel drop filters in a plasmon-polaritons metal,” Opt. Express 14, 2932-2937 (2006).
[CrossRef] [PubMed]

2005 (4)

D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30, 1186-1188 (2005).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7, S97-S101 (2005).
[CrossRef]

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[CrossRef] [PubMed]

T. A. Leskova, A. A. Maradudin, and W. Zierau, “Surface plasmon polariton propagation near an index step,” Opt. Commun. 249, 23-35 (2005).
[CrossRef]

2004 (2)

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: an analytical study,” Phys. Rev. B 69, 045422 (2004).
[CrossRef]

J. Sánchez-Gil and A. Maradudin, “Dynamic near-field calculations of surface-plasmon polariton pulses resonantly scattered at sub-micron metal defects,” Opt. Express 12, 883-894 (2004).
[CrossRef] [PubMed]

2002 (2)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820-822 (2002).
[CrossRef] [PubMed]

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66, 354031-3540313 (2002).
[CrossRef]

1999 (2)

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

J. A. Sánchez-Gil and A. A. Maradudin, “Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B 60, 8359-8367 (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, 667-669 (1998).
[CrossRef]

1996 (2)

H. Ogura and Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358-10371 (1996).
[CrossRef]

J. A. Sánchez-Gil, “Coupling, resonance transmission, and tunneling of surface-plasmon polaritons through metallic gratings of finite length,” Phys. Rev. B 53, 10317-10327 (1996).
[CrossRef]

1968 (2)

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398-410 (1968).
[CrossRef]

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530-1533 (1968).
[CrossRef]

1963 (1)

E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Naturforsch. Teil A 23, 2135-2136 (1963).

1957 (1)

H. Ritchie, “Plasmon losses by fast electrons in thin films,” Phys. Rev. 106, 874-881 (1957).
[CrossRef]

1941 (1)

1902 (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. Phys. Soc. London 18, 269-275 (1902).
[CrossRef]

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530-1533 (1968).
[CrossRef]

Bachmann, G.

G. Bachmann, L. Narici, and E. Beckenstein, Fourier and Wavelet Analysis (Universitext Series, Springer, 2000).
[CrossRef]

Beckenstein, E.

G. Bachmann, L. Narici, and E. Beckenstein, Fourier and Wavelet Analysis (Universitext Series, Springer, 2000).
[CrossRef]

Bohr, M. T.

M. T. Bohr, R. S. Chau, T. Ghani, and K. Mistry, “The high-k solution,” IEEE Spectrum 44, 29-35 (2007).
[CrossRef]

Bozhevolnyi, S. I.

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]

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: an analytical study,” Phys. Rev. B 69, 045422 (2004).
[CrossRef]

Brambilla, G.

Brucoli, G.

F. De León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).
[CrossRef]

Chau, R. S.

M. T. Bohr, R. S. Chau, T. Ghani, and K. Mistry, “The high-k solution,” IEEE Spectrum 44, 29-35 (2007).
[CrossRef]

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogenous Media, 2nd ed. (Wiley-IEEE Press, 1999).
[CrossRef]

Chichkov, B.

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves, 2nd ed. (Wiley-IEEE Press, 1990).
[CrossRef]

Cowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530-1533 (1968).
[CrossRef]

De León-Pérez, F.

F. De León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).
[CrossRef]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Devaux, E.

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]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Ebbesen, T. W.

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]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820-822 (2002).
[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, 667-669 (1998).
[CrossRef]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Fano, U.

Forsberg, E.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photonics Technol. Lett. 19, 91-93 (2007).
[CrossRef]

Fukui, M.

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7, S97-S101 (2005).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820-822 (2002).
[CrossRef] [PubMed]

García-Vidal, F. J.

F. De León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).
[CrossRef]

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3-15 (1999).
[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, 667-669 (1998).
[CrossRef]

Ghani, T.

M. T. Bohr, R. S. Chau, T. Ghani, and K. Mistry, “The high-k solution,” IEEE Spectrum 44, 29-35 (2007).
[CrossRef]

Gobi, K. V.

D. R. Shankaran, K. V. Gobi, and N. Miura, “Recent advancements in surface plasmon resonance immunosensors for detection of small molecules of biomedical, food and environmental interest,” Sens. Actuators B 121, 158-177 (2007).
[CrossRef]

Gramotnev, D. K.

K. C. Vernon, D. K. Gramotnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103, 034304 (2008).
[CrossRef]

D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30, 1186-1188 (2005).
[CrossRef] [PubMed]

Hamm, R. N.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530-1533 (1968).
[CrossRef]

Han, Z.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photonics Technol. Lett. 19, 91-93 (2007).
[CrossRef]

Haraguchi, M.

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Wiley-IEEE Press, 1993).
[CrossRef]

He, S.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photonics Technol. Lett. 19, 91-93 (2007).
[CrossRef]

Homola, J.

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

Horak, P.

Huang, X.-G.

Kiyan, R.

Kretschmann, E.

E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Naturforsch. Teil A 23, 2135-2136 (1963).

Laluet, J.-Y.

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]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Leskova, T. A.

T. A. Leskova, A. A. Maradudin, and W. Zierau, “Surface plasmon polariton propagation near an index step,” Opt. Commun. 249, 23-35 (2005).
[CrossRef]

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820-822 (2002).
[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, 667-669 (1998).
[CrossRef]

Lin, X.-S.

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Liu, L.

Lopez-Tejeira, F.

A. Y. Nikitin, F. Lopez-Tejeira, and L. Martin-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007).
[CrossRef]

Maier, S.

S. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007), Chap. 9.

Maradudin, A.

Maradudin, A. A.

T. A. Leskova, A. A. Maradudin, and W. Zierau, “Surface plasmon polariton propagation near an index step,” Opt. Commun. 249, 23-35 (2005).
[CrossRef]

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66, 354031-3540313 (2002).
[CrossRef]

J. A. Sánchez-Gil and A. A. Maradudin, “Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B 60, 8359-8367 (1999).
[CrossRef]

Martin-Moreno, L.

A. Y. Nikitin, F. Lopez-Tejeira, and L. Martin-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Martín-Moreno, L.

F. De León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).
[CrossRef]

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7, S97-S101 (2005).
[CrossRef]

Matsuzaki, Y.

Mistry, K.

M. T. Bohr, R. S. Chau, T. Ghani, and K. Mistry, “The high-k solution,” IEEE Spectrum 44, 29-35 (2007).
[CrossRef]

Miura, N.

D. R. Shankaran, K. V. Gobi, and N. Miura, “Recent advancements in surface plasmon resonance immunosensors for detection of small molecules of biomedical, food and environmental interest,” Sens. Actuators B 121, 158-177 (2007).
[CrossRef]

Nakagaki, M.

Narici, L.

G. Bachmann, L. Narici, and E. Beckenstein, Fourier and Wavelet Analysis (Universitext Series, Springer, 2000).
[CrossRef]

Nikitin, A. Y.

A. Y. Nikitin, F. Lopez-Tejeira, and L. Martin-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007).
[CrossRef]

Novikov, I. V.

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66, 354031-3540313 (2002).
[CrossRef]

Ogura, H.

H. Ogura and Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358-10371 (1996).
[CrossRef]

Ohrt, C.

Okamoto, T.

Otto, A.

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398-410 (1968).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189-193 (2006).
[CrossRef] [PubMed]

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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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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, 667-669 (1998).
[CrossRef]

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[CrossRef]

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Xu, F.

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

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N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

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T. A. Leskova, A. A. Maradudin, and W. Zierau, “Surface plasmon polariton propagation near an index step,” Opt. Commun. 249, 23-35 (2005).
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Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photonics Technol. Lett. 19, 91-93 (2007).
[CrossRef]

IEEE Spectrum (1)

M. T. Bohr, R. S. Chau, T. Ghani, and K. Mistry, “The high-k solution,” IEEE Spectrum 44, 29-35 (2007).
[CrossRef]

J. Appl. Phys. (1)

K. C. Vernon, D. K. Gramotnev, and D. F. P. Pile, “Channel plasmon-polariton modes in V grooves filled with dielectric,” J. Appl. Phys. 103, 034304 (2008).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

F. J. Garcia-Vidal, L. Martín-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. Opt. Soc. Am. (1)

Nature (2)

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, 667-669 (1998).
[CrossRef]

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]

New J. Phys. (1)

F. De León-Pérez, G. Brucoli, F. J. García-Vidal, and L. Martín-Moreno, “Theory on the scattering of light and surface plasmon polaritons by arrays of holes and dimples in a metal film,” New J. Phys. 10, 105017 (2008).
[CrossRef]

Opt. Commun. (1)

T. A. Leskova, A. A. Maradudin, and W. Zierau, “Surface plasmon polariton propagation near an index step,” Opt. Commun. 249, 23-35 (2005).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. (1)

H. Ritchie, “Plasmon losses by fast electrons in thin films,” Phys. Rev. 106, 874-881 (1957).
[CrossRef]

Phys. Rev. B (6)

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B 66, 354031-3540313 (2002).
[CrossRef]

H. Ogura and Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358-10371 (1996).
[CrossRef]

J. A. Sánchez-Gil, “Coupling, resonance transmission, and tunneling of surface-plasmon polaritons through metallic gratings of finite length,” Phys. Rev. B 53, 10317-10327 (1996).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Surface plasmon polariton scattering by a small particle placed near a metal surface: an analytical study,” Phys. Rev. B 69, 045422 (2004).
[CrossRef]

A. Y. Nikitin, F. Lopez-Tejeira, and L. Martin-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007).
[CrossRef]

J. A. Sánchez-Gil and A. A. Maradudin, “Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B 60, 8359-8367 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530-1533 (1968).
[CrossRef]

Proc. Phys. Soc. London (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. Phys. Soc. London 18, 269-275 (1902).
[CrossRef]

Science (3)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189-193 (2006).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820-822 (2002).
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J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

SPP impinging on a dielectric-filled rectangular channel discontinuity.

Fig. 2
Fig. 2

Branch cuts (solid lines) that ensure Re [ γ 0 ( k ) ] 0 and Re [ γ m ( k ) ] 0 for every k. To draw the branch cuts, we have assumed a very small negative Im ( k 0 ) and non-negligible ohmic loss in the metal ( Re ( k m ) > 0 ) . The path of integration along the real axis is named R. Note that the abscissa (ordinate) in the k plane is Re ( k ) [ Im ( k ) ] .

Fig. 3
Fig. 3

Contour integration in the upper half-plane for the application of Cauchy’s residue theorem for z > 0 .

Fig. 4
Fig. 4

Integration contours on the complex κ plane. The SDC passes through the saddle point κ s = θ with slope 1. The branch cuts Re ( γ m ) = 0 run from the branch points ± κ b , ± ( κ b π ) to infinity, κ b = sin 1 ( n m ) , and define Re ( γ m ) > 0 everywhere. The shadowed strips are the images of the proper Riemann surface of Fig. 2 on the κ plane. Also shown are the SPP poles at ± κ p , κ p = sin 1 ( β k 0 ) .

Fig. 5
Fig. 5

Transmitted (upper curves) and reflected (lower curves) power fractions versus wavelength for a void channel with W = 50 nm and D = 50 , 100 , 150 nm , obtained through the rigorous MFIE method (solid curves) and through the FDTD method (dotted curves).

Fig. 6
Fig. 6

Wavelength of the transmission minimum versus the depth of a void channel with width W = 50 nm (circles) and W = 30 nm (squares).

Fig. 7
Fig. 7

Power fraction reflected by a shallow ( D = 0.05 λ ) and void channel versus its width at λ = 600 nm . The dashed curve corresponds to the approximate analytical formula from [26]: 4 ( n eff 2 1 ) ( k 0 D ) 2 sin 2 ( 2 π n eff W λ ) .

Fig. 8
Fig. 8

Transmission spectra (solid lines) for a channel with W = 50 nm , D = 100 nm , and increasing refractive index n d = 1.0 , 1.1 , 1.2 , 1.3 , 1.4 , 1.5 . The dotted lines correspond to the radiated power fraction 1 | τ | 2 | ρ | 2 .

Fig. 9
Fig. 9

Wavelength of the transmission minimum versus the refractive index of a channel with W = 50 nm and D = 100 nm . The dashed linear regression line has a slope S = Δ λ Δ n d 563 nm /RIU.

Fig. 10
Fig. 10

Normalized field radiation patterns for a void channel with W = 50 nm and D = 50 nm (dashed line), D = 100 nm (thin solid lines), and D = 150 nm (thick solid line) at the wavelengths of minimum transmission shown by circles in Fig. 6. The multiple solid lines correspond to increasing channel refractive index with values and corresponding wavelengths taken from Fig. 9. The arrow indicates the increase of n d . Also shown (dots) is the pattern for W = 30 nm , D = 50 nm , at λ = 625 nm taken from the squares in Fig. 6.

Fig. 11
Fig. 11

Normalized field radiation patterns for a void and shallow ( D = 0.05 λ ) channel with W = 0.1 λ (thin solid line), W = 0.25 λ (thick solid line), W = 0.4 λ (dashed line) and W = 0.8 λ (dotted line), at λ = 600 nm .

Equations (31)

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[ 2 + k 2 ( r ) ] G ( r , r ) = δ ( r r ) , k ( r ) = { k 0 , x > 0 k m , x < 0 } ,
| ϵ m G ( r , r ) | x 0 = | ϵ 0 G ( r , r ) | x 0 + ,
| G ( r , r ) x | x 0 = | G ( r , r ) x | x 0 +
[ 2 + k 2 ( r ) ] H y ( r ) = 0 , k ( r ) = { k 0 , x > 0 k d , r C k m , { x < 0 r C } } ,
H y ( r ) = H y inc ( r ) + ( k d 2 k m 2 ) C G ( r , r ) H y ( r ) d x d z + ( 1 ϵ m ϵ d ) C G ( r , r ) H y ( r ) n out d l ,
H y ( r ) = H y inc ( r ) + ( k d 2 k m 2 ) C G ( r , r ) H y ( r ) d x d z + ( 1 ϵ m ϵ d ) C G ( r , r ) H y ( r ) n out d l ,
H y ( r ) = H y inc ( r ) + ( k d 2 k m 2 ) ϵ 0 ϵ m C G ( r , r ) H y ( r ) d x d z + ( 1 ϵ m ϵ d ) ϵ 0 ϵ m C G ( r , r ) H y ( r ) n out d l .
G m ( r , r ) = + d k e j k ( z z ) γ m | x x | 4 π γ m ,
( G r ( r , r ) G t ( r , r ) ) = + d k 4 π γ m ( k ) ( R ( k ) e γ m ( k ) x T ( k ) e γ 0 ( k ) x ) e j k ( z z ) + γ m ( k ) x ,
R ( k ) = γ m ϵ 0 γ 0 ϵ m γ m ϵ 0 + γ 0 ϵ m , T ( k ) = 2 γ m ϵ m γ m ϵ 0 + γ 0 ϵ m ,
H y inc ( r ) = H 0 { e γ 0 ( β ) x j β z , x > 0 e + γ m ( β ) x j β z , x < 0 } ,
H y ( r ) = n = s = ± 1 + c n s e j ( k x n s x + k z n z ) ,
k x n ± 1 = ± k d 2 k z n 2 , k z n = 2 n π W .
C d x d z e j ( k x m s x + k z m z ) × ,
C d x d z e j ( k x m s x + k z m z ) H y ( r ) = D W n = s = ± 1 + K obs ( m , s , n , s ) c n s ,
C d x d z e j ( k x m s x + k z m z ) H y inc ( r ) = D W K inc ( m , s ) H 0 ,
K obs ( m , s , n , s ) = e j ( k x n s k x m s ) D 2 sinc [ ( k x m s k x n s ) D 2 π ] sinc [ ( k z m k z n ) W 2 π ] ,
K inc ( m , s ) = e [ γ m ( β ) + j k x m s ] D 2 sinc { [ k x m s j γ m ( β ) ] D 2 π } sinc [ ( k z m β ) W 2 π ] ,
C d x d z e + j ( k x m s x + k z m z ) [ ( k d 2 k m 2 ) C G ( r , r ) H y ( r ) d x d z + ( 1 ϵ m ϵ d ) C G ( r , r ) H y ( r ) n out d l ] = D W n = s = ± 1 + K g ( m , s , n , s ) c n s
K g ( m , s , n , s ) = + f ( k , m , s , n , s ) d k ,
where f ( k , m , s , n , s ) = ( ϵ m ϵ d 1 ) D W 4 π γ m e j ( k x n s k x m s ) D 2 sinc [ ( k + k z m ) W 2 π ] sinc [ ( k + k z n ) W 2 π ] × { R ( k ) e γ m D sinc [ ( k x m s j γ m ) D 2 π ] sinc [ ( k x n s + j γ m ) D 2 π ] ( j k x n s γ m + k z n k ) + sinc [ ( k x m s k x n s ) D 2 π ] [ 2 γ m D [ γ m 2 + ( k x n s ) 2 ] D 2 ] [ k z n k ( k x n s ) 2 ] + sinc [ ( k x m s + j γ m ) D 2 π ] [ e ( j k x n s γ m ) D 2 ( j k x n s γ m ) D ] ( k z n k + j k x n s γ m ) sinc [ ( k x m s j γ m ) D 2 π ] [ e ( j k x n s + γ m ) D 2 ( j k x n s + γ m ) D ] ( k z n k j k x n s γ m ) } .
n = s = ± 1 + [ K obs ( m , s , n , s ) K g ( m , s , n , s ) ] c n s = K inc ( m , s ) H 0 ,
K g ( m , s , n , s ) = 0 + [ f ( k , m , s , n , s ) + f ( k , m , s , n , s ) ] d k ,
H y ( r ) = H y inc ( r ) + ( ϵ m ϵ d 1 ) ϵ 0 ϵ m H 0 + d k S ( k ) T ( k ) 4 π γ m e j k z γ 0 x ,
S ( k ) = D W × { n = s = ± 1 + c n s e ( j k x n s γ m ) D 2 sinc [ ( k + k z n ) W 2 π ] sinc [ ( k x n s + j γ m ) D 2 π ] ( j k x n s γ m + k z n k ) } .
C = B 0 B m + 2 π j × ( Residue at k = β ) ,
( τ 1 ρ ) = ± 2 π j × { ( ϵ m ϵ d 1 ) ϵ 0 ϵ m S ( β ) 4 π γ m ( β ) Res ( T ( k ) ; β ) } ,
Res ( T ( k ) ; β ) = 2 γ 0 ( β ) γ m ( β ) β × ϵ m 2 ( ϵ m 2 ϵ 0 2 ) ,
H y scat ( r ) = ( 1 ϵ m ϵ d ) ϵ 0 ϵ m H 0 ( j 4 π ) C d κ γ 0 ( κ ) S ( κ ) T ( κ ) γ m ( κ ) e j k 0 r cos ( κ + θ ) ,
SDC d κ F ( κ ) e j k 0 r cos ( κ + θ ) F ( θ ) 2 π j × ( e j k 0 r k 0 r ) ,
ϵ m ( ω ) = ϵ 0 ( ϵ ω p 2 ω 2 j γ ω ) ,

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