Abstract

This paper demonstrates the efficiency of the differential method, a conventional grating theory, to investigate dielectric loaded surface plasmon polariton waveguides (DLSPPWs), known to be a potential solution for optical interconnects. The method is used to obtain the mode effective indices (both real and imaginary parts) and the mode profiles. The results obtained with the differential method are found to be in good agreement with those provided by the effective index method or finite elements. The versatility of the differential method is demonstrated by considering complex configurations such as trapezoidal waveguides or DLSPPWs lying on a finite width metal stripe.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  6. A. V. Krasavin and A. V. Zayats, "Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides," Appl. Phys. Lett. 90, 211101 (2007).
    [CrossRef]
  7. B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides," Appl. Phys. Lett. 88, 094104 (2006).
    [CrossRef]
  8. B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers," Appl. Phys. Lett. 91, 081111 (2007).
    [CrossRef]
  9. A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005).
    [CrossRef] [PubMed]
  10. R. Kiyan, C. Reinhardt, S. Passinger, A. L. Stepanov, A. Hohenau, J. R. Krenn, and B. N. Chichkov, "Rapid prototyping of optical components for surface plasmon polaritons," Opt. Express 15, 4205-4215 (2007).
    [CrossRef] [PubMed]
  11. S. Massenot, J. Grandidier, A. Bouhelier, G. Colas des Francs, L. Markey, J.-C. Weeber, A. Dereux, J. Renger, M. U. Gonz`alez and R. Quidant, "Polymer-metal waveguides characterization by Fourier plane leakage radiation microscopy," Appl. Phys. Lett. 91, 243102 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  19. R. Zia, J. A. schuller and M. L. Brongersma, "Near-field characterization of guided polariton propagation and cutoff in surface plasmons waveguides," Phys. Rev. B 74, 165415 (2006).
    [CrossRef]

2007 (5)

T. Holmgaard and S. I. Bozhevolnyi, "Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides," Phys. Rev. B 75, 245405 (2007).
[CrossRef]

A. V. Krasavin and A. V. Zayats, "Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides," Appl. Phys. Lett. 90, 211101 (2007).
[CrossRef]

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers," Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

S. Massenot, J. Grandidier, A. Bouhelier, G. Colas des Francs, L. Markey, J.-C. Weeber, A. Dereux, J. Renger, M. U. Gonz`alez and R. Quidant, "Polymer-metal waveguides characterization by Fourier plane leakage radiation microscopy," Appl. Phys. Lett. 91, 243102 (2007).
[CrossRef]

R. Kiyan, C. Reinhardt, S. Passinger, A. L. Stepanov, A. Hohenau, J. R. Krenn, and B. N. Chichkov, "Rapid prototyping of optical components for surface plasmon polaritons," Opt. Express 15, 4205-4215 (2007).
[CrossRef] [PubMed]

2006 (2)

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides," Appl. Phys. Lett. 88, 094104 (2006).
[CrossRef]

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

2005 (2)

2003 (1)

J.-C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distribution of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
[CrossRef]

2001 (1)

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

1999 (1)

1998 (1)

1996 (1)

1995 (1)

1994 (1)

P. Dawson, F. de Fornel and J.-P. Goudonnet, "Imaging of surface plasmon propagating and edge interaction using a photon scanning tunnelling microscope," Phys. Rev. Lett. 72, 2927 (1994).
[CrossRef] [PubMed]

Amenogiannis, E.

Aussenegg, F. R.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers," Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides," Appl. Phys. Lett. 88, 094104 (2006).
[CrossRef]

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005).
[CrossRef] [PubMed]

Berini, P.

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

Bouhelier, A.

S. Massenot, J. Grandidier, A. Bouhelier, G. Colas des Francs, L. Markey, J.-C. Weeber, A. Dereux, J. Renger, M. U. Gonz`alez and R. Quidant, "Polymer-metal waveguides characterization by Fourier plane leakage radiation microscopy," Appl. Phys. Lett. 91, 243102 (2007).
[CrossRef]

Bozhevolnyi, S. I.

T. Holmgaard and S. I. Bozhevolnyi, "Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides," Phys. Rev. B 75, 245405 (2007).
[CrossRef]

Chichkov, B. N.

Cho, M. H.

Dawson, P.

P. Dawson, F. de Fornel and J.-P. Goudonnet, "Imaging of surface plasmon propagating and edge interaction using a photon scanning tunnelling microscope," Phys. Rev. Lett. 72, 2927 (1994).
[CrossRef] [PubMed]

de Fornel, F.

P. Dawson, F. de Fornel and J.-P. Goudonnet, "Imaging of surface plasmon propagating and edge interaction using a photon scanning tunnelling microscope," Phys. Rev. Lett. 72, 2927 (1994).
[CrossRef] [PubMed]

Dereux, A.

J.-C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distribution of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
[CrossRef]

Ditlbacher, H.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers," Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides," Appl. Phys. Lett. 88, 094104 (2006).
[CrossRef]

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005).
[CrossRef] [PubMed]

Drezet, A.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides," Appl. Phys. Lett. 88, 094104 (2006).
[CrossRef]

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005).
[CrossRef] [PubMed]

Gaylord, T. K.

Glytsis, E. N.

Goudonnet, J.-P.

P. Dawson, F. de Fornel and J.-P. Goudonnet, "Imaging of surface plasmon propagating and edge interaction using a photon scanning tunnelling microscope," Phys. Rev. Lett. 72, 2927 (1994).
[CrossRef] [PubMed]

Grandidier, J.

S. Massenot, J. Grandidier, A. Bouhelier, G. Colas des Francs, L. Markey, J.-C. Weeber, A. Dereux, J. Renger, M. U. Gonz`alez and R. Quidant, "Polymer-metal waveguides characterization by Fourier plane leakage radiation microscopy," Appl. Phys. Lett. 91, 243102 (2007).
[CrossRef]

Hohenau, A.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers," Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

R. Kiyan, C. Reinhardt, S. Passinger, A. L. Stepanov, A. Hohenau, J. R. Krenn, and B. N. Chichkov, "Rapid prototyping of optical components for surface plasmon polaritons," Opt. Express 15, 4205-4215 (2007).
[CrossRef] [PubMed]

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides," Appl. Phys. Lett. 88, 094104 (2006).
[CrossRef]

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005).
[CrossRef] [PubMed]

Holmgaard, T.

T. Holmgaard and S. I. Bozhevolnyi, "Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides," Phys. Rev. B 75, 245405 (2007).
[CrossRef]

Kim, P. S.

Kim, Y. S.

Kiyan, R.

Kostuk, R. K.

Krasavin, A. V.

A. V. Krasavin and A. V. Zayats, "Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides," Appl. Phys. Lett. 90, 211101 (2007).
[CrossRef]

Krenn, J. R.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers," Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

R. Kiyan, C. Reinhardt, S. Passinger, A. L. Stepanov, A. Hohenau, J. R. Krenn, and B. N. Chichkov, "Rapid prototyping of optical components for surface plasmon polaritons," Opt. Express 15, 4205-4215 (2007).
[CrossRef] [PubMed]

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides," Appl. Phys. Lett. 88, 094104 (2006).
[CrossRef]

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005).
[CrossRef] [PubMed]

Lacroute, Y.

J.-C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distribution of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
[CrossRef]

Leitner, A.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers," Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005).
[CrossRef] [PubMed]

Li, L.

Massenot, S.

S. Massenot, J. Grandidier, A. Bouhelier, G. Colas des Francs, L. Markey, J.-C. Weeber, A. Dereux, J. Renger, M. U. Gonz`alez and R. Quidant, "Polymer-metal waveguides characterization by Fourier plane leakage radiation microscopy," Appl. Phys. Lett. 91, 243102 (2007).
[CrossRef]

Oh, C. H.

Park, S.

Passinger, S.

Reinhardt, C.

Song, S. H.

Steinberger, B.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers," Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides," Appl. Phys. Lett. 88, 094104 (2006).
[CrossRef]

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005).
[CrossRef] [PubMed]

Stepanov, A. L.

Weeber, J.-C.

J.-C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distribution of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
[CrossRef]

Wu, S.-D.

Wu, Y.-M.

Yeh, J.-H.

Zayats, A. V.

A. V. Krasavin and A. V. Zayats, "Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides," Appl. Phys. Lett. 90, 211101 (2007).
[CrossRef]

Zia, R.

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

Appl. Opt. (1)

Appl. Phys. Lett. (4)

A. V. Krasavin and A. V. Zayats, "Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides," Appl. Phys. Lett. 90, 211101 (2007).
[CrossRef]

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides," Appl. Phys. Lett. 88, 094104 (2006).
[CrossRef]

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, "Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers," Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

S. Massenot, J. Grandidier, A. Bouhelier, G. Colas des Francs, L. Markey, J.-C. Weeber, A. Dereux, J. Renger, M. U. Gonz`alez and R. Quidant, "Polymer-metal waveguides characterization by Fourier plane leakage radiation microscopy," Appl. Phys. Lett. 91, 243102 (2007).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (4)

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

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

J.-C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distribution of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
[CrossRef]

T. Holmgaard and S. I. Bozhevolnyi, "Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides," Phys. Rev. B 75, 245405 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

P. Dawson, F. de Fornel and J.-P. Goudonnet, "Imaging of surface plasmon propagating and edge interaction using a photon scanning tunnelling microscope," Phys. Rev. Lett. 72, 2927 (1994).
[CrossRef] [PubMed]

Other (3)

S. Kawai, Handbook of Optical interconnects, (Marcel Dekker Inc., New-York 2005).

K. Kawano and T. Kitoh, Introduction to optical waveguide analysis, (Wiley, New-York, 2001).

M. Neviere and E. Popov, Light Propagation in Periodic Media, Differential Theory and Design, (Marcel Dekker Inc., New-York, 2003).

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Figures (6)

Fig. 1.
Fig. 1.

Illustration of the notations used by the differential method for a lamellar grating in conical diffraction.

Fig. 2.
Fig. 2.

Illustration of a dielectric loaded surface plasmon polariton waveguide, cross-section (a) and excitation scheme in ATR along the longitudinal axis of the waveguide (b).

Fig. 3.
Fig. 3.

Angular reflectivity curve (a) and its numerical derivative (b). Near-field intensity in the xy plane 5 nm above the top of the dielectric waveguide with a gaussian beam excitation (beam waist w 0=5 µm) (c) and along the longitudinal axis (x=0) (d).

Fig. 4.
Fig. 4.

Intensity mode profiles and confinement factors Γ for DLSPPWs having different structural parameters (thicknesses and widths).

Fig. 5.
Fig. 5.

Illustration of the studied trapezoidal DLSPPW.

Fig. 6.
Fig. 6.

(a): Illustration of a DLSPPW on a finite-width metal stripe; b: Evolution of the propagation length of the guided mode according the width of the metal stripe. The parameters are w=600 nm, t=600 nm and h=100 nm.

Tables (2)

Tables Icon

Table 1. Comparison of the results obtained by the differential method (DM) to those provided by the Effective Index Method (EIM) and Finite Elements (FEM) for waveguides of different widths (t=600 nm, nw=1.535, nm=0.55+11.5ι and λ=1.55 µm)

Tables Icon

Table 2. Calculated effective index and propagation length for different trapezoidal DLSPP-Ws with the differential method

Equations (3)

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

E y ( i ) ( x , y , z ) = m = N N A m ( i ) exp [ i ( k x , m ( i ) x + k y ( i ) y k z , m ( i ) z ) ] + B m ( i ) exp [ i ( k x , m ( i ) x + k y ( i ) y + k z , m i z ) ]
d F dz = M ( z ) F
E inc = exp [ x 2 + y 2 w 0 2 ] = w 0 2 4 π exp [ ( k x 2 + k y 2 ) w 0 2 4 ] exp [ i ( k x x + k y y ) ] dk x dk y

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