Abstract

We report on the observation of discrete diffraction in surface plasmon polariton waveguide arrays at a wavelength of 1550nm. We also adopt the effective index method to reduce our simulation geometry to two-dimensions, predict the spread of single-waveguide excitation in parallel waveguide arrays, and explore changing the excitation angle to detune the waveguides. Our experimental results show discrete diffraction compensation at an angle of 2.2° as predicted by simulations.

© 2009 Optical Society of America

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  1. F. Bloch, Z. Phys. 52, 555 (1928).
  2. C. Zener, Proc. R. Soc. London Ser. A 145, 523 (1934).
    [CrossRef]
  3. R. Iyer, J. S. Aitchison, J. Wan, M. M. Dignam, and C. M. de Sterke, Opt. Express 15, 3212 (2007).
    [CrossRef] [PubMed]
  4. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
    [CrossRef] [PubMed]
  5. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef] [PubMed]
  6. B. Wang and G. P. Wang, Opt. Lett. 29, 1992 (2004).
    [CrossRef] [PubMed]
  7. X. Fan and G. P. Wang, Opt. Lett. 31, 1322 (2006).
    [CrossRef] [PubMed]
  8. E. N. Economou, Phys. Rev. 182, 539 (1969).
    [CrossRef]
  9. P. Berini, Phys. Rev. B 63, 125417 (2001).
    [CrossRef]
  10. I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).
    [CrossRef]
  11. J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, Europhys. Lett. 60, 663 (2002).
    [CrossRef]
  12. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
    [CrossRef] [PubMed]
  13. G. I. Stegeman, R. F. Wallis, and A. A. Maradudin, Opt. Lett. 8, 386 (1983).
    [CrossRef] [PubMed]
  14. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
    [CrossRef] [PubMed]
  15. R. Zia and M. L. Brongersma, Nat. Nanotechnol. 2, 426 (2007).
    [CrossRef]
  16. A. Yariv, Optical Electronics (HRW/Saunders, 1991), Chap. 13.8.
  17. R. Zia, A. Chandran, and M. L. Brongersma, Opt. Lett. 30, 1473 (2005).
    [CrossRef] [PubMed]
  18. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  19. H. R. Philipp, SiO2, Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), p. 749.

2007 (2)

2006 (2)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

X. Fan and G. P. Wang, Opt. Lett. 31, 1322 (2006).
[CrossRef] [PubMed]

2005 (2)

R. Zia, A. Chandran, and M. L. Brongersma, Opt. Lett. 30, 1473 (2005).
[CrossRef] [PubMed]

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

2002 (2)

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

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, Europhys. Lett. 60, 663 (2002).
[CrossRef]

2001 (1)

P. Berini, Phys. Rev. B 63, 125417 (2001).
[CrossRef]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

1991 (1)

A. Yariv, Optical Electronics (HRW/Saunders, 1991), Chap. 13.8.

1985 (1)

H. R. Philipp, SiO2, Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), p. 749.

1983 (1)

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1969 (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

1934 (1)

C. Zener, Proc. R. Soc. London Ser. A 145, 523 (1934).
[CrossRef]

1928 (1)

F. Bloch, Z. Phys. 52, 555 (1928).

Aitchison, J. S.

R. Iyer, J. S. Aitchison, J. Wan, M. M. Dignam, and C. M. de Sterke, Opt. Express 15, 3212 (2007).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

Alkemade, F. A.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Aussenegg, F. R.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, Europhys. Lett. 60, 663 (2002).
[CrossRef]

Berini, P.

P. Berini, Phys. Rev. B 63, 125417 (2001).
[CrossRef]

Bloch, F.

F. Bloch, Z. Phys. 52, 555 (1928).

Blok, H.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Brongersma, M. L.

Chandran, A.

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Cianci, E.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

de Sterke, C. M.

Dignam, M. M.

Ditlbacher, H.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, Europhys. Lett. 60, 663 (2002).
[CrossRef]

Dubois, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Economou, E. N.

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

Eliel, E. R.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Fan, X.

Foglietti, V.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Gbur, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Hooft, G. W.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Iyer, R.

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Krenn, J. R.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, Europhys. Lett. 60, 663 (2002).
[CrossRef]

Kuzmin, N.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Lamprecht, B.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, Europhys. Lett. 60, 663 (2002).
[CrossRef]

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Leitner, A.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, Europhys. Lett. 60, 663 (2002).
[CrossRef]

Lenstra, D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Lobino, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Longhi, S.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Maradudin, A. A.

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

Novikov, I. V.

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

Philipp, H. R.

H. R. Philipp, SiO2, Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), p. 749.

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Salerno, M.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, Europhys. Lett. 60, 663 (2002).
[CrossRef]

Schider, G.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, Europhys. Lett. 60, 663 (2002).
[CrossRef]

Schouten, H. F.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

Stegeman, G. I.

Visser, T. D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Wallis, R. F.

Wan, J.

Wang, B.

Wang, G. P.

Yariv, A.

A. Yariv, Optical Electronics (HRW/Saunders, 1991), Chap. 13.8.

Zener, C.

C. Zener, Proc. R. Soc. London Ser. A 145, 523 (1934).
[CrossRef]

Zia, R.

Europhys. Lett. (1)

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, Europhys. Lett. 60, 663 (2002).
[CrossRef]

Nat. Mater. (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Nat. Nanotechnol. (1)

R. Zia and M. L. Brongersma, Nat. Nanotechnol. 2, 426 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Phys. Rev. B (3)

P. Berini, Phys. Rev. B 63, 125417 (2001).
[CrossRef]

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

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. Lett. (3)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A (1)

C. Zener, Proc. R. Soc. London Ser. A 145, 523 (1934).
[CrossRef]

Z. Phys. (1)

F. Bloch, Z. Phys. 52, 555 (1928).

Other (2)

H. R. Philipp, SiO2, Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), p. 749.

A. Yariv, Optical Electronics (HRW/Saunders, 1991), Chap. 13.8.

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Figures (3)

Fig. 1
Fig. 1

Illustration of the structure and the excitation scheme. The waveguides are 5 μ m in width and 20 nm in thickness. The waveguide center-to-center separation is 10 μ m . The sample is 1 mm in length.

Fig. 2
Fig. 2

Coupling coefficients as a function of silver stripe thickness. Dashed curves represent values calculated using the mode interference method, and dotted curves represent values calculated using the beam propagation method. Open circles, triangles, and squares represent the coupling coefficients calculated for parallel silver stripes, each having widths of 4, 5, and 6 μ m and center-to-center separations of 8, 10, and 12 μ m , respectively.

Fig. 3
Fig. 3

Intensity pattern detected at output of the waveguide array. (a) compares the TE and TM polarized components of the output intensity patterns, both excited at θ = 0 . (b) shows the spatial distribution of the output intensity pattern for θ = 0 ° , 0.9°, 1.5°, 2.2°, and 2.9°. Vertical bars show the simulated results, and solid curves show the experimental results. The heights of the bars represent the relative SPP intensities guided in the waveguides. All plots are normalized for visual clarity.

Equations (3)

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

d A n d z = i β A n + i C ( A n 1 + A n + 1 ) ,
D d = 2 C d 2 cos ( k x d ) ,
α = sin 1 ( π 2 k spp d ) ,

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