Abstract

Based on finite-difference time-domain simulation of the propagation characteristics of surface plasmon polaritons (SPPs) in optical circuits made from metal gap waveguides (MGWs) with nanometric gap widths, we theoretically demonstrate that two structures that consist of splitting and recombining MGWs and of coupling MGWs can be used as nanoscale Mach–Zehnder interferometers. MGW arrays show capabilities for array imaging and for controlling the flow of SPPs. Other potential applications of coupling MGWs, as SPP switches, directional couplers, and even as a nanoscale counterpart for observing linear and nonlinear dynamic behavior of electromagnetic fields, are also predicted and discussed. Our results point to an interesting way to manipulate optical signals and provide efficient sensing in nanophotonic architectures.

© 2004 Optical Society of America

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  1. S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, Appl. Phys. Lett. 79, 1076 (2001).
    [CrossRef]
  2. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nature Mater. 2, 229 (2003).
    [CrossRef]
  3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003), and references therein.
    [CrossRef] [PubMed]
  4. K. Tanaka and M. Tanaka, Appl. Phys. Lett. 82, 1158 (2003).
    [CrossRef]
  5. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985).
  6. I. P. Kaminow, W. L. Mammel, and H. P. Weber, Appl. Opt. 13, 396 (1974).
    [CrossRef] [PubMed]
  7. G. Mur, IEEE Trans. Electromagn. Compat. EMC-23, 377 (1981).
    [CrossRef]
  8. H. A. Haus and L. Molter-Orr, IEEE J. Quantum Electron. QE-19, 840 (1983).
    [CrossRef]
  9. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1984).
  10. S. A. Darmanyan and A. V. Zayats, Phys. Rev. B 67, 035424 (2003).
    [CrossRef]
  11. H. Raether, Surface Plasmon (Springer-Verlag, Berlin, 1988).
  12. J. Topol’ancik, P. Bhattacharya, J. Sabarinathan, and P.-C. Yu, Appl. Phys. Lett. 82, 1143 (2003).
    [CrossRef]
  13. Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
    [CrossRef] [PubMed]
  14. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  15. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
    [CrossRef] [PubMed]

2003

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

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003), and references therein.
[CrossRef] [PubMed]

K. Tanaka and M. Tanaka, Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

S. A. Darmanyan and A. V. Zayats, Phys. Rev. B 67, 035424 (2003).
[CrossRef]

J. Topol’ancik, P. Bhattacharya, J. Sabarinathan, and P.-C. Yu, Appl. Phys. Lett. 82, 1143 (2003).
[CrossRef]

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
[CrossRef] [PubMed]

2001

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, Appl. Phys. Lett. 79, 1076 (2001).
[CrossRef]

1998

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1983

H. A. Haus and L. Molter-Orr, IEEE J. Quantum Electron. QE-19, 840 (1983).
[CrossRef]

1981

G. Mur, IEEE Trans. Electromagn. Compat. EMC-23, 377 (1981).
[CrossRef]

1974

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Atwater, H. A.

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

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003), and references therein.
[CrossRef] [PubMed]

Betts, R. E.

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[CrossRef] [PubMed]

Bhatia, S. N.

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[CrossRef] [PubMed]

Bhattacharya, P.

J. Topol’ancik, P. Bhattacharya, J. Sabarinathan, and P.-C. Yu, Appl. Phys. Lett. 82, 1143 (2003).
[CrossRef]

Boltasseva, A.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, Appl. Phys. Lett. 79, 1076 (2001).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, Appl. Phys. Lett. 79, 1076 (2001).
[CrossRef]

Chin, V.

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[CrossRef] [PubMed]

Christodoulides, D. N.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
[CrossRef] [PubMed]

Cunin, F.

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[CrossRef] [PubMed]

Darmanyan, S. A.

S. A. Darmanyan and A. V. Zayats, Phys. Rev. B 67, 035424 (2003).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003), and references therein.
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003), and references therein.
[CrossRef] [PubMed]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Gao, T.

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[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, Nature Mater. 2, 229 (2003).
[CrossRef]

Haus, H. A.

H. A. Haus and L. Molter-Orr, IEEE J. Quantum Electron. QE-19, 840 (1983).
[CrossRef]

Hunsperger, R. G.

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1984).

Kaminow, I. P.

Kik, P. G.

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

Koel, B. E.

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

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
[CrossRef] [PubMed]

Leosson, K.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, Appl. Phys. Lett. 79, 1076 (2001).
[CrossRef]

Li, Y. Y.

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[CrossRef] [PubMed]

Link, J. R.

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[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, Nature Mater. 2, 229 (2003).
[CrossRef]

Mammel, W. L.

Meltzer, S.

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

Molter-Orr, L.

H. A. Haus and L. Molter-Orr, IEEE J. Quantum Electron. QE-19, 840 (1983).
[CrossRef]

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Mur, G.

G. Mur, IEEE Trans. Electromagn. Compat. EMC-23, 377 (1981).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmon (Springer-Verlag, Berlin, 1988).

Reirer, S. H.

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[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, Nature Mater. 2, 229 (2003).
[CrossRef]

Sabarinathan, J.

J. Topol’ancik, P. Bhattacharya, J. Sabarinathan, and P.-C. Yu, Appl. Phys. Lett. 82, 1143 (2003).
[CrossRef]

Sailor, M. J.

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Tanaka, K.

K. Tanaka and M. Tanaka, Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

Tanaka, M.

K. Tanaka and M. Tanaka, Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

Topol’ancik, J.

J. Topol’ancik, P. Bhattacharya, J. Sabarinathan, and P.-C. Yu, Appl. Phys. Lett. 82, 1143 (2003).
[CrossRef]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, Appl. Phys. Lett. 79, 1076 (2001).
[CrossRef]

Weber, H. P.

Yu, P.-C.

J. Topol’ancik, P. Bhattacharya, J. Sabarinathan, and P.-C. Yu, Appl. Phys. Lett. 82, 1143 (2003).
[CrossRef]

Zayats, A. V.

S. A. Darmanyan and A. V. Zayats, Phys. Rev. B 67, 035424 (2003).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

K. Tanaka and M. Tanaka, Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, Appl. Phys. Lett. 79, 1076 (2001).
[CrossRef]

J. Topol’ancik, P. Bhattacharya, J. Sabarinathan, and P.-C. Yu, Appl. Phys. Lett. 82, 1143 (2003).
[CrossRef]

IEEE J. Quantum Electron.

H. A. Haus and L. Molter-Orr, IEEE J. Quantum Electron. QE-19, 840 (1983).
[CrossRef]

IEEE Trans. Electromagn. Compat.

G. Mur, IEEE Trans. Electromagn. Compat. EMC-23, 377 (1981).
[CrossRef]

Nature

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003), and references therein.
[CrossRef] [PubMed]

Nature Mater.

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

Phys. Rev. B

S. A. Darmanyan and A. V. Zayats, Phys. Rev. B 67, 035424 (2003).
[CrossRef]

Phys. Rev. Lett.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Science

Y. Y. Li, F. Cunin, J. R. Link, T. Gao, R. E. Betts, S. H. Reirer, V. Chin, S. N. Bhatia, and M. J. Sailor, Science 299, 2045 (2003).
[CrossRef] [PubMed]

Other

H. Raether, Surface Plasmon (Springer-Verlag, Berlin, 1988).

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1984).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985).

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Figures (3)

Fig. 1
Fig. 1

a, M-Z interferometric structure with splitting and recombining MGWs; b–e, E2 time evolution of light through the structure. N denotes elapsed time.

Fig. 2
Fig. 2

a, M-Z interferometric structure with coupling MGWs; b, E2 distributions when the overlap length between adjacent waveguides is Lc.

Fig. 3
Fig. 3

a, Schematic of a MGW array structure; b, E2 distribution in a MGW array with silver film thickness D=20 nm as SPPs are coupled only into the center waveguide; c, E2 profiles in a plane 1.5 µm away from the input light for D=15,20,30 nm.

Equations (2)

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

Ej=2/2A0 cos2Czexpiβz  j=1,3,  E2=iA0 sin2Czexpiβz,
Enz=A0in expiβzJn2Cz,

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