Abstract

We report critical coupling of electromagnetic waves to plasmonic cavity arrays fabricated on Moiré surfaces. Dark field plasmon microscopy imaging and polarization dependent spectroscopic reflection measurements reveal the critical coupling conditions of the cavities. The critical coupling conditions depend on the superperiod of the Moiré surface, which also defines the coupling between the cavities. Complete transfer of the incident power can be achieved for traveling wave plasmonic resonators, which have a relatively short superperiod. When the superperiod of the resonators increases, the coupled resonators become isolated standing wave resonators in which complete transfer of the incident power is not possible. Analytical and finite difference time domain calculations support the experimental observations.

© 2011 Optical Society of America

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2011 (1)

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 98, 031101 (2011).
[CrossRef]

2010 (2)

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 97, 131103 (2010).
[CrossRef]

S. Balci, M. Karabiyik, A. Kocabas, C. Kocabas, and A. Aydinli, Plasmonics 5, 429 (2010).
[CrossRef]

2009 (1)

A. Kocabas, S. S. Senlik, and A. Aydinli, Phys. Rev. Lett. 102, 063901 (2009).
[CrossRef] [PubMed]

2007 (1)

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, S. Massenot, J. Grandidier, L. Markey, and A. Dereux, Phys. Rev. B 76, 113405 (2007).
[CrossRef]

2006 (2)

2005 (1)

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

2004 (1)

P. Andrew and W. L. Barnes, Science 306, 1002 (2004).
[CrossRef] [PubMed]

2000 (1)

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

1999 (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

1991 (1)

1975 (1)

H. J. Simon, D. E. Mitchell, and J. G. Watson, Am. J. Phys. 43, 630 (1975).
[CrossRef]

Andrew, P.

P. Andrew and W. L. Barnes, Science 306, 1002 (2004).
[CrossRef] [PubMed]

Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Aydinli, A.

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 98, 031101 (2011).
[CrossRef]

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 97, 131103 (2010).
[CrossRef]

S. Balci, M. Karabiyik, A. Kocabas, C. Kocabas, and A. Aydinli, Plasmonics 5, 429 (2010).
[CrossRef]

A. Kocabas, S. S. Senlik, and A. Aydinli, Phys. Rev. Lett. 102, 063901 (2009).
[CrossRef] [PubMed]

Balci, S.

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 98, 031101 (2011).
[CrossRef]

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 97, 131103 (2010).
[CrossRef]

S. Balci, M. Karabiyik, A. Kocabas, C. Kocabas, and A. Aydinli, Plasmonics 5, 429 (2010).
[CrossRef]

Barnes, W. L.

P. Andrew and W. L. Barnes, Science 306, 1002 (2004).
[CrossRef] [PubMed]

Bechinger, C.

Bouhelier, A.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, S. Massenot, J. Grandidier, L. Markey, and A. Dereux, Phys. Rev. B 76, 113405 (2007).
[CrossRef]

Capasso, F.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Crozier, K. B.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Cubukcu, E.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Dereux, A.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, S. Massenot, J. Grandidier, L. Markey, and A. Dereux, Phys. Rev. B 76, 113405 (2007).
[CrossRef]

des Francs, G. Colas

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, S. Massenot, J. Grandidier, L. Markey, and A. Dereux, Phys. Rev. B 76, 113405 (2007).
[CrossRef]

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Eremin, Y.

Eremina, E.

Fan, S.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Grandidier, J.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, S. Massenot, J. Grandidier, L. Markey, and A. Dereux, Phys. Rev. B 76, 113405 (2007).
[CrossRef]

Haus, H. A.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Helden, L.

Hertlein, C.

Hill, W.

P. Horowitz and W. Hill, The Arts of Electronics (Cambridge University, 1989).

Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Hohenau, A.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Horowitz, P.

P. Horowitz and W. Hill, The Arts of Electronics (Cambridge University, 1989).

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Karabiyik, M.

S. Balci, M. Karabiyik, A. Kocabas, C. Kocabas, and A. Aydinli, Plasmonics 5, 429 (2010).
[CrossRef]

Khan, M. J.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Kocabas, A.

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 98, 031101 (2011).
[CrossRef]

S. Balci, M. Karabiyik, A. Kocabas, C. Kocabas, and A. Aydinli, Plasmonics 5, 429 (2010).
[CrossRef]

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 97, 131103 (2010).
[CrossRef]

A. Kocabas, S. S. Senlik, and A. Aydinli, Phys. Rev. Lett. 102, 063901 (2009).
[CrossRef] [PubMed]

Kocabas, C.

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 98, 031101 (2011).
[CrossRef]

S. Balci, M. Karabiyik, A. Kocabas, C. Kocabas, and A. Aydinli, Plasmonics 5, 429 (2010).
[CrossRef]

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 97, 131103 (2010).
[CrossRef]

Kort, E. A.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Krenn, J.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Manolatou, C.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Markey, L.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, S. Massenot, J. Grandidier, L. Markey, and A. Dereux, Phys. Rev. B 76, 113405 (2007).
[CrossRef]

Massenot, S.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, S. Massenot, J. Grandidier, L. Markey, and A. Dereux, Phys. Rev. B 76, 113405 (2007).
[CrossRef]

Mitchell, D. E.

H. J. Simon, D. E. Mitchell, and J. G. Watson, Am. J. Phys. 43, 630 (1975).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons (Springer-Verlag, 1986).

Riefler, N.

Rogers, M.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Senlik, S. S.

A. Kocabas, S. S. Senlik, and A. Aydinli, Phys. Rev. Lett. 102, 063901 (2009).
[CrossRef] [PubMed]

Simon, H. J.

H. J. Simon, D. E. Mitchell, and J. G. Watson, Am. J. Phys. 43, 630 (1975).
[CrossRef]

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Wagner, D.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Watson, J. G.

H. J. Simon, D. E. Mitchell, and J. G. Watson, Am. J. Phys. 43, 630 (1975).
[CrossRef]

Weeber, J.-C.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, S. Massenot, J. Grandidier, L. Markey, and A. Dereux, Phys. Rev. B 76, 113405 (2007).
[CrossRef]

Wriedt, T.

Yariv, A.

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

Zervas, M. N.

Am. J. Phys. (1)

H. J. Simon, D. E. Mitchell, and J. G. Watson, Am. J. Phys. 43, 630 (1975).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 97, 131103 (2010).
[CrossRef]

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

S. Balci, A. Kocabas, C. Kocabas, and A. Aydinli, Appl. Phys. Lett. 98, 031101 (2011).
[CrossRef]

Electron. Lett. (1)

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, S. Massenot, J. Grandidier, L. Markey, and A. Dereux, Phys. Rev. B 76, 113405 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

A. Kocabas, S. S. Senlik, and A. Aydinli, Phys. Rev. Lett. 102, 063901 (2009).
[CrossRef] [PubMed]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Plasmonics (1)

S. Balci, M. Karabiyik, A. Kocabas, C. Kocabas, and A. Aydinli, Plasmonics 5, 429 (2010).
[CrossRef]

Science (1)

P. Andrew and W. L. Barnes, Science 306, 1002 (2004).
[CrossRef] [PubMed]

Other (2)

P. Horowitz and W. Hill, The Arts of Electronics (Cambridge University, 1989).

H. Raether, Surface Plasmons (Springer-Verlag, 1986).

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Figures (4)

Fig. 1
Fig. 1

AFM images of Moiré surfaces with a superperiod of (a) 9.0 and (b)  2.5 μm . Line profiles extracted from (c) the AFM image in (a), and (d) the AFM image in (b).

Fig. 2
Fig. 2

(a) Kretschmann configuration used for coupling of light to SPPs where d is the Ag film thickness. (b) Analytically calculated reflection curves under coupling conditions for an SWR and a TWR. FDTD calculated SPP electric field distribution for (c) 2.5 and (d)  15.0 μm coupled plasmonic resonator arrays indicating TWR and SWR properties, respectively. The scale bars are (c) 1 and (d)  5 μm long. The vertical length of images in (c) and (d) is 1 μm long.

Fig. 3
Fig. 3

FDTD calculated two-dimensional electric field distribution at the cavity wavelength for 15.0 μm long plasmonic resonators with Ag film thickness of (a) 20, (b) 30, (c) 40, and (d)  60 nm . The vertical length of images in (a)–(d) is 1 μm long. DFPM images of coupled resonators at the resonance wavelength for Ag film thicknesses of (e) 20, (f) 30, (g) 40, and (h)  60 nm . The white bars indicate a 10 μm long distance. Line scans perpendicular to the long axis of plasmonic resonator arrays with Ag film thicknesses of (i) 20, (j) 30, (k) 40, and (l)  60 nm .

Fig. 4
Fig. 4

Reflection curves from Moiré surfaces containing (a) 4.5 and (b)  9.0 μm long SPP cavities. The reflection curves have been obtained at an incidence angle of 42.5 ° , where the maximum coupling of incident light to SPPs can be achieved for a given Ag film thickness. It should be noted that reflection from the band edges also goes to zero under critical coupling in (a). (c) Using the reflection curves in (a) and (b), minima of the reflection curves have been drawn. At 25 nm Ag film thickness, reflection from the SPP cavities reaches a minimum value. (d) Reflection from the cavity mode calculated from the dispersion curves for cavity sizes of 2.5, 4.5, 9.0, and 15.0 μm with varying Ag film thicknesses from 10 to 60 nm . (e) The reflection from the cavity mode at a Ag film thickness of 25 nm increases with the increase in cavity size.

Equations (5)

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

d ψ d t = ( i ω 0 1 τ 0 1 τ 1 1 τ 2 ) ψ + κ s 1 + + κ s 2 + ,
s 1 = e i β L c ( s 2 + κ * ψ ) ,
s 2 = e i β L c ( s 1 + κ * ψ ) ,
s 2 s 1 + = e i β L c ( 1 1 τ f i ( ω ω 0 ) + 1 τ 0 + 1 τ 1 + 1 τ 2 ) .
d ψ n d t = ( i ω n 1 τ 0 1 τ 1 1 τ 2 ) ψ n + i κ 1 ψ n + 1 + i κ 1 ψ n 1 + κ s 1 + + κ s 2 + ,

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