Abstract

We analyze the propagation of electromagnetic modes guided by periodic plasmonic structures. We use full-wave solutions of Maxwell equations to calculate dispersion of these modes and derive analytical description of their optical properties. Finally, we demonstrate that, at a certain frequency range that can be controlled by the geometry, diffraction of these guided states is strongly suppressed, leading to formation of low-diffraction beams. A beaming phenomenon, consistent with earlier experiments, can be used as the foundation for on-chip communication or microscopy.

© 2012 Optical Society of America

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References

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2011 (2)

2010 (2)

B. Stein, J. Laluet, E. Devaux, C. Genet, and T. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

B. Stein, J. N. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

2009 (1)

2008 (2)

Z. Jacob and E. Narimanov, Appl. Phys. Lett. 93, 221109 (2008).
[CrossRef]

T. W. Ebbesen, G. Cyriaque, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

2007 (3)

I. I. Smolyaninov, Y-U. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Phys. Rev. B 76, 205424 (2007).
[CrossRef]

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, Phys. Rev. B 76, 035408 (2007).
[CrossRef]

2005 (1)

T. Sondergaard and S. I. Bozhevolnyi, Phys. Rev. B 71, 125429 (2005).
[CrossRef]

2001 (1)

P. Bienstman and R. Baets, Opt. Quantum Electron. 33, 327 (2001).
[CrossRef]

2000 (1)

H. S. Eisenberg and Y. Silberberg, Phys. Rev. Lett. 85, 1863 (2000).

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).

1997 (1)

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and C. C. Davis, Phys. Rev. B 56, 1601 (1997).
[CrossRef]

1977 (1)

1956 (1)

S. M. Rytov, Sov. Phys. JETP 2, 466 (1956).

Andreev, S.

Baets, R.

P. Bienstman and R. Baets, Opt. Quantum Electron. 33, 327 (2001).
[CrossRef]

Belotelov, V.

Bienstman, P.

P. Bienstman and R. Baets, Opt. Quantum Electron. 33, 327 (2001).
[CrossRef]

Bozhevolnyi, S. I.

T. W. Ebbesen, G. Cyriaque, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

T. Sondergaard and S. I. Bozhevolnyi, Phys. Rev. B 71, 125429 (2005).
[CrossRef]

Bykov, D.

Cyriaque, G.

T. W. Ebbesen, G. Cyriaque, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

Davis, C. C.

I. I. Smolyaninov, Y-U. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Phys. Rev. B 76, 205424 (2007).
[CrossRef]

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and C. C. Davis, Phys. Rev. B 56, 1601 (1997).
[CrossRef]

Devaux, E.

B. Stein, J. N. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

B. Stein, J. Laluet, E. Devaux, C. Genet, and T. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Doskolovich, L.

Ebbesen, T.

B. Stein, J. Laluet, E. Devaux, C. Genet, and T. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Ebbesen, T. W.

B. Stein, J. N. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

T. W. Ebbesen, G. Cyriaque, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg and Y. Silberberg, Phys. Rev. Lett. 85, 1863 (2000).

Elser, J.

Genet, C.

B. Stein, J. N. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

B. Stein, J. Laluet, E. Devaux, C. Genet, and T. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Hong, C.

Hung, Y.-J.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Phys. Rev. B 76, 205424 (2007).
[CrossRef]

Hung, Y-U.

I. I. Smolyaninov, Y-U. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Jacob, Z.

Z. Jacob and E. Narimanov, Appl. Phys. Lett. 93, 221109 (2008).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).

Laluet, J.

B. Stein, J. Laluet, E. Devaux, C. Genet, and T. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Laluet, J. N.

B. Stein, J. N. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Liu, Y.

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, Phys. Rev. B 76, 035408 (2007).
[CrossRef]

Mait, J.

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and C. C. Davis, Phys. Rev. B 56, 1601 (1997).
[CrossRef]

Mazzoni, D. L.

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and C. C. Davis, Phys. Rev. B 56, 1601 (1997).
[CrossRef]

Narimanov, E.

Z. Jacob and E. Narimanov, Appl. Phys. Lett. 93, 221109 (2008).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).

Oulton, R. F.

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, Phys. Rev. B 76, 035408 (2007).
[CrossRef]

Pile, D. F. P.

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, Phys. Rev. B 76, 035408 (2007).
[CrossRef]

Podolskiy, V. A.

Rytov, S. M.

S. M. Rytov, Sov. Phys. JETP 2, 466 (1956).

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).

Schevchenko, V. V.

V. V. Schevchenko, Continuous Transitions in Open Waveguides (Golem, 1971).

Silberberg, Y.

H. S. Eisenberg and Y. Silberberg, Phys. Rev. Lett. 85, 1863 (2000).

Smolyaninov, I. I.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Phys. Rev. B 76, 205424 (2007).
[CrossRef]

I. I. Smolyaninov, Y-U. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and C. C. Davis, Phys. Rev. B 56, 1601 (1997).
[CrossRef]

Sondergaard, T.

T. Sondergaard and S. I. Bozhevolnyi, Phys. Rev. B 71, 125429 (2005).
[CrossRef]

Stein, B.

B. Stein, J. N. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

B. Stein, J. Laluet, E. Devaux, C. Genet, and T. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Stocksman, M. I.

M. I. Stocksman, Phys. Today 64(2), 39 (2011).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).

Tarakanov, V.

Thongrattanasiri, S.

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).

Yariv, A.

Yeh, P.

Zhang, X.

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, Phys. Rev. B 76, 035408 (2007).
[CrossRef]

Zvezdin, A.

Appl. Phys. Lett. (2)

Z. Jacob and E. Narimanov, Appl. Phys. Lett. 93, 221109 (2008).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).

J. Opt. Soc. Am. (1)

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

Opt. Quantum Electron. (1)

P. Bienstman and R. Baets, Opt. Quantum Electron. 33, 327 (2001).
[CrossRef]

Phys. Rev. B (4)

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Phys. Rev. B 76, 205424 (2007).
[CrossRef]

T. Sondergaard and S. I. Bozhevolnyi, Phys. Rev. B 71, 125429 (2005).
[CrossRef]

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, Phys. Rev. B 76, 035408 (2007).
[CrossRef]

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and C. C. Davis, Phys. Rev. B 56, 1601 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

B. Stein, J. N. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

B. Stein, J. Laluet, E. Devaux, C. Genet, and T. Ebbesen, Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

H. S. Eisenberg and Y. Silberberg, Phys. Rev. Lett. 85, 1863 (2000).

Phys. Today (2)

M. I. Stocksman, Phys. Today 64(2), 39 (2011).
[CrossRef]

T. W. Ebbesen, G. Cyriaque, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

Science (1)

I. I. Smolyaninov, Y-U. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Sov. Phys. JETP (1)

S. M. Rytov, Sov. Phys. JETP 2, 466 (1956).

Other (2)

www.comsol.com .

V. V. Schevchenko, Continuous Transitions in Open Waveguides (Golem, 1971).

Supplementary Material (2)

» Media 1: AVI (1554 KB)     
» Media 2: AVI (1538 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

(a) Geometry of the system (d1=230nm, d2=110nm, h=90nm) and the profiles of guided modes supported by its components; (b)–(d) propagation of the surface plasmon polariton (SPP) incident on corrugated structure. (b) and (c) show intensity distribution obtained with finite element method (FEM) and mode-matching calculations, respectively; note the logarithmic scale. (d) SPP amplitude (dashes) and its field intensity (at x=0, solid line) throughout the system; intensity of SPP on the smooth metal surface (dotted line), normalized to the intensity of SPP in corrugated structure after initial scattering (reported for comparison).

Fig. 2.
Fig. 2.

Dispersion of the guided mode; (a) real and (b) imaginary parts of quasi-wave-vector q as a function of frequency and ky shown. Surfaces, numerical calculations; dots, Eq. (2). See Media 1 and Media 2 for more details.

Fig. 3.
Fig. 3.

(a) Refraction in the system; box illustrates the diffraction-suppressed region. (b) Diffraction of the beams (characterized by widening of the beam profile at z=2μm) in plasmonic (dashed line) and PMMA guides (dots) and in corrugated plasmonic crystal (solid line and inset). (c), (d) Intensity distribution caused by a point emitter in the homogeneous plasmonic system (c) and in plasmonic crystal (d). Surface: FEM calculations. Arrows: analytical Eqs. (2) and (3) with θ being the angle between beam direction and local normal.

Equations (3)

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

det|^eiqΛI^|=0.
cos(qΛ)=cos(k1d1)cos(k2d2)γsin(k1d1)sin(k2d2),
θ=tan1(vgy/vgz),

Metrics