Abstract

In the elementary scattering of surface plasmon polaritons (SPPs) at individual subwavelength (sub-λ) objects on metallic surfaces, the in-plane transmission and reflection of SPPs are shown to be two related scattering processes and to satisfy some novel symmetry relations, provided that the objects are mirror symmetric and are narrow enough (<0.1λ approximately). To interpret these symmetry relations, a new generalized symmetry principle for the scattered field is put forward, which is much less limited than the classical one and is shown to have wide applications for other sub-λ scattering problems.

© 2010 Optical Society of America

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    [CrossRef]
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2010 (1)

2009 (2)

2008 (1)

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef] [PubMed]

2007 (2)

A. B. Evlyukhin, G. Brucoli, L. Martín-Moreno, S. I. Bozhevolnyi, and F. J. García-Vidal, Phys. Rev. B 76, 075426 (2007).
[CrossRef]

C. Genet and T. W. Ebbesen, Nature 445, 39 (2007).
[CrossRef] [PubMed]

2006 (2)

E. Ozbay, Science 311, 189 (2006).
[CrossRef] [PubMed]

P. Lalanne and J. P. Hugonin, Nature Phys. 2, 551 (2006).
[CrossRef]

2005 (1)

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

2003 (1)

J. Seidel, S. Grafstrom, L. Eng, and L. Bischoff, Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

2001 (1)

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

1995 (1)

’t Hooft, G. W.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Alkemade, P. F. A.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Bischoff, L.

J. Seidel, S. Grafstrom, L. Eng, and L. Bischoff, Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

Blok, H.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

A. B. Evlyukhin, G. Brucoli, L. Martín-Moreno, S. I. Bozhevolnyi, and F. J. García-Vidal, Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Brongersma, M. L.

Brucoli, G.

A. B. Evlyukhin, G. Brucoli, L. Martín-Moreno, S. I. Bozhevolnyi, and F. J. García-Vidal, Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Cai, L.

Cao, Q.

Dubois, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, Nature 445, 39 (2007).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Eliel, E. R.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Eng, L.

J. Seidel, S. Grafstrom, L. Eng, and L. Bischoff, Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

Evlyukhin, A. B.

A. B. Evlyukhin, G. Brucoli, L. Martín-Moreno, S. I. Bozhevolnyi, and F. J. García-Vidal, Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Fan, S.

García-Vidal, F. J.

A. B. Evlyukhin, G. Brucoli, L. Martín-Moreno, S. I. Bozhevolnyi, and F. J. García-Vidal, Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Gaylord, T. K.

Gbur, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Genet, C.

C. Genet and T. W. Ebbesen, Nature 445, 39 (2007).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Grafstrom, S.

J. Seidel, S. Grafstrom, L. Eng, and L. Bischoff, Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

Grann, E. B.

Hugonin, J. P.

P. Lalanne and J. P. Hugonin, Nature Phys. 2, 551 (2006).
[CrossRef]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, J. Opt. Soc. Am. A 18, 2865 (2001).
[CrossRef]

J. P. Hugonin and P. Lalanne, Reticolo Software for Grating Analysis (Institut d’Optique, 2005).

Kuzmin, N.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Lalanne, P.

X. Y. Yang, H. T. Liu, and P. Lalanne, Phys. Rev. Lett. 102, 153903 (2009).
[CrossRef] [PubMed]

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef] [PubMed]

P. Lalanne and J. P. Hugonin, Nature Phys. 2, 551 (2006).
[CrossRef]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, J. Opt. Soc. Am. A 18, 2865 (2001).
[CrossRef]

J. P. Hugonin and P. Lalanne, Reticolo Software for Grating Analysis (Institut d’Optique, 2005).

Lenstra, D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Li, G. Y.

Liu, H. T.

X. Y. Yang, H. T. Liu, and P. Lalanne, Phys. Rev. Lett. 102, 153903 (2009).
[CrossRef] [PubMed]

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef] [PubMed]

Liu, J. S. Q.

Martín-Moreno, L.

A. B. Evlyukhin, G. Brucoli, L. Martín-Moreno, S. I. Bozhevolnyi, and F. J. García-Vidal, Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Moharam, M. G.

Ozbay, E.

E. Ozbay, Science 311, 189 (2006).
[CrossRef] [PubMed]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids, Part II (Academic, 1985).

Pommet, D. A.

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Schouten, H. F.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Seidel, J.

J. Seidel, S. Grafstrom, L. Eng, and L. Bischoff, Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

Silberstein, E.

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Vassallo, C.

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

Visser, T. D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Wang, Z. H.

White, J. S.

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Xu, A. S.

Yang, X. Y.

X. Y. Yang, H. T. Liu, and P. Lalanne, Phys. Rev. Lett. 102, 153903 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. Seidel, S. Grafstrom, L. Eng, and L. Bischoff, Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

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

Nature (3)

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef] [PubMed]

C. Genet and T. W. Ebbesen, Nature 445, 39 (2007).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Nature Phys. (1)

P. Lalanne and J. P. Hugonin, Nature Phys. 2, 551 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

A. B. Evlyukhin, G. Brucoli, L. Martín-Moreno, S. I. Bozhevolnyi, and F. J. García-Vidal, Phys. Rev. B 76, 075426 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

X. Y. Yang, H. T. Liu, and P. Lalanne, Phys. Rev. Lett. 102, 153903 (2009).
[CrossRef] [PubMed]

Science (1)

E. Ozbay, Science 311, 189 (2006).
[CrossRef] [PubMed]

Other (4)

E. D. Palik, Handbook of Optical Constants of Solids, Part II (Academic, 1985).

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

J. P. Hugonin and P. Lalanne, Reticolo Software for Grating Analysis (Institut d’Optique, 2005).

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Figures (3)

Fig. 1
Fig. 1

Modulus (upper row) and argument (lower row) of τ 1 (red solid curves) and of (a) ρ or (b) ρ (blue dashed curves). The results are obtained for (a) a gold ridge and for (b) a gold groove with heights h = 0.5 λ ( λ = 1 μm , ε m = 46.45 + 3.51 i ) and with various widths w.

Fig. 2
Fig. 2

Magnetic field Re ( H y ) scattered by (a) a gold ridge and by (b) a gold groove. The objects (black superimposed lines) are illuminated by a normalized ( H y = 1 at x = z = 0 ) SPP ( λ = 1 μm ) sent from the left-hand side, which is loaded as an eigenmode of the air–gold interface in our a-FMM calculation of the field [13]. The incident SPP field has been removed to show the scattered field only. The results are obtained for ridge and groove widths w = 0.1 λ and heights h = 0.5 λ . In (b), the field below the interface ( z < 0 ) is divided by a factor of 5 to show the relatively strong field in the groove.

Fig. 3
Fig. 3

EOT data obtained for a period a = 0.94 μm , a side length 0.27 μm of square holes, and a wave length λ = 0.97 μm . (a) Scattered magnetic field Re ( H y ) on the cross section y = 0 calculated for a membrane thickness d = 0.1 λ with the fully vectorial rigorous coupled wave analysis (RCWA) [16]. A normally incident x-polarized plane wave illuminates the membrane (black superimposed lines) from the top and is normalized to have H y = 1 on the illuminated surface. The incident plane-wave field has been removed to show the scattered field only. (b) Modulus (upper row) and argument (lower row) of t 1 (red solid curves) and r (blue dashed curves) calculated with the RCWA for various d.

Equations (3)

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τ 1 ρ ,
τ 1 ρ ,
E ( s ) ( r ) = i ω D Δ ε ( r ) G ( r ; r ) [ E ( i ) ( r ) + E ( s ) ( r ) ] d 3 r ,

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