Abstract

We observe and theoretically analyze the plasmonic analog of the critical angle phenomenon in optical transmission through subwavelength gratings milled in an optically thick metal film. The total transmission from a denser medium to a less dense one vanishes while the total reflection holds very strong, providing the incidence angle increases past the plasmonic critical angle (PCA). The conditions and physical origins of the total internal reflection above the PCA are clarified.

© 2011 Optical Society of America

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2011 (2)

A. Alù, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef] [PubMed]

M. Guillaumée, L. A. Dunbar, and R. P. Stanley, Opt. Express 19, 4740 (2011).
[CrossRef] [PubMed]

2010 (2)

2009 (1)

2007 (2)

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]

2002 (1)

Q. Cao and P. Lalanne, Phys. Rev. Lett. 88, 057403(2002).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1997 (1)

1995 (1)

1992 (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]

Alù, A.

A. Alù, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef] [PubMed]

Bloemer, M. J.

A. Alù, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef] [PubMed]

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]

Brongersma, M. L.

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

Cao, Q.

Q. Cao and P. Lalanne, Phys. Rev. Lett. 88, 057403(2002).
[CrossRef] [PubMed]

D’Aguanno, G.

A. Alù, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef] [PubMed]

Dennis, M. R.

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]

Dunbar, L. A.

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]

Gao, H.

García de Abajo, F. J.

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]

Grann, E. B.

Gray, S. K.

Guillaumée, M.

Henzie, J.

Kobayashi, T.

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.

B. Wang and P. Lalanne, J. Opt. Soc. Am. A 27, 1432 (2010).
[CrossRef]

Q. Cao and P. Lalanne, Phys. Rev. Lett. 88, 057403(2002).
[CrossRef] [PubMed]

Lee, M. H.

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]

Liu, S.

Mattiucci, N.

A. Alù, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef] [PubMed]

Maystre, D.

McMahon, J. M.

Moharam, M. G.

Morimoto, A.

Nieto-Vesperinas, M.

Odom, T. W.

Palik, E. D.

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

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Petit, R.

R. Petit, Electromagnetic Theory of Gratings (Springer, 1980).
[CrossRef]

Pommet, D. A.

Schatz, G. C.

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]

Song, Y.

Stanley, R. P.

Takahara, J.

Taki, H.

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, B.

Wang, Y.

Yamagishi, S.

Yang, K.

Zhang, X.

Zheludev, N. I.

Zhou, K.

Zia, R.

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

J. Opt. Soc. Am. A (3)

Nat. Nanotechnol. (1)

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

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (4)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

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]

A. Alù, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef] [PubMed]

Q. Cao and P. Lalanne, Phys. Rev. Lett. 88, 057403(2002).
[CrossRef] [PubMed]

Other (2)

R. Petit, Electromagnetic Theory of Gratings (Springer, 1980).
[CrossRef]

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

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Figures (4)

Fig. 1
Fig. 1

Schematics of periodic metallic slits of period p, width w, milled in an optically thick metal film of thickness h, and refractive index n m , filled with a medium of refractive index n s , sandwiched in two media of refractive indices n 1 and n 2 on the top and the bottom, respectively, and illuminated by the TM-polarized (magnetic vector along the y axis) optical plane wave of incidence angle θ and wavelength λ.

Fig. 2
Fig. 2

(a), (c), (e) Total transmission T and (b), (d), (f) total reflection R as functions of θ and p. Vertical thick black dashed lines stand for θ c and thin blue dashed curves indicate θ B . The calculations are performed with λ = 2 μm , n 1 = n s = 1.8 , n 2 = 1.75 , and n m = n Au . (a), (b)  f = 0.25 , h = 200 nm , (c), (d)  f = 0.5 , h = 200 nm , and (e), (f)  f = 0.25 , h = 300 nm .

Fig. 3
Fig. 3

(a), (c), (e) T and (b), (d), (f) R as functions of θ and λ. Vertical thick black dashed lines are for θ c , horizontal thin blue solid lines indicate FP resonances, thin blue dashed curves stand for θ B . The calculations are performed with p = 100 nm , f = 0.25 , h = 200 nm , and n m = n Au . (a), (b)  n 1 = n s = 1.75 , n 2 = 1.8 , (c), (d)  n 1 = n s = 1.8 , n 2 = 1.75 , and (e), (f)  n 1 = n s = 1.9 , n 2 = 1.75 .

Fig. 4
Fig. 4

Total magnetic fields | H y | of the (a)–(c) dielectric bilayer ( n m = n s = n 1 ), (d)–(f) dielectric–metal–dielectric trilayer ( n m = n s = n Au ), and (g)–(i) metallic grating sandwiched in the dielectric bilayer ( n m = n Au , n s = n 1 ) for three cases: θ < θ c , θ = θ c , and θ > θ c , where the structures are outlined by thin blue lines. The calculations are performed with λ = 2 μm , p = 500 nm , f = 0.2 , h = 200 nm , n 1 = 1.8 , and n 2 = 1.75 , where θ c = 76.5 ° .

Equations (6)

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θ c = arcsin ( n 2 / n 1 ) .
H y ( 1 ) ( x , z ) = exp ( i k x , 0 x + i k z , 0 ( 1 ) z ) + m r m exp ( i k x , m x i k z , m ( 1 ) z ) ,
H y ( 2 ) ( x , z ) = m t m exp [ i k x , m x + i k z , m ( 2 ) ( z h ) ] ,
T m = | t m | 2 Re ( n 1 k z , m ( 2 ) ) / [ ( n 2 ) 2 k 0 cos θ ] ,
R m = | r m | 2 Re ( k z , m ( 1 ) ) / ( n 1 k 0 cos θ ) ,
± n d = n 1 sin θ RA , m ( d ) + m λ / p ,

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