Abstract

We present the theoretical analysis of surface plasmon polaritons induced by a tightly focused light beam at oblique incidence. Firstly, we propose a geometrical model to explain the evolution of SPPs effect as light deviating from normal incidence, and introduce a concept of critical oblique angle (θco) which is one of the key factors affecting the stability, efficiency and lateral resolution of SPPs. Secondly, the integral expressions for the transmitted SPP field excited by a linearly polarized vortex beam are derived, using angular spectrum representation and rotation matrix trans-formation, for the oblique directions as parallel and perpendicular to polarization plane. An interesting finding is that the system completely goes out of SPP self-interference resonance at an incident angle smaller than θco at parallel obliquity, while larger than θco at perpendicular obliquity.

© 2013 Optical Society of America

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  1. H. Raether, Surface-Plasmons on Smooth and Rough Surfaces and on Grating, Springer Tracts in Modern Physics (Springer Berlin, 1988).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. E.  Wolf, “Electromagnetic diffraction in optical systems. I. an integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
    [CrossRef]
  15. L. Novotny and B. Hetch, Principle of Nano-optics (Cambridge U. Press, 2006).
  16. J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, Cambridge MA, 2005).
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    [CrossRef]
  18. T. M.  Hsu, C. C.  Chang, Y. F.  Hwang, K. C.  Lee, “The Dielectric Function of Silver by ATR Technique,” Chin. J. Phys. 21(1), 26–32 (1983).

2008 (1)

2007 (1)

2006 (2)

2004 (1)

T.  Nikolajsen, K.  Leosson, S. I.  Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833 (2004).
[CrossRef]

2003 (1)

2002 (1)

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762 (2002).
[CrossRef]

2000 (1)

1998 (2)

H.  Kano, S.  Mizuguchi, S.  Kawata, “Excitation of surface-plasmon polaritons by a focused laser beam,” J. Opt. Soc. Am. B 15(4), 1381–1386 (1998).
[CrossRef]

T. W.  Ebbesen, H. J.  Lezec, H. F.  Ghaemi, T.  Thio, P. A.  Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

1993 (1)

B.  Bailey, D. L.  Farkas, D. L.  Taylor, F.  Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993).
[CrossRef] [PubMed]

1983 (1)

T. M.  Hsu, C. C.  Chang, Y. F.  Hwang, K. C.  Lee, “The Dielectric Function of Silver by ATR Technique,” Chin. J. Phys. 21(1), 26–32 (1983).

1972 (1)

P. B.  Johnson, R. W.  Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1959 (2)

B.  Richards, E.  Wolf, “Electromagnetic diffraction in optical systems. II. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

E.  Wolf, “Electromagnetic diffraction in optical systems. I. an integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[CrossRef]

Aussenegg, F. R.

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762 (2002).
[CrossRef]

Bailey, B.

B.  Bailey, D. L.  Farkas, D. L.  Taylor, F.  Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993).
[CrossRef] [PubMed]

Bouhelier, A.

Bozhevolnyi, S. I.

T.  Nikolajsen, K.  Leosson, S. I.  Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833 (2004).
[CrossRef]

Bruyant, A.

Burge, R. E.

Chang, C. C.

T. M.  Hsu, C. C.  Chang, Y. F.  Hwang, K. C.  Lee, “The Dielectric Function of Silver by ATR Technique,” Chin. J. Phys. 21(1), 26–32 (1983).

Christy, R. W.

P. B.  Johnson, R. W.  Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Chung, E.

Colas des Francs, G.

Cragg, G. E.

Dereux, A.

Ditlbacher, H.

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762 (2002).
[CrossRef]

Ebbesen, T. W.

T. W.  Ebbesen, H. J.  Lezec, H. F.  Ghaemi, T.  Thio, P. A.  Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Farkas, D. L.

B.  Bailey, D. L.  Farkas, D. L.  Taylor, F.  Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993).
[CrossRef] [PubMed]

Gan, X. S.

Ganic, D.

Ghaemi, H. F.

T. W.  Ebbesen, H. J.  Lezec, H. F.  Ghaemi, T.  Thio, P. A.  Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Gu, M.

Hsu, T. M.

T. M.  Hsu, C. C.  Chang, Y. F.  Hwang, K. C.  Lee, “The Dielectric Function of Silver by ATR Technique,” Chin. J. Phys. 21(1), 26–32 (1983).

Huang, C.

Hwang, Y. F.

T. M.  Hsu, C. C.  Chang, Y. F.  Hwang, K. C.  Lee, “The Dielectric Function of Silver by ATR Technique,” Chin. J. Phys. 21(1), 26–32 (1983).

Ignatovich, F.

Johnson, P. B.

P. B.  Johnson, R. W.  Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kano, H.

Kawata, S.

Kim, D. K.

Krenn, J. R.

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762 (2002).
[CrossRef]

Lanni, F.

B.  Bailey, D. L.  Farkas, D. L.  Taylor, F.  Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993).
[CrossRef] [PubMed]

Lee, K. C.

T. M.  Hsu, C. C.  Chang, Y. F.  Hwang, K. C.  Lee, “The Dielectric Function of Silver by ATR Technique,” Chin. J. Phys. 21(1), 26–32 (1983).

Leitner, A.

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762 (2002).
[CrossRef]

Leosson, K.

T.  Nikolajsen, K.  Leosson, S. I.  Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833 (2004).
[CrossRef]

Lezec, H. J.

T. W.  Ebbesen, H. J.  Lezec, H. F.  Ghaemi, T.  Thio, P. A.  Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Lin, J.

Mizuguchi, S.

Nikolajsen, T.

T.  Nikolajsen, K.  Leosson, S. I.  Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833 (2004).
[CrossRef]

Novotny, L.

Richards, B.

B.  Richards, E.  Wolf, “Electromagnetic diffraction in optical systems. II. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Schider, G.

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762 (2002).
[CrossRef]

So, P. T. C.

Tan, P. S.

Taylor, D. L.

B.  Bailey, D. L.  Farkas, D. L.  Taylor, F.  Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993).
[CrossRef] [PubMed]

Thio, T.

T. W.  Ebbesen, H. J.  Lezec, H. F.  Ghaemi, T.  Thio, P. A.  Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Wang, Q.

Weeber, J.-C.

Wiederrecht, G. P.

Wolf, E.

B.  Richards, E.  Wolf, “Electromagnetic diffraction in optical systems. II. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

E.  Wolf, “Electromagnetic diffraction in optical systems. I. an integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[CrossRef]

Wolff, P. A.

T. W.  Ebbesen, H. J.  Lezec, H. F.  Ghaemi, T.  Thio, P. A.  Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Yuan, X. C.

Zhan, Q. W.

Appl. Phys. Lett. (2)

H.  Ditlbacher, J. R.  Krenn, G.  Schider, A.  Leitner, F. R.  Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762 (2002).
[CrossRef]

T.  Nikolajsen, K.  Leosson, S. I.  Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833 (2004).
[CrossRef]

Chin. J. Phys. (1)

T. M.  Hsu, C. C.  Chang, Y. F.  Hwang, K. C.  Lee, “The Dielectric Function of Silver by ATR Technique,” Chin. J. Phys. 21(1), 26–32 (1983).

J. Opt. Soc. Am. B (1)

Nature (2)

T. W.  Ebbesen, H. J.  Lezec, H. F.  Ghaemi, T.  Thio, P. A.  Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

B.  Bailey, D. L.  Farkas, D. L.  Taylor, F.  Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. B (1)

P. B.  Johnson, R. W.  Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Proc. R. Soc. Lond. A Math. Phys. Sci. (2)

B.  Richards, E.  Wolf, “Electromagnetic diffraction in optical systems. II. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

E.  Wolf, “Electromagnetic diffraction in optical systems. I. an integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[CrossRef]

Other (3)

L. Novotny and B. Hetch, Principle of Nano-optics (Cambridge U. Press, 2006).

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, Cambridge MA, 2005).

H. Raether, Surface-Plasmons on Smooth and Rough Surfaces and on Grating, Springer Tracts in Modern Physics (Springer Berlin, 1988).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of SPPs excitation by a tightly focused vortex beam obliquely incident on a metal film.

Fig. 2
Fig. 2

Schematic of focused light beam converging towards the geometric focus o on the metal/glass interface located at the z = 0 plane. The cross-sectional circle in dash line represents the light rays with cone semi-angle being equal to SPPs resonant angle θsp in the vicinity of the focal plane, while the circle in solid line represents light rays with cone semi-angle being equal to the maximum convergence angle θmax. Cn and Co are the positions of the optical axis on the cross-sectional plane at normal and oblique incidence, respectively. (a) normal incidence; (b)oblique incidence in the xoz plane;(c) 3-D plot of a focused beam which is geometrically at critical obliquity for SPPs excitation.

Fig. 3
Fig. 3

(a) Schematic of oblique incidence of light focused on a gold film deposited on glass, θmax = 55°, α = 5° ; (b)The SPP waves excited by light with incident angle of θA = 50° and θB = 60°, respectively.

Fig. 4
Fig. 4

SPP interference pattern maps on the Au film surface excited by a x-polarized 532nm vortex beam at (a) 10° of parallel obliquity and (b) 30° of perpendicular obliquity.

Fig. 5
Fig. 5

SPP intensity profiles (a) along x-axis at different angle of parallel obliquity and (b) along y-axis at different angle of perpendicular obliquity.

Fig. 6
Fig. 6

The normalized peak intensity of SPPs self-interference on Ag film excited by a 532nm vortex beam at different angle of (a) parallel and (b) perpendicular obliquity.

Fig. 7
Fig. 7

The FWHM of the SPPs self-interference intensity profile on Ag film excited by a 532nm vortex beam at different angle of (a) parallel and (b) perpendicular obliquity.

Equations (17)

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θ co = cos 1 ( cos θ max / cos θ sp )
E inc ( k x , k y )= E inc x= E 0 exp(- k x 2 + k y 2 k 1 2 NA 2 n 1 2 +ilϕ)x
E t (x,y,z)= if e i k 1 f 2π k x k y t p ( k zj )( E inc n ρ ) n θ k z1 / k 1 k z1 exp[i( k x x+ k y y+ k z3 z)]d k x d k y
t p ( k zj )= 4exp[i( k z2 k z3 )d] (1+ p 12 )(1+ p 23 )[1+ r 12 r 23 exp(i2 k z2 d)] p ij = ε i k zj ε j k zi , r ij = 1 p ij 1+ p ij , k zj = k j 2 ( k x 2 + k y 2 )
E t ( x , y , z )= if e i k 1 f 2π k x k y t p ( k z j )( E inc n ρ ) n θ k z1 / k 1 k z 1 exp[i( k x x + k y y + k z 3 z )]d k x d k y
[ x y z ]=R[ x y z ],[ k x k y k z 1 ]=R[ k x k y k z1 ]
R=[ cosα 0 sinα 0 1 0 sinα 0 cosα ]
n ρ = k x k x 2 + k y 2 x+ k y k x 2 + k y 2 y= k x cosα k x 2 + k y 2 x+ k y k x 2 + k y 2 y k x sinα k x 2 + k y 2 z
E inc n ρ = E inc k x cosα k x 2 + k y 2
| ( k x , k y ) ( k x , k y ) |=cosα+ k x k z1 sinα
E t ( x , y ) z = if e i k 1 f 2π k x k y E inc ( k x , k y ) t p [ k z j ( k x , k y )]exp(i k z 3 d)( k x cosα k z1 sinα ) ×exp{ i[( k x cosα k z1 sinα) x + k y y ] }cosα k z1 / k 1 k 1 k z1 d k x d k y
E t ( x , y ) z = if k 1 e i k 1 f 2π 0 θ max 0 2π E inc (θ,ϕ) t p [ k z j (θ,ϕ)]exp(i k z 3 d)(sinθcosϕcosαcosθsinα)× exp{ i k 1 [(sinθcosϕcosαcosθsinα) x +sinθsinϕ y ] }cosα cosθ sinθdθdϕ
R=[ 1 0 0 0 cosβ sinβ 0 sinβ cosβ ]
E inc n ρ = E inc k x k x 2 + k y 2
| ( k x , k y ) ( k x , k y ) |=cosβ k y k z1 sinβ
E t ( x , y ) z = if e i k 1 f 2π k x k y E inc ( k x , k y ) t p [ k z j ( k x , k y )]exp(i k z 3 d) × k x exp{ i[( k x x +( k y cosβ+ k z1 sinβ) y ] } k z1 / k 1 k 1 k z1 d k x d k y
E t ( x , y ) z = if k 1 e i k 1 f 2π 0 θ max 0 2π E inc (θ,ϕ) t p [ k z j (θ,ϕ)] exp(i k z 3 d) sin 2 θ cosθ ×exp{ i k 1 [sinθcosϕ x +(sinθsinϕcosβ+cosθsinβ) y ] }cosϕdθdϕ

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