Abstract

The cross conversion between surface plasmon polaritons (SPPs) and quasi-cylindrical waves (CWs) is theoretically reexamined. Except for the CW-to-SPP conversion, we find the SPP-to-CW conversion, as well as the reflection and transmission of the CW, plays an indispensable role in the interaction between SPPs and light via periodic grooves. The completeness of the whole scattering coefficients is emphasized by an SPP–CW model proposed to quantitatively predict the SPP excitation efficiency for any number of periodic grooves.

© 2010 Optical Society of America

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  1. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
    [CrossRef]
  2. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401(2003).
    [CrossRef] [PubMed]
  3. G. Leveque and O. J. F. Martin, J. Appl. Phys. 100, 124301 (2006).
    [CrossRef]
  4. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, Phys. Rev. Lett. 99, 043902 (2007).
    [CrossRef] [PubMed]
  5. L. Cai, G. Li, Z. Wang, and A. Xu, Opt. Lett. 35, 127(2010).
    [CrossRef] [PubMed]
  6. X. Y. Yang, H. T. Liu, and P. Lalanne, Phys. Rev. Lett. 102, 153903 (2009).
    [CrossRef] [PubMed]
  7. P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
    [CrossRef]
  8. E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, J. Opt. Soc. Am. A 18, 2865 (2001).
    [CrossRef]
  9. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).
  10. P. Lalanne, J. P. Hugonin, and J. C. Rodier, J. Opt. Soc. Am. A 23, 1608 (2006).
    [CrossRef]
  11. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, Opt. Express 14, 11823 (2006).
    [CrossRef] [PubMed]

2010

2009

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

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
[CrossRef]

2007

O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, Phys. Rev. Lett. 99, 043902 (2007).
[CrossRef] [PubMed]

2006

2003

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401(2003).
[CrossRef] [PubMed]

2001

’t Hooft, G. W.

O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, Phys. Rev. Lett. 99, 043902 (2007).
[CrossRef] [PubMed]

O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, Opt. Express 14, 11823 (2006).
[CrossRef] [PubMed]

Cai, L.

Cao, Q.

Degiron, A.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401(2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401(2003).
[CrossRef] [PubMed]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401(2003).
[CrossRef] [PubMed]

Hugonin, J. P.

Janssen, O. T. A.

O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, Phys. Rev. Lett. 99, 043902 (2007).
[CrossRef] [PubMed]

O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, Opt. Express 14, 11823 (2006).
[CrossRef] [PubMed]

Lalanne, P.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
[CrossRef]

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

P. Lalanne, J. P. Hugonin, and J. C. Rodier, J. Opt. Soc. Am. A 23, 1608 (2006).
[CrossRef]

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

Leveque, G.

G. Leveque and O. J. F. Martin, J. Appl. Phys. 100, 124301 (2006).
[CrossRef]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401(2003).
[CrossRef] [PubMed]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

Li, G.

Linke, R. A.

Liu, H. T.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
[CrossRef]

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

Martin, O. J. F.

G. Leveque and O. J. F. Martin, J. Appl. Phys. 100, 124301 (2006).
[CrossRef]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401(2003).
[CrossRef] [PubMed]

Palik, E. D.

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

Pellerin, K. M.

Rodier, J. C.

Silberstein, E.

Thio, T.

Urbach, H. P.

O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, Phys. Rev. Lett. 99, 043902 (2007).
[CrossRef] [PubMed]

O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, Opt. Express 14, 11823 (2006).
[CrossRef] [PubMed]

Wang, B.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
[CrossRef]

Wang, Z.

Xu, A.

Yang, X. Y.

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

J. Appl. Phys.

G. Leveque and O. J. F. Martin, J. Appl. Phys. 100, 124301 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, Phys. Rev. Lett. 99, 043902 (2007).
[CrossRef] [PubMed]

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

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401(2003).
[CrossRef] [PubMed]

Surf. Sci. Rep.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
[CrossRef]

Other

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

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Figures (4)

Fig. 1
Fig. 1

(a) Electromagnetic fields scattered by N periodic grooves with groove width w, depth h, and period p under normal illumination of a plane wave polarized along the x axis. The elementary processes include (b) the scattering of the light, (c) an SPP, and (d) a CW at a single groove. A 0 , B 0 , C 0 , D 0 , , A N 1 , B N 1 , C N 1 , D N 1 , and the elementary scattering coefficients are all defined in the text.

Fig. 2
Fig. 2

Magnetic fields at the surface when (a) an SPP, (b) a CW impinges on a single groove. CWs (thick solid lines) are extracted by subtracting SPPs (dashed lines) from the total (transmitted and reflected) fields (thin solid lines). Dots show the SPPs and the generated CWs fitted with Eqs. (2). The calculations are performed for w = 0.2 λ , h = 0.1 λ with λ = 974 nm .

Fig. 3
Fig. 3

Wavelength dependence of the cross-conversion coefficients (a) r sp cw , (b) t sp cw , (c) r cw sp , and (d) t cw sp , showing good agreement with r sp , t sp 1 , r cw , and t cw , respectively. The results are obtained for w = h = 0.2 λ .

Fig. 4
Fig. 4

Comparisons between a-FMM computational data, the pure SPP model, the SPP–CW model, and the incomplete model predictions on the SPP excitation efficiency as a function of p for (a) N = 2 and (b) N = 10 , and as a function of N for (c) p = λ / Re ( n sp ) . The results are obtained for w = h = 0.2 λ with λ = 974 nm .

Equations (14)

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H y sc ( x ) = β sp exp ( i k 0 n sp | x | ) + β cw v ( | x | ) ,
H y , SPP in ref ( x < 0 ) = r sp exp ( i k 0 n sp x ) + r cw sp v ( x ) ,
H y , SPP in trans ( x > 0 ) = t sp exp ( i k 0 n sp x ) + t cw sp v ( x ) ,
H y , CW in ref ( x < 0 ) = r sp cw exp ( i k 0 n sp x ) + r cw v ( x ) ,
H y , CW in sc , trans ( x > 0 ) = t sp cw exp ( i k 0 n sp x ) + t cw v ( x ) ,
r sp cw r sp , t sp cw t sp 1 ,
r cw sp r cw , t cw sp t cw ,
B 0 = β sp + t sp u B 1 + t sp cw m = 1 N 1 D m V m ,
A 0 = β sp + r sp u B 1 + r sp cw m = 1 N 1 D m V m ,
B j = β sp + r sp u A j 1 + t sp u B j + 1 + r sp cw m = 0 j 1 C m V j m + t sp cw m = j + 1 N - 1 D m V m j for 1 j N 2 ,
A j = β sp + t sp u A j 1 + r sp u B j + 1 + t sp cw m = 0 j 1 C m V j m + r sp cw m = j + 1 N - 1 D m V m - j for 1 j N 2 ,
B N 1 = β sp + r sp u A N 2 + r sp cw m = 0 N - 2 C m V N 1 m ,
A N 1 = β sp + t sp u A N 2 + t sp cw m = 0 N - 2 C m V N 1 m ,
β 2 = β sp ( 1 + u t sp 1 - u r sp ) + β cw V 1 ( t sp cw + r sp cw u t sp 1 - u r sp ) ,

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