Abstract

The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Helmholtz equation for two dielectrics with flat interface is found and applied for the numerical calculation of the scattered field by the boundary elements method. The Green function keeps close track of scattering, including multiple reflections. The result may be applicable for the data analysis in near-field optical microscopy.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).
  2. C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
    [CrossRef]
  3. C. Girard, Rep. Prog. Phys. 68, 1883 (2005).
    [CrossRef]
  4. J. C. Chao, F. J. Rizzo, I. Elshafiey, Y. J. Liu, L. Upda, and P. A. Martin, J. Opt. Soc. Am. A 13, 338 (1996).
    [CrossRef]
  5. A. Madrazo and M. Nieto-Vesperinas, J. Opt. Soc. Am. A 12, 1298 (1995).
    [CrossRef]
  6. F. Pincemin, A. Sentenac, and J.-J. Greffet, J. Opt. Soc. Am. A 11, 1117 (1994).
    [CrossRef]
  7. A. Madrazo and M. Nieto-Vesperinas, J. Opt. Soc. Am. A 14, 2768 (1997).
    [CrossRef]
  8. I. V. Lindell, A. H. Sihvola, K. O. Muinonen, and P. W. Barber, J. Opt. Soc. Am. A 8, 472 (1991).
    [CrossRef]
  9. G. Videen, J. Opt. Soc. Am. A 8, 483 (1991).
    [CrossRef]
  10. J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133(1997).
    [CrossRef]
  11. B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, J. Chem. Phys. 112, 7761 (2000).
    [CrossRef]
  12. M. Lester and M. Nieto-Vesperinas, Opt. Lett. 24, 936(1999).
    [CrossRef]
  13. L. Novotny, R. X. Bian, and X. S. Xie, Phys. Rev. Lett. 79, 645 (1997).
    [CrossRef]
  14. K. Okamoto and S. Kawata, Phys. Rev. Lett. 83, 4534 (1999).
    [CrossRef]
  15. S. V. Perminov, V. P. Drachev, and S. G. Rautian, Opt. Express 15, 8639 (2007).
    [CrossRef] [PubMed]
  16. S. G. Rautian, Introduction to Physical Optics (URSS, 2009).
  17. F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).
  18. L. M. Brekhovskikh, Usp. Fiz. Nauk 38, 1 (1949).
  19. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Course of Theoretical Physics) (Pergamon, 1959), Vol.  6.
  20. D. L. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, 1983).
  21. C. A. Brebbia, J. C. F. Telles, and L. C. Wrobel, Boundary Element Techniques (Springer, 1984).
  22. T.W.Wu, ed., Boundary Element Acoustics: Fundamentals and Computer Codes (WIT Press, 2000).
  23. G. Beer, I. Smith, and C. Duenser, The Boundary Element Method with Programming: for Engineers and Scientists (Springer, 2008).
  24. S. V. Zymovetz and P. I. Geshev, Tech. Phys. 51, 291(2006).
    [CrossRef]
  25. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge University, 1992).
  26. R. F. Harrington, Time-Harmonic Electromagnetic Fields (Wiley, 2001).
    [CrossRef]

2007 (1)

2006 (1)

S. V. Zymovetz and P. I. Geshev, Tech. Phys. 51, 291(2006).
[CrossRef]

2005 (1)

C. Girard, Rep. Prog. Phys. 68, 1883 (2005).
[CrossRef]

2000 (1)

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, J. Chem. Phys. 112, 7761 (2000).
[CrossRef]

1999 (2)

K. Okamoto and S. Kawata, Phys. Rev. Lett. 83, 4534 (1999).
[CrossRef]

M. Lester and M. Nieto-Vesperinas, Opt. Lett. 24, 936(1999).
[CrossRef]

1997 (3)

A. Madrazo and M. Nieto-Vesperinas, J. Opt. Soc. Am. A 14, 2768 (1997).
[CrossRef]

L. Novotny, R. X. Bian, and X. S. Xie, Phys. Rev. Lett. 79, 645 (1997).
[CrossRef]

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133(1997).
[CrossRef]

1996 (2)

1995 (1)

1994 (1)

1991 (2)

1949 (1)

L. M. Brekhovskikh, Usp. Fiz. Nauk 38, 1 (1949).

Barber, P. W.

Beer, G.

G. Beer, I. Smith, and C. Duenser, The Boundary Element Method with Programming: for Engineers and Scientists (Springer, 2008).

Bian, R. X.

L. Novotny, R. X. Bian, and X. S. Xie, Phys. Rev. Lett. 79, 645 (1997).
[CrossRef]

Boisvert, R. F.

F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Brebbia, C. A.

C. A. Brebbia, J. C. F. Telles, and L. C. Wrobel, Boundary Element Techniques (Springer, 1984).

Brekhovskikh, L. M.

L. M. Brekhovskikh, Usp. Fiz. Nauk 38, 1 (1949).

Carminati, R.

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133(1997).
[CrossRef]

Chao, J. C.

Clark, C. W.

F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Colton, D. L.

D. L. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, 1983).

Deckert, V.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, J. Chem. Phys. 112, 7761 (2000).
[CrossRef]

Dereux, A.

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Drachev, V. P.

Duenser, C.

G. Beer, I. Smith, and C. Duenser, The Boundary Element Method with Programming: for Engineers and Scientists (Springer, 2008).

Elshafiey, I.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge University, 1992).

Geshev, P. I.

S. V. Zymovetz and P. I. Geshev, Tech. Phys. 51, 291(2006).
[CrossRef]

Girard, C.

C. Girard, Rep. Prog. Phys. 68, 1883 (2005).
[CrossRef]

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Greffet, J.-J.

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (Wiley, 2001).
[CrossRef]

Hecht, B.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, J. Chem. Phys. 112, 7761 (2000).
[CrossRef]

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).

Kawata, S.

K. Okamoto and S. Kawata, Phys. Rev. Lett. 83, 4534 (1999).
[CrossRef]

Kress, R.

D. L. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, 1983).

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Course of Theoretical Physics) (Pergamon, 1959), Vol.  6.

Lester, M.

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Course of Theoretical Physics) (Pergamon, 1959), Vol.  6.

Lindell, I. V.

Liu, Y. J.

Lozier, D. W.

F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Madrazo, A.

Martin, O. J. F.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, J. Chem. Phys. 112, 7761 (2000).
[CrossRef]

Martin, P. A.

Muinonen, K. O.

Nieto-Vesperinas, M.

Novotny, L.

L. Novotny, R. X. Bian, and X. S. Xie, Phys. Rev. Lett. 79, 645 (1997).
[CrossRef]

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).

Okamoto, K.

K. Okamoto and S. Kawata, Phys. Rev. Lett. 83, 4534 (1999).
[CrossRef]

Ovler, F. W. J.

F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Perminov, S. V.

Pincemin, F.

Pohl, D. W.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, J. Chem. Phys. 112, 7761 (2000).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge University, 1992).

Rautian, S. G.

Rizzo, F. J.

Sentenac, A.

Sick, B.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, J. Chem. Phys. 112, 7761 (2000).
[CrossRef]

Sihvola, A. H.

Smith, I.

G. Beer, I. Smith, and C. Duenser, The Boundary Element Method with Programming: for Engineers and Scientists (Springer, 2008).

Telles, J. C. F.

C. A. Brebbia, J. C. F. Telles, and L. C. Wrobel, Boundary Element Techniques (Springer, 1984).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge University, 1992).

Upda, L.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge University, 1992).

Videen, G.

Wild, U. P.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, J. Chem. Phys. 112, 7761 (2000).
[CrossRef]

Wrobel, L. C.

C. A. Brebbia, J. C. F. Telles, and L. C. Wrobel, Boundary Element Techniques (Springer, 1984).

Xie, X. S.

L. Novotny, R. X. Bian, and X. S. Xie, Phys. Rev. Lett. 79, 645 (1997).
[CrossRef]

Zenobi, R.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, J. Chem. Phys. 112, 7761 (2000).
[CrossRef]

Zymovetz, S. V.

S. V. Zymovetz and P. I. Geshev, Tech. Phys. 51, 291(2006).
[CrossRef]

J. Chem. Phys. (1)

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, J. Chem. Phys. 112, 7761 (2000).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (2)

L. Novotny, R. X. Bian, and X. S. Xie, Phys. Rev. Lett. 79, 645 (1997).
[CrossRef]

K. Okamoto and S. Kawata, Phys. Rev. Lett. 83, 4534 (1999).
[CrossRef]

Prog. Surf. Sci. (1)

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133(1997).
[CrossRef]

Rep. Prog. Phys. (2)

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

C. Girard, Rep. Prog. Phys. 68, 1883 (2005).
[CrossRef]

Tech. Phys. (1)

S. V. Zymovetz and P. I. Geshev, Tech. Phys. 51, 291(2006).
[CrossRef]

Usp. Fiz. Nauk (1)

L. M. Brekhovskikh, Usp. Fiz. Nauk 38, 1 (1949).

Other (10)

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Course of Theoretical Physics) (Pergamon, 1959), Vol.  6.

D. L. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, 1983).

C. A. Brebbia, J. C. F. Telles, and L. C. Wrobel, Boundary Element Techniques (Springer, 1984).

T.W.Wu, ed., Boundary Element Acoustics: Fundamentals and Computer Codes (WIT Press, 2000).

G. Beer, I. Smith, and C. Duenser, The Boundary Element Method with Programming: for Engineers and Scientists (Springer, 2008).

S. G. Rautian, Introduction to Physical Optics (URSS, 2009).

F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge University, 1992).

R. F. Harrington, Time-Harmonic Electromagnetic Fields (Wiley, 2001).
[CrossRef]

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Geometry of light scattering.

Fig. 2
Fig. 2

Scattered intensity | H s / H inc | 2 at circle Γ as a function of angle in polar coordinates for cylinder radius R = 0.25 (dashed curve), 0.5 (dotted curve), 0.75 μm (solid curve).

Fig. 3
Fig. 3

Scattered intensity at R = 0.1 μm (solid curve) and symmetric case G 2 = 0 (dashed curve).

Equations (10)

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

( Δ + k 2 ) H = 0 , k 2 = ε ω 2 c 2 ,
[ H ] = [ 1 ε H n ] = 0 ,
( Δ + k 2 ) G = δ ( x x ) δ ( y y )
[ G ( x , y ; x , y ) ] = [ 1 ε G ( ( x , y ; x , y ) ) y ] = 0.
G ( x , y ; 0 , y ) = G q ( y , y ) e i q x d q 2 π
G q = { 1 + r ( q ) 2 μ 2 e μ 1 y μ 2 y , y < 0 1 2 μ 2 ( e μ 2 | y y | + r ( q ) e μ 2 ( y + y ) , y > 0. }
r ( q ) = ε 1 μ 2 ε 2 μ 1 ε 1 μ 2 + ε 2 μ 1 , μ 1 , 2 = q 2 k 1 , 2 2
G 1 ( x , y ; x , y ) = 1 4 i H 0 ( 1 ) ( k 2 ( x x ) 2 + ( y y ) 2 ) ,
1 2 H ( r ) = Γ ( G n H G H n ) d s + H 0 ( r ) ,
1 2 H ( r ) = Γ ( g n H g ε 3 ε 2 H n ) d s ,

Metrics