Abstract

We present numerical experiments of light scattering by a circular dielectric cylinder embedded in a stratified background, using the Green’s tensor technique. The stratified background consists of two or three dielectric layers, the latter forming an anti–reflection system. We show movies of the scattered field as a function of different parameters: polarization, angle of incidence, and relative position of the cylinder with respect to the background interfaces.

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References

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  1. Lord Rayleigh, "On the Electromagnetic Theory of Light," Philos. Mag. 12, 81-101 (1881).
    [CrossRef]
  2. T.C. Rao and R. Barakat, "Plane-wave scattering by a conducting cylinder partially buried in a ground plane. 1. TM case," J. Opt. Soc. Am. A 6, 1270-1280 (1989).
    [CrossRef]
  3. T.C. Rao and R. Barakat, "Plane-wave scattering by a conducting cylinder partially buried in a ground plane II: TE case," J. Opt. Soc. Am. A 8, 1986-1990 (1991).
    [CrossRef]
  4. G. Videen and D. Ngo, "Light scattering from a cylinder near a plane interface: theory and comparison with experimental data," J. Opt. Soc. Am. A 14, 70-78 (1997).
    [CrossRef]
  5. P. J. Valle, F. Gonzalez, and F. Moreno, "Electromagnetic wave scattering from conducting cylindrical structures on flat substraes: study by means of the extinction theorem," Appl. Opt. 33, 512-523 (1994).
    [CrossRef] [PubMed]
  6. A. Madrazo and M. Nieto-Vesperinas, "Scattering of electromagnetic waves from a cylinder in front of a conducting plane," J. Opt. Soc. Am. A 12, 1298-1309 (1995).
    [CrossRef]
  7. R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, "Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach," J. Opt. Soc. Am. A 13, 483-493 (1996).
    [CrossRef]
  8. R. Borghi, M. Santarsiero, F. Frezza, and G. Schettini, "Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface," J. Opt. Soc. Am. A 14, 1500-1504 (1997).
    [CrossRef]
  9. J.-J.Greffet, "Scattering of s-polarized electromagnetic waves by a 2d obstacle near an interface," Opt. Commun. 72, 274-278 (1989).
    [CrossRef]
  10. M. A. Taubenblatt, "Light scattering from cylindrical structures on surfaces," Opt. Lett. 15, 255-257 (1990).
    [CrossRef] [PubMed]
  11. F. Pincemin, A. Sentenac, and J.-J. Greffet, "Near field scattered by a dielectric rod below a metallic surface," J. Opt. Soc. Am. A 11, 1117-1127 (1994).
    [CrossRef]
  12. N. P. Zhuck and A. G. Yarovoy, "Two-Dimensional Scattering from an Inhomogeneous Dielectric Cylinder Embedded in a Stratified Medium: Case of TM Polarization," IEEE Trans. Antennas & Propag. 42, 16-21 (1994).
    [CrossRef]
  13. M. Totzeck and H.J. Tiziani, "Interference microscopy of sub-lambda structures: A rigorous computation method and measurements," Opt. Commun. 136, 61-74 (1997).
    [CrossRef]
  14. M. Paulus and O.J.F. Martin, "Green's tensor technique for scattering in 2D stratified media," Phys. Rev. E 63, 066615.1-066615.8 (2001).
    [CrossRef]
  15. O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998).
    [CrossRef]
  16. J. D. Jackson, Classical electrodynamics, 3rd ed. (Wiley, New York, 1999).
  17. O. J. F. Martin, C. Girard, and A. Dereux, "Dielectric vs.topographic contrast in near-field microscopy," J. Opt. Soc. Am. A 13, 1801-1808 (1996).
    [CrossRef]
  18. C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (Wiley, New York, 1983).
  19. M. Born and E. Wolf, Principles of Optics, 6th. ed. (Pergamon Press, Oxford, 1987).

Other

Lord Rayleigh, "On the Electromagnetic Theory of Light," Philos. Mag. 12, 81-101 (1881).
[CrossRef]

T.C. Rao and R. Barakat, "Plane-wave scattering by a conducting cylinder partially buried in a ground plane. 1. TM case," J. Opt. Soc. Am. A 6, 1270-1280 (1989).
[CrossRef]

T.C. Rao and R. Barakat, "Plane-wave scattering by a conducting cylinder partially buried in a ground plane II: TE case," J. Opt. Soc. Am. A 8, 1986-1990 (1991).
[CrossRef]

G. Videen and D. Ngo, "Light scattering from a cylinder near a plane interface: theory and comparison with experimental data," J. Opt. Soc. Am. A 14, 70-78 (1997).
[CrossRef]

P. J. Valle, F. Gonzalez, and F. Moreno, "Electromagnetic wave scattering from conducting cylindrical structures on flat substraes: study by means of the extinction theorem," Appl. Opt. 33, 512-523 (1994).
[CrossRef] [PubMed]

A. Madrazo and M. Nieto-Vesperinas, "Scattering of electromagnetic waves from a cylinder in front of a conducting plane," J. Opt. Soc. Am. A 12, 1298-1309 (1995).
[CrossRef]

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, "Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach," J. Opt. Soc. Am. A 13, 483-493 (1996).
[CrossRef]

R. Borghi, M. Santarsiero, F. Frezza, and G. Schettini, "Plane-wave scattering by a dielectric circular cylinder parallel to a general reflecting flat surface," J. Opt. Soc. Am. A 14, 1500-1504 (1997).
[CrossRef]

J.-J.Greffet, "Scattering of s-polarized electromagnetic waves by a 2d obstacle near an interface," Opt. Commun. 72, 274-278 (1989).
[CrossRef]

M. A. Taubenblatt, "Light scattering from cylindrical structures on surfaces," Opt. Lett. 15, 255-257 (1990).
[CrossRef] [PubMed]

F. Pincemin, A. Sentenac, and J.-J. Greffet, "Near field scattered by a dielectric rod below a metallic surface," J. Opt. Soc. Am. A 11, 1117-1127 (1994).
[CrossRef]

N. P. Zhuck and A. G. Yarovoy, "Two-Dimensional Scattering from an Inhomogeneous Dielectric Cylinder Embedded in a Stratified Medium: Case of TM Polarization," IEEE Trans. Antennas & Propag. 42, 16-21 (1994).
[CrossRef]

M. Totzeck and H.J. Tiziani, "Interference microscopy of sub-lambda structures: A rigorous computation method and measurements," Opt. Commun. 136, 61-74 (1997).
[CrossRef]

M. Paulus and O.J.F. Martin, "Green's tensor technique for scattering in 2D stratified media," Phys. Rev. E 63, 066615.1-066615.8 (2001).
[CrossRef]

O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998).
[CrossRef]

J. D. Jackson, Classical electrodynamics, 3rd ed. (Wiley, New York, 1999).

O. J. F. Martin, C. Girard, and A. Dereux, "Dielectric vs.topographic contrast in near-field microscopy," J. Opt. Soc. Am. A 13, 1801-1808 (1996).
[CrossRef]

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (Wiley, New York, 1983).

M. Born and E. Wolf, Principles of Optics, 6th. ed. (Pergamon Press, Oxford, 1987).

Supplementary Material (8)

» Media 1: MOV (528 KB)     
» Media 2: MOV (479 KB)     
» Media 3: MOV (530 KB)     
» Media 4: MOV (452 KB)     
» Media 5: MOV (227 KB)     
» Media 6: MOV (204 KB)     
» Media 7: MOV (1052 KB)     
» Media 8: MOV (959 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Electric field amplitude distribution for the scattering by a cylinder in an infinite homogeneous background. Two different polarizations are investigated: (a) s polarization, (b) p polarization.

Fig. 2.
Fig. 2.

Electric field amplitude distribution for the scattering by a cylinder above a dielectric surface with same permittivity, as a function of the distance h between the cylinder center and the interface. Normal incidence (Θ=0°, the arrow represents the propagation direction of the illumination wave) (a) s polarization (528 KB), (b) p polarization (479 KB).

Fig. 3.
Fig. 3.

Same situation as in Fig. 2, but now the illumination field is incident at a Θ=30° angle. (a) s polarization (530 KB), (b) p polarization (452 KB).

Fig. 4.
Fig. 4.

Electric field amplitude distribution for the scattering by a cylinder above a dielectric surface with same permittivity, as a function of the illumination angle Θ (the arrow indicates the propagation direction of the illumination field). The cylinder position is kept fixed: h=615 nm. (a) s polarization (227 KB), (b) p polarization (204 KB).

Fig. 5.
Fig. 5.

Relative reflected amplitude Arefl for a two–layer medium with ε 1=1, ε 2=2, and a three–layer medium with ε 1=1,ε 2=1.334, ε 3=1.78, as a function of the angle of incidence Θ. Incident s and p polarizations are compared. The minima for p polarization correspond to the Brewster angle.

Fig. 6.
Fig. 6.

Electric field amplitude distribution for the scattering by a cylinder in a three–layer system, including an anti–reflection slab, as a function of the cylinder altitude h above the top interface. Normal incidence (Θ=0°, the arrow represents the propagation direction of the illumination wave). (a) s polarization (1052 KB), (b) p polarization (959 KB).

Equations (16)

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E ( r ) = E 0 ( r ) + A d r G ( r , r ) · k 0 2 Δ ε ( r ) E ( r ) ,
Δ ε ( r ) = ε ( r ) ε k , r layer k .
E 0 ( x , z ) = A 0 exp ( i kr ) = A 0 exp ( ik z z ) ,
E 0 ( x , z ) = A 0 [ exp ( ik 1 z z ) + R exp ( ik 1 z z ) ] , z 0 ,
E 0 ( x , z ) = A 0 T exp ( ik 2 z z ) , z < 0 ,
R = ε 1 ε 2 ε 1 + ε 2 ,
T = 2 ε 1 ε 1 + ε 2 .
A = ( E 0 · E 0 * ) 1 2 = A 0 [ 1 + R 2 + 2 R cos ( 2 k 1 z z ) ] 1 2 , z 0 ,
E α 0 ( x , z ) = A α 0 [ exp ( ik 1 z z ) + R α exp ( ik 1 z z ) ] exp ( ik x x ) , z 0 , α = x , y , z ,
R s = k 1 z k 2 z k 1 z + k 2 z ,
R P = ε 2 k 1 z ε 1 k 2 z ε 2 k 1 z + ε 1 k 2 z .
A = { A x 0 2 [ 1 + R p 2 2 R p cos ( 2 k 1 z z ) ] + A y 0 2 [ 1 + R s 2 + 2 R s cos ( 2 k 1 z z ) ]
+ A z 0 2 [ 1 + R p 2 + 2 R p cos ( 2 k 1 z z ) ] } 1 2 , z 0 .
A = A 0 ( 1 + R p 2 ) 1 2 .
ε 2 = ε 1 ε 3 1.334 ,
d = ( n + 1 2 ) λ 2 ε 2 , n = 1 , 2 , 3 ,

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