Abstract

It is shown that the presence of an arbitrary body buried near a dielectric highly rough random surface produces a remarkable enhanced backscattering peak in the angular distribution of mean scattered intensity. This is in contrast with the distribution that the dielectric rough surface yields in the absence of the body. In order for the peak to appear, the surface must be very rough and the contrast between the dielectric constants of the body and the medium in which it is immersed must be 2 at least. We illustrate the results with a two-dimensional (2-D) calculation of a cylinder in front of a 2-D rough profile immersed in a dielectric medium. Different cases have been addressed in order to investigate the dependence of the backscattering enhancement on several physical parameters such as the width of the incident beam; the size, position, and optical constant of the buried cylinder; and the surface correlation function, as well as the difficult task of performing averages that resemble the ideal ensemble averaging of the rough surface in this system.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1990).
  2. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 7.
  3. D. Maystre, J. C. Dainty, eds., feature issue on “Modern Analysis of Scattering Phenomena,” Waves Random Media1, (No. 3) (1991).
  4. J. M. Bennett, ed., Surface Finish and Its Measurement, Vol. 2 of Collected Works in Optics (Optical Society of America, Washington, D.C., 1992).
  5. K. A. O’Donnell, E. R. Mendez, “Experimental study of scattering of electromagnetic waves from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
    [CrossRef]
  6. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monte Carlo simulations for scattering of electromagnetic waves from perfectly conductive random rough surfaces,” Opt. Lett. 12, 979–981 (1987).
    [CrossRef] [PubMed]
  7. A. A. Maradudin, E. R. Mendez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random metallic grating,” Opt. Lett. 14, 151–153 (1989).
    [CrossRef]
  8. M. J. Kim, J. C. Dainty, A. T. Friberg, A. J. Sant, “Experimental study of enhanced backscattering from one- and two-dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
    [CrossRef]
  9. J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Light scattering from rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991).
    [CrossRef]
  10. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).
  11. L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
    [CrossRef]
  12. K. O’Neill, R. F. Lussky, K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
    [CrossRef]
  13. L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
    [CrossRef] [PubMed]
  14. S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photonics News 7(3), 17 (1996).
    [CrossRef]
  15. A. Madrazo, 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]
  16. R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
    [CrossRef]
  17. A. Madrazo, M. Nieto-Vesperinas, “Surface structure and polariton interactions in the scattering of electromagnetic waves from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 785–795 (1996);A. Madrazo, M. Nieto-Vesperinas, “Reconstruction of corrugated dielectric surfaces with a model of a photon scanning tunneling microscope: influence of the tip in the near field,” J. Opt. Soc. Am. A 14, 612–628 (1997).
    [CrossRef]
  18. J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
    [CrossRef]
  19. E. Jakeman, “Enhanced backscattering through a deep random phase screen,” J. Opt. Soc. Am. A 5, 1638–1648 (1988);Ref. 1, pp. 111–123.
    [CrossRef]
  20. C. S. West, K. A. O’Donnell, “Observations of backscattering enhancement from polaritons on a rough metal surface,” J. Opt. Soc. Am. A 12, 390–397 (1995);C. S. West, K. A. O’Donnell, “Scattering by plasmon polaritons on a metal surface with a detuned roughness spectrum,” Opt. Lett. 21, 1–3 (1996).
    [CrossRef] [PubMed]
  21. A. A. Maradudin, A. R. McGurn, E. R. Mendez, “Surface plasmon polariton mechanism for enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995);A. Madrazo, A. A. Maradudin, “Numerical solutions of the reduced Rayleigh equations for the scattering of electromagnetic waves from rough dielectric films on perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
    [CrossRef]
  22. P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
    [CrossRef]

1996 (4)

L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
[CrossRef]

K. O’Neill, R. F. Lussky, K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photonics News 7(3), 17 (1996).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Surface structure and polariton interactions in the scattering of electromagnetic waves from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 785–795 (1996);A. Madrazo, M. Nieto-Vesperinas, “Reconstruction of corrugated dielectric surfaces with a model of a photon scanning tunneling microscope: influence of the tip in the near field,” J. Opt. Soc. Am. A 14, 612–628 (1997).
[CrossRef]

1995 (3)

1994 (2)

R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
[CrossRef]

1992 (1)

J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

1991 (2)

J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Light scattering from rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991).
[CrossRef]

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

1988 (1)

E. Jakeman, “Enhanced backscattering through a deep random phase screen,” J. Opt. Soc. Am. A 5, 1638–1648 (1988);Ref. 1, pp. 111–123.
[CrossRef]

1987 (2)

Alfano, R. R.

S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photonics News 7(3), 17 (1996).
[CrossRef]

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Carminati, R.

R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

Celli, V.

Dainty, J. C.

Friberg, A. T.

Gayen, S. K.

S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photonics News 7(3), 17 (1996).
[CrossRef]

Ho, P. P.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Jakeman, E.

E. Jakeman, “Enhanced backscattering through a deep random phase screen,” J. Opt. Soc. Am. A 5, 1638–1648 (1988);Ref. 1, pp. 111–123.
[CrossRef]

Kim, M. J.

Kong, J. A.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Liu, C.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Lussky, R. F.

K. O’Neill, R. F. Lussky, K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

Madrazo, A.

Maradudin, A. A.

McGurn, A. R.

Mendez, E. R.

Michel, T.

Nieto-Vesperinas, M.

A. Madrazo, M. Nieto-Vesperinas, “Surface structure and polariton interactions in the scattering of electromagnetic waves from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 785–795 (1996);A. Madrazo, M. Nieto-Vesperinas, “Reconstruction of corrugated dielectric surfaces with a model of a photon scanning tunneling microscope: influence of the tip in the near field,” J. Opt. Soc. Am. A 14, 612–628 (1997).
[CrossRef]

A. Madrazo, 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. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Light scattering from rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991).
[CrossRef]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monte Carlo simulations for scattering of electromagnetic waves from perfectly conductive random rough surfaces,” Opt. Lett. 12, 979–981 (1987).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 7.

O’Donnell, K. A.

O’Neill, K.

K. O’Neill, R. F. Lussky, K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

Pak, K.

L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
[CrossRef]

Paulsen, K. D.

K. O’Neill, R. F. Lussky, K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

Sanchez-Gil, J. A.

J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Light scattering from rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991).
[CrossRef]

Sant, A. J.

Shin, R. T.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Soto-Crespo, J. M.

Tran, P.

Tsang, L.

L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
[CrossRef]

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Wang, L.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

West, C. S.

Zhang, G.

L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
[CrossRef]

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

IEEE Trans. Geosci. Remote Sens. (1)

K. O’Neill, R. F. Lussky, K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

J. Opt. Soc. Am. A (9)

A. Madrazo, 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]

A. Madrazo, M. Nieto-Vesperinas, “Surface structure and polariton interactions in the scattering of electromagnetic waves from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 785–795 (1996);A. Madrazo, M. Nieto-Vesperinas, “Reconstruction of corrugated dielectric surfaces with a model of a photon scanning tunneling microscope: influence of the tip in the near field,” J. Opt. Soc. Am. A 14, 612–628 (1997).
[CrossRef]

K. A. O’Donnell, E. R. Mendez, “Experimental study of scattering of electromagnetic waves from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
[CrossRef]

M. J. Kim, J. C. Dainty, A. T. Friberg, A. J. Sant, “Experimental study of enhanced backscattering from one- and two-dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
[CrossRef]

J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Light scattering from rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991).
[CrossRef]

E. Jakeman, “Enhanced backscattering through a deep random phase screen,” J. Opt. Soc. Am. A 5, 1638–1648 (1988);Ref. 1, pp. 111–123.
[CrossRef]

C. S. West, K. A. O’Donnell, “Observations of backscattering enhancement from polaritons on a rough metal surface,” J. Opt. Soc. Am. A 12, 390–397 (1995);C. S. West, K. A. O’Donnell, “Scattering by plasmon polaritons on a metal surface with a detuned roughness spectrum,” Opt. Lett. 21, 1–3 (1996).
[CrossRef] [PubMed]

A. A. Maradudin, A. R. McGurn, E. R. Mendez, “Surface plasmon polariton mechanism for enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995);A. Madrazo, A. A. Maradudin, “Numerical solutions of the reduced Rayleigh equations for the scattering of electromagnetic waves from rough dielectric films on perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
[CrossRef]

P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
[CrossRef]

Opt. Commun. (1)

R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

Opt. Lett. (2)

Opt. Photonics News (1)

S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photonics News 7(3), 17 (1996).
[CrossRef]

Phys. Rev. B (1)

J. A. Sanchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

Science (1)

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Other (5)

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1990).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 7.

D. Maystre, J. C. Dainty, eds., feature issue on “Modern Analysis of Scattering Phenomena,” Waves Random Media1, (No. 3) (1991).

J. M. Bennett, ed., Surface Finish and Its Measurement, Vol. 2 of Collected Works in Optics (Optical Society of America, Washington, D.C., 1992).

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 (15)

Fig. 1
Fig. 1

Scattering geometry.

Fig. 2
Fig. 2

Angular distribution of the mean reflected intensity averaged over N=800 realizations. The parameters are T=3.16λ0, σ=1.9λ0, =2.04, d=10λ0, =1, and W=8λ0. Dashed curves no cylinder; solid curves, a=1λ0; solid curves with triangles, a=2λ0; solid curves with circles, a=5λ0. (a) s polarization, θ0=0°; (b) s polarization, θ0=30°; (c) p polarization, θ0=0°; (d) p polarization, θ0=30°.

Fig. 3
Fig. 3

Same as Fig. 2, but for the mean transmitted intensity.

Fig. 4
Fig. 4

Same as Fig. 2, but for =7.5.

Fig. 5
Fig. 5

Angular distribution of the mean reflected intensity averaged over N=800 realizations (s polarization). The parameters are T=3.16λ0, σ=1.9λ0, =2.04, d=10λ0, =7.5, and a=2λ0. Dashed curves, no cylinder; solid curves, W=32λ0; solid curves with triangles, W=16λ0; solid curves with circles, W=8λ0. (a) θ0=0°, (b) θ0=30°.

Fig. 6
Fig. 6

Same as Fig. 5, but for p polarization and =1.

Fig. 7
Fig. 7

Angular distribution of the mean reflected intensity averaged over N=800 realizations (s polarization). The parameters are T=3.16λ0, σ=1.9λ0, =2.04, d=10λ0, =7.5, W=8λ0, and a=2λ0. Dashed curve, no cylinder; curve (1) cylinder located at the center of the incident beam, curve (2) cylinder shifted -8λ0 away from the beam center, curve (3) cylinder shifted -16λ0 away from the beam center. (a) θ0=0°, (b) θ0=30°.

Fig. 8
Fig. 8

Same as Fig. 7, but for p polarization and =1.

Fig. 9
Fig. 9

Angular distribution of the mean reflected intensity versus distance d (s polarization). The parameters are T=3.16λ0, σ =1.9λ0, =2.04, a=5λ0, and =7.5. (a) θ0=0°, (b) θ0=30°.

Fig. 10
Fig. 10

Backscattering peak versus d. The parameters are T=3.16λ0, σ=1.9λ0, =2.04, a=1λ0, and =1. Squares, θ0=0°; circles, θ0=30°; triangles, θ0=60°. (a) s polarization, (b) p polarization.

Fig. 11
Fig. 11

Angular distribution of the mean reflected intensity with use of the West–O’Donnell surface spectrum (see the text for details) averaged over N=800 realizations (s polarization). The parameters are kmax=0.1k0, kmin=10-4k0, σ=2λ0, =2.04, d =10λ0, =7.5, and a=2λ0. Dashed curves, no cylinder; solid curves, plane incident wave solid curves with triangles, W =16λ0; solid curves with circles, W=8λ0. (a) θ0=0°, (b) θ0=5°, (c) θ0=10°.

Fig. 12
Fig. 12

Same as Fig. 11, but for p polarization and =1.

Fig. 13
Fig. 13

Total (scattered+incident) field intensity distribution at z=8λ0. The parameters are T=3.16λ0, σ=1.9λ0, =2.04, =7.5, a=5λ0, and d=10λ0. Solid curves, average over N=500 realizations; Dotted curves, average over N =2 realizations; dashed curves, average over N=500 realizations in the absence of the cylinder; solid curves with circles, flat interface with cylinder. (a) s polarization, θ0=0°; (b) p polarization, θ0=0°; (c) s polarization, θ0=30°; (d) p polarization, θ0=30°.

Fig. 14
Fig. 14

Angular distribution of the mean reflected intensity averaged over N=400 incidence wavelengths taken from the interval [0.95λ0, 1.05λ0] (s polarization). The parameters are T=3.16λ0, σ=1.9λ0, =2.04, a=2λ0, =7.5, and W=8λ0. Dotted line curves, no cylinder; solid curves, d=10λ0; long-dashed curves: d=8λ. (a) θ0=0°, (b) θ0=10°.

Fig. 15
Fig. 15

Same as Fig. 14, but for p polarization.

Equations (9)

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

E(inc)(r, t)=(0, Φs(inc)(r), 0)exp(-iωt),
H(inc)(r, t)=(0, Φp(inc)(r), 0)exp(-iωt),
Φα(inc)(r)=exp[ik0(x sin θ0-z cos θ0)g(x, z)]×exp[-(x cos θ0+z sin θ0)2/W2],
g(x, z)=1+1k02W2 2W2 (x cos θ0+z sin θ0)2-1.
Φα(0)(r)=Φα(inc)(r)+i4D dsH0(1)(k0|r-r|)n×Φα(0)(r)-H0(1)(k0|r-r|) Φα(0)(r)n,
Φα(1)(r)=-i4 D dsH0(1)(k0|r-r|)n Φα(1)(r)-H0(1)(k0|r-r|) Φα(1)(r)n+i4 C dsH0(1)(k0|r-r|)n Φα(1)(r)-H0(1)(k0|r-r|) Φα(1)(r)n,
Φα(2)(r)=-i4 C dsH0(1)(k0|r-r|)n Φα(2)(r)-H0(1)(k0|r-r|) Φα(2)(r)n,
Iα(r, t)(θs, θ0)=rN n=1N 1Fn |Φα,n(r, t)(θs, θ0)|2,
g(|k|)=πkmax-kmin [θ(k-kmin)θ(kmax-k)+θ(-k-kmin)θ(k+kmax)],

Metrics