Abstract

We study the scattering of a p-polarized beam incident onto a random grating whose grooves are perpendicular to the plane of incidence. The scattered field is expressed in terms of the total magnetic field and its normal derivative on the surface of the grating. The integral equations satisfied by these functions are solved numerically for each of several hundred realizations of the surface profile possessing a Gaussian spectrum. The diffuse component of the differential reflection coefficient averaged over these realizations displays a well-defined peak in the retroreflection direction for metallic and perfectly conducting random gratings but not for random gratings on dielectric surfaces.

© 1989 Optical Society of America

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References

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  1. A. R. McGurn, A. A. Maradudin, V. Celli, Phys. Rev. B 31, 4866 (1985).
    [CrossRef]
  2. V. Celli, A. A. Maradudin, A. M. Marvin, A. R. McGurn, J. Opt. Soc. Am. A 2, 2225 (1985).
    [CrossRef]
  3. A. R. McGurn, A. A. Maradudin, J. Opt. Soc. Am. B 4, 910 (1987).
    [CrossRef]
  4. E. R. Méndez, K. A. O’Donnell, Opt. Commun. 61, 91 (1987).
    [CrossRef]
  5. K. A. O’Donnell, E. R. Méndez, J. Opt. Soc. Am. A 4, 1194 (1987).
    [CrossRef]
  6. Zu-Han Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, “Opposition effect in the scattering of light from a randomly rough metal surface,” Appl. Opt. (to be published).
  7. E. Bahar, M. A. Fitzwater, Opt. Commun. 63, 355 (1987).
    [CrossRef]
  8. Ya-Qiu in, M. Lax, “Backscattering enhancement from a randomly rough surface,” Phys. Rev. B (to be published).
  9. This approach was used effectively in several recent papers. See, for example, E. I. Thorsos, J. Acoust. Soc. Am. 83, 78 (1988);S. L. Broschat, E. I. Thorsos, A. Ishimaru, “The phase perturbation technique vs. an exact numerical method for random surface scattering,” J. Electromag. Waves Appl. (to be published).
    [CrossRef]
  10. R. R. Lentz, Radio Sci. 9, 1139 (1974).
    [CrossRef]
  11. R. M. Axline, A. K. Fung, IEEE Trans. Antennas Propag. AP-26, 482 (1978); IEEE Trans. Antennas Propag. AP-28, 949 (1980).
    [CrossRef]
  12. H. L. Chan, A. K. Fung, Radio Sci. 13, 811 (1978).
    [CrossRef]
  13. A. K. Fung, M. F. Chen, J. Opt. Soc. Am. A 2, 2274 (1985).
    [CrossRef]
  14. M. Nieto-Vesperinas, J. M. Soto-Crespo, Opt. Lett. 12, 979 (1987).
    [CrossRef] [PubMed]
  15. N. García, E. Stoll, Phys. Rev. Lett. 52, 1798 (1984).
    [CrossRef]
  16. N. García, E. Stoll, J. Opt. Soc. Am. A 2, 2240 (1985).
    [CrossRef]
  17. P. Tran, V. Celli, J. Opt. Soc. Am. A 5, 1635 (1988).
    [CrossRef]
  18. R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).
  19. A. A. Bulgakov, S. I. Khankina, Solid State Commun. 44, 55 (1982).
    [CrossRef]
  20. Xuemei Huang, A. A. Maradudin, Phys. Rev. B 36, 7827 (1987).
    [CrossRef]

1988 (2)

This approach was used effectively in several recent papers. See, for example, E. I. Thorsos, J. Acoust. Soc. Am. 83, 78 (1988);S. L. Broschat, E. I. Thorsos, A. Ishimaru, “The phase perturbation technique vs. an exact numerical method for random surface scattering,” J. Electromag. Waves Appl. (to be published).
[CrossRef]

P. Tran, V. Celli, J. Opt. Soc. Am. A 5, 1635 (1988).
[CrossRef]

1987 (6)

M. Nieto-Vesperinas, J. M. Soto-Crespo, Opt. Lett. 12, 979 (1987).
[CrossRef] [PubMed]

A. R. McGurn, A. A. Maradudin, J. Opt. Soc. Am. B 4, 910 (1987).
[CrossRef]

E. R. Méndez, K. A. O’Donnell, Opt. Commun. 61, 91 (1987).
[CrossRef]

K. A. O’Donnell, E. R. Méndez, J. Opt. Soc. Am. A 4, 1194 (1987).
[CrossRef]

E. Bahar, M. A. Fitzwater, Opt. Commun. 63, 355 (1987).
[CrossRef]

Xuemei Huang, A. A. Maradudin, Phys. Rev. B 36, 7827 (1987).
[CrossRef]

1985 (4)

1984 (1)

N. García, E. Stoll, Phys. Rev. Lett. 52, 1798 (1984).
[CrossRef]

1982 (1)

A. A. Bulgakov, S. I. Khankina, Solid State Commun. 44, 55 (1982).
[CrossRef]

1978 (2)

R. M. Axline, A. K. Fung, IEEE Trans. Antennas Propag. AP-26, 482 (1978); IEEE Trans. Antennas Propag. AP-28, 949 (1980).
[CrossRef]

H. L. Chan, A. K. Fung, Radio Sci. 13, 811 (1978).
[CrossRef]

1974 (1)

R. R. Lentz, Radio Sci. 9, 1139 (1974).
[CrossRef]

Axline, R. M.

R. M. Axline, A. K. Fung, IEEE Trans. Antennas Propag. AP-26, 482 (1978); IEEE Trans. Antennas Propag. AP-28, 949 (1980).
[CrossRef]

Bahar, E.

E. Bahar, M. A. Fitzwater, Opt. Commun. 63, 355 (1987).
[CrossRef]

Bulgakov, A. A.

A. A. Bulgakov, S. I. Khankina, Solid State Commun. 44, 55 (1982).
[CrossRef]

Celli, V.

Chan, H. L.

H. L. Chan, A. K. Fung, Radio Sci. 13, 811 (1978).
[CrossRef]

Chen, M. F.

Dummer, R. S.

Zu-Han Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, “Opposition effect in the scattering of light from a randomly rough metal surface,” Appl. Opt. (to be published).

Fitzwater, M. A.

E. Bahar, M. A. Fitzwater, Opt. Commun. 63, 355 (1987).
[CrossRef]

Fung, A. K.

A. K. Fung, M. F. Chen, J. Opt. Soc. Am. A 2, 2274 (1985).
[CrossRef]

H. L. Chan, A. K. Fung, Radio Sci. 13, 811 (1978).
[CrossRef]

R. M. Axline, A. K. Fung, IEEE Trans. Antennas Propag. AP-26, 482 (1978); IEEE Trans. Antennas Propag. AP-28, 949 (1980).
[CrossRef]

García, N.

N. García, E. Stoll, J. Opt. Soc. Am. A 2, 2240 (1985).
[CrossRef]

N. García, E. Stoll, Phys. Rev. Lett. 52, 1798 (1984).
[CrossRef]

Gu, Zu-Han

Zu-Han Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, “Opposition effect in the scattering of light from a randomly rough metal surface,” Appl. Opt. (to be published).

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

Huang, Xuemei

Xuemei Huang, A. A. Maradudin, Phys. Rev. B 36, 7827 (1987).
[CrossRef]

in, Ya-Qiu

Ya-Qiu in, M. Lax, “Backscattering enhancement from a randomly rough surface,” Phys. Rev. B (to be published).

Khankina, S. I.

A. A. Bulgakov, S. I. Khankina, Solid State Commun. 44, 55 (1982).
[CrossRef]

Lax, M.

Ya-Qiu in, M. Lax, “Backscattering enhancement from a randomly rough surface,” Phys. Rev. B (to be published).

Lentz, R. R.

R. R. Lentz, Radio Sci. 9, 1139 (1974).
[CrossRef]

Maradudin, A. A.

A. R. McGurn, A. A. Maradudin, J. Opt. Soc. Am. B 4, 910 (1987).
[CrossRef]

Xuemei Huang, A. A. Maradudin, Phys. Rev. B 36, 7827 (1987).
[CrossRef]

V. Celli, A. A. Maradudin, A. M. Marvin, A. R. McGurn, J. Opt. Soc. Am. A 2, 2225 (1985).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, Phys. Rev. B 31, 4866 (1985).
[CrossRef]

Zu-Han Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, “Opposition effect in the scattering of light from a randomly rough metal surface,” Appl. Opt. (to be published).

Marvin, A. M.

McGurn, A. R.

A. R. McGurn, A. A. Maradudin, J. Opt. Soc. Am. B 4, 910 (1987).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, Phys. Rev. B 31, 4866 (1985).
[CrossRef]

V. Celli, A. A. Maradudin, A. M. Marvin, A. R. McGurn, J. Opt. Soc. Am. A 2, 2225 (1985).
[CrossRef]

Zu-Han Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, “Opposition effect in the scattering of light from a randomly rough metal surface,” Appl. Opt. (to be published).

Méndez, E. R.

E. R. Méndez, K. A. O’Donnell, Opt. Commun. 61, 91 (1987).
[CrossRef]

K. A. O’Donnell, E. R. Méndez, J. Opt. Soc. Am. A 4, 1194 (1987).
[CrossRef]

Nieto-Vesperinas, M.

O’Donnell, K. A.

E. R. Méndez, K. A. O’Donnell, Opt. Commun. 61, 91 (1987).
[CrossRef]

K. A. O’Donnell, E. R. Méndez, J. Opt. Soc. Am. A 4, 1194 (1987).
[CrossRef]

Soto-Crespo, J. M.

Stoll, E.

N. García, E. Stoll, J. Opt. Soc. Am. A 2, 2240 (1985).
[CrossRef]

N. García, E. Stoll, Phys. Rev. Lett. 52, 1798 (1984).
[CrossRef]

Thorsos, E. I.

This approach was used effectively in several recent papers. See, for example, E. I. Thorsos, J. Acoust. Soc. Am. 83, 78 (1988);S. L. Broschat, E. I. Thorsos, A. Ishimaru, “The phase perturbation technique vs. an exact numerical method for random surface scattering,” J. Electromag. Waves Appl. (to be published).
[CrossRef]

Tran, P.

IEEE Trans. Antennas Propag. (1)

R. M. Axline, A. K. Fung, IEEE Trans. Antennas Propag. AP-26, 482 (1978); IEEE Trans. Antennas Propag. AP-28, 949 (1980).
[CrossRef]

J. Acoust. Soc. Am. (1)

This approach was used effectively in several recent papers. See, for example, E. I. Thorsos, J. Acoust. Soc. Am. 83, 78 (1988);S. L. Broschat, E. I. Thorsos, A. Ishimaru, “The phase perturbation technique vs. an exact numerical method for random surface scattering,” J. Electromag. Waves Appl. (to be published).
[CrossRef]

J. Opt. Soc. Am. A (5)

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

Opt. Commun. (2)

E. R. Méndez, K. A. O’Donnell, Opt. Commun. 61, 91 (1987).
[CrossRef]

E. Bahar, M. A. Fitzwater, Opt. Commun. 63, 355 (1987).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (2)

Xuemei Huang, A. A. Maradudin, Phys. Rev. B 36, 7827 (1987).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, Phys. Rev. B 31, 4866 (1985).
[CrossRef]

Phys. Rev. Lett. (1)

N. García, E. Stoll, Phys. Rev. Lett. 52, 1798 (1984).
[CrossRef]

Radio Sci. (2)

H. L. Chan, A. K. Fung, Radio Sci. 13, 811 (1978).
[CrossRef]

R. R. Lentz, Radio Sci. 9, 1139 (1974).
[CrossRef]

Solid State Commun. (1)

A. A. Bulgakov, S. I. Khankina, Solid State Commun. 44, 55 (1982).
[CrossRef]

Other (3)

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

Ya-Qiu in, M. Lax, “Backscattering enhancement from a randomly rough surface,” Phys. Rev. B (to be published).

Zu-Han Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, “Opposition effect in the scattering of light from a randomly rough metal surface,” Appl. Opt. (to be published).

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Figures (3)

Fig. 1
Fig. 1

Drc for a silver surface characterized by δ = 1.2 μm and a = 2 μm. λ = 612.7 nm, (ω) = −17.2 + i0.498, while g = 6.4 μm, L = 25.6 μm, and NL = 256. (a) θ0 = 0°; (b) θ0 = 20°.

Fig. 2
Fig. 2

Drc for a perfect conductor characterized by δ/a = 0.6. k0a = (ω/c)a = 20, g = L/(4.6875), and NL = 300. (a) θ0 = 0°, (b) θ0 = 20°.

Fig. 3
Fig. 3

Drc for a BaSO4 surface characterized by δ = 1.2 μm and a = 2 μm. λ = 632.8 nm, nc = 1.628 + i0.0003, while g = 6.4 μm, λ= 25.6 μm, and NL = 256. (a) θ0 = 0°; (b) θ0 = −20°.

Equations (4)

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H 2 > ( x 1 , x 3 | ω ) inc = exp { i ω c ( x 1 sin θ 0 x 3 cos θ 0 ) [ 1 + w ( x 1 , x 3 ) ] } × exp [ ( x 1 cos θ 0 + x 3 sin θ 0 ) 2 / w 2 ] ,
P sc = ( π / 2 ) π / 2 d θ s P sc ( θ s ) ,
R θ s = 1 2 ( 2 π ) 3 / 2 c ωw | r ( θ s ) | 2 [ 1 c 2 ( 1 + 2 tan 2 θ 0 ) / ( 2 ω 2 w 2 ) ] , | θ s | < π / 2 ,
r ( θ s ) = d x 1 exp { i ω c [ x 1 sin θ s + ζ ( x 1 ) cos θ s ] } × { i ω c [ ζ ( x 1 ) sin θ s cos θ s ] H ( x 1 | ω ) L ( x 1 | ω ) } .

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