Abstract

Random wave fields on the surface of a random rough metallic grating are investigated with the stochastic functional approach. For Bragg incidence the fields are expanded as the harmonics of the central spatial frequency of the grating with stochastic amplitudes that are numerically calculated by a discretized approximation that is valid for a wider spectrum than the one treated in a preceding paper [Ogura et al., Opt. Commun. 134, 1 (1997)]. It is demonstrated that the wave localization is caused by the random roughness of the surface rather than by the surface shape-dependent resonances.

© 1998 Optical Society of America

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References

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  1. P. Sheng, ed., Scattering and Localization of Classical Waves in Random Media, (World Scientific, London, 1990).
  2. M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1990).
  3. D. Maystre, J. C. Dainty, eds., Modern Analysis of Scattering Phenomena (Hilger, New York, 1991).
  4. A. A. Maradudin, T. R. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
    [CrossRef]
  5. A. Ishimaru, J. S. Chen, P. Phu, K. Yoshimoto, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, S91–S107 (1991).
    [CrossRef]
  6. L. Tsang, C. H. Chan, K. Pak, “Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations,” J. Opt. Soc. Am. A 11, 711–715 (1994).
    [CrossRef]
  7. M. Saillard, D. Maystre, “Scattering from metallic and dielectric rough surfaces,” J. Opt. Soc. Am. A 7, 982–990 (1990).
    [CrossRef]
  8. M. Saillard, “Numerical evidence of Anderson localization for electromagnetic surface waves,” Opt. Commun. 96, 1–7 (1993).
    [CrossRef]
  9. D. Maystre, M. Saillard, “Localization of light by random rough surfaces: concept of localiton,” J. Opt. Soc. Am. A 11, 680–690 (1994).
    [CrossRef]
  10. M. Saillard, “Pulse scattering by random rough surfaces: application to the study of localization,” J. Opt. Soc. Am. A 11, 2704–2709 (1994).
    [CrossRef]
  11. V. D. Freilikher, I. Yurkevich, “Backscattering enhancement from surfaces with random impedance,” Phys. Lett. A 183, 247–252 (1993).
    [CrossRef]
  12. H. Ogura, N. Takahashi, “Wave scattering from a random rough surface: reciprocal theorem and backscattering enhancement,” Waves Random Media 5, 223–242 (1995).
    [CrossRef]
  13. Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
    [CrossRef]
  14. H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
    [CrossRef]
  15. H. Ogura, Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358–10371 (1996).
    [CrossRef]
  16. H. Ogura, Z. L. Wang, Y. Sasakura, V. Freilikher, “Localization of surface plasmon waves on the surface of a random rough metallic grating with a narrow-band spectrum,” Opt. Commun. 134, 1–6 (1997).
    [CrossRef]

1997 (1)

H. Ogura, Z. L. Wang, Y. Sasakura, V. Freilikher, “Localization of surface plasmon waves on the surface of a random rough metallic grating with a narrow-band spectrum,” Opt. Commun. 134, 1–6 (1997).
[CrossRef]

1996 (1)

H. Ogura, Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358–10371 (1996).
[CrossRef]

1995 (3)

H. Ogura, N. Takahashi, “Wave scattering from a random rough surface: reciprocal theorem and backscattering enhancement,” Waves Random Media 5, 223–242 (1995).
[CrossRef]

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

1994 (3)

1993 (2)

V. D. Freilikher, I. Yurkevich, “Backscattering enhancement from surfaces with random impedance,” Phys. Lett. A 183, 247–252 (1993).
[CrossRef]

M. Saillard, “Numerical evidence of Anderson localization for electromagnetic surface waves,” Opt. Commun. 96, 1–7 (1993).
[CrossRef]

1991 (1)

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshimoto, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, S91–S107 (1991).
[CrossRef]

1990 (2)

A. A. Maradudin, T. R. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

M. Saillard, D. Maystre, “Scattering from metallic and dielectric rough surfaces,” J. Opt. Soc. Am. A 7, 982–990 (1990).
[CrossRef]

Chan, C. H.

Chen, J. S.

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshimoto, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, S91–S107 (1991).
[CrossRef]

Freilikher, V.

H. Ogura, Z. L. Wang, Y. Sasakura, V. Freilikher, “Localization of surface plasmon waves on the surface of a random rough metallic grating with a narrow-band spectrum,” Opt. Commun. 134, 1–6 (1997).
[CrossRef]

Freilikher, V. D.

V. D. Freilikher, I. Yurkevich, “Backscattering enhancement from surfaces with random impedance,” Phys. Lett. A 183, 247–252 (1993).
[CrossRef]

Ishimaru, A.

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshimoto, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, S91–S107 (1991).
[CrossRef]

Kawanishi, T.

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

Maradudin, A. A.

A. A. Maradudin, T. R. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

Maystre, D.

McGurn, A. R.

A. A. Maradudin, T. R. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

Méndez, E. R.

A. A. Maradudin, T. R. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

Michel, T. R.

A. A. Maradudin, T. R. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

Ogura, H.

H. Ogura, Z. L. Wang, Y. Sasakura, V. Freilikher, “Localization of surface plasmon waves on the surface of a random rough metallic grating with a narrow-band spectrum,” Opt. Commun. 134, 1–6 (1997).
[CrossRef]

H. Ogura, Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358–10371 (1996).
[CrossRef]

H. Ogura, N. Takahashi, “Wave scattering from a random rough surface: reciprocal theorem and backscattering enhancement,” Waves Random Media 5, 223–242 (1995).
[CrossRef]

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

Pak, K.

Phu, P.

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshimoto, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, S91–S107 (1991).
[CrossRef]

Saillard, M.

Sasakura, Y.

H. Ogura, Z. L. Wang, Y. Sasakura, V. Freilikher, “Localization of surface plasmon waves on the surface of a random rough metallic grating with a narrow-band spectrum,” Opt. Commun. 134, 1–6 (1997).
[CrossRef]

Takahashi, N.

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

H. Ogura, N. Takahashi, “Wave scattering from a random rough surface: reciprocal theorem and backscattering enhancement,” Waves Random Media 5, 223–242 (1995).
[CrossRef]

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

Tsang, L.

Wang, Z. L.

H. Ogura, Z. L. Wang, Y. Sasakura, V. Freilikher, “Localization of surface plasmon waves on the surface of a random rough metallic grating with a narrow-band spectrum,” Opt. Commun. 134, 1–6 (1997).
[CrossRef]

H. Ogura, Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358–10371 (1996).
[CrossRef]

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

Yoshimoto, K.

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshimoto, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, S91–S107 (1991).
[CrossRef]

Yurkevich, I.

V. D. Freilikher, I. Yurkevich, “Backscattering enhancement from surfaces with random impedance,” Phys. Lett. A 183, 247–252 (1993).
[CrossRef]

Ann. Phys. (N.Y.) (1)

A. A. Maradudin, T. R. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Commun. (2)

M. Saillard, “Numerical evidence of Anderson localization for electromagnetic surface waves,” Opt. Commun. 96, 1–7 (1993).
[CrossRef]

H. Ogura, Z. L. Wang, Y. Sasakura, V. Freilikher, “Localization of surface plasmon waves on the surface of a random rough metallic grating with a narrow-band spectrum,” Opt. Commun. 134, 1–6 (1997).
[CrossRef]

Phys. Lett. A (1)

V. D. Freilikher, I. Yurkevich, “Backscattering enhancement from surfaces with random impedance,” Phys. Lett. A 183, 247–252 (1993).
[CrossRef]

Phys. Rev. B (2)

H. Ogura, Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358–10371 (1996).
[CrossRef]

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

Waves Random Media (3)

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

H. Ogura, N. Takahashi, “Wave scattering from a random rough surface: reciprocal theorem and backscattering enhancement,” Waves Random Media 5, 223–242 (1995).
[CrossRef]

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshimoto, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, S91–S107 (1991).
[CrossRef]

Other (3)

P. Sheng, ed., Scattering and Localization of Classical Waves in Random Media, (World Scientific, London, 1990).

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

D. Maystre, J. C. Dainty, eds., Modern Analysis of Scattering Phenomena (Hilger, New York, 1991).

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Figures (6)

Fig. 1
Fig. 1

Quick varying of μ2(λ) near the plasmon pole.

Fig. 2
Fig. 2

Intensities of random wave fields on the surface of a rough grating having normalized roughness kσ=0.1 and normalized correlation length kl=20.

Fig. 3
Fig. 3

Same as Fig. 2 but for kl=70.

Fig. 4
Fig. 4

Intensities of random wave fields on the surface of a rough grating having normalized roughness kσ=0.1 and normalized correlation length kl=30.

Fig. 5
Fig. 5

Same as Fig. 4 but for kσ=0.02.

Fig. 6
Fig. 6

Corresponding grating surface of Fig. 5.

Equations (29)

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|F(λ)|2=|F0(λ+2λ0)|2+|F0(λ-2λ0)|2=σ2 l2π{exp[-l2(λ+2λ0)2]+exp[-l2(λ-2λ0)2]},2λ0l1,
F(λ)=F0(λ+2λ0)+F0(λ-2λ0).
f(x, ω)=f(Τxω)= exp(iλx)F(λ)dB(λ, ω),
=exp(i2λ0x)f1(x, ω)+exp(-i2λ0x)f1(x, ω)¯,
f1(x, ω)= exp(iμx)F0(μ)dB(2λ0+μ),
ψj(z, x;ω)=exp(iλ0x)U(j)(z, Τxω),j=1, 2,
U(1)(z, Τxω)=exp[-iμ1(λ0)z]+n=- exp(i2nλ0x)Un(1)(z, x;ω),
U(2)(z, Τxω)=n=- exp(i2nλ0x)Un(2)(z, x;ω),
Un(j)(z, x;ω)
= exp[iνx+iμj(2nλ0+ν)z]dMn(j)(ν, ω).
dMn(j)(ν, Τxω)=exp[i(2nλ0+ν)x]dMn(j)(ν, ω).
iμ1(λ0)1k+μ2(λ0+ν)2kdM0(2)(ν)+μ1(λ0)μ2(λ0-ν)1k+μ22(λ0-ν)2kf1-λ0(2λ0+ν)k11-12f1dM-1(2)(ν)
=i21kμ1(λ0).
μ1(λ0)μ2(λ0+ν)1k+μ22(λ0+ν)2kf1¯-λ0(2λ0+ν)k11-12f1¯dM0(2)(ν)+iμ1(λ0)1k+μ2(λ0-ν)2kdM-1(2)(ν)
=i21kμ12(λ0)f1¯,
f1(x)= exp(iνx)dβ1(ν)= exp(iνx)F0(ν)dB(2λ0+ν),
μj(mλ0+ν)μj(mλ0),
Λnνn-Λ2,νn+Λ2,
νnnΛ,νn-l=νn-νl.
ΔMj(2)(νn)Mj(2)(Λn)=ΛndMj(2)(ν),
Δβ1(νn)β1(Λn)=Λndβ1(ν).
iμ1(λ0)1k+μ2(λ0+νn)2kΔM0(2)(νn)+lΔβ1(νn-l)×μ1(λ0)μ2(λ0-νl)1k+μ22(λ0-νl)2k-2λ02k11-12ΔM-1(2)(νl)=δn,0i21kμ1(λ0),
lΔβ1(νl-n)¯μ1(λ0)μ2(λ0+νl)1k+μ22(λ0+νl)2k-2λ02k11-12ΔM0(2)(νl)+iμ1(λ0)1k+μ2(λ0-νn)2kΔM-1(2)(νn)
=i21kμ12(λ0)Δβ1(ν-n)¯,
 n=0,±1,±2,,±N,
Δβ1(νn, x)=Λn exp(iνx)dβ1(ν)=exp(inΛx)-Λ/2Λ/2 exp(iνx)dβ1(nΛ+ν),
f1(x)=Ωβ exp(iνx)dβ1(ν)n=-N1N1Δβ1(νn, x).
M0(2)(x)=ΩM exp(iνx)dM0(2)(ν)n=-NNΔM0(2)(νn, x),
M-1(2)(x)=ΩM exp(iνx)dM-1(2)(ν)n=-NNΔM-1(2)(νn, x).

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