Abstract

We present a rigorous numerical simulation analysis of the second-harmonic generation of p-polarized light in reflection from a one-dimensional, randomly rough, metal surface when the plane of incidence is perpendicular to the generators of the surface. When the incident light cannot couple to surface electromagnetic waves supported by the metal surface at the fundamental frequency, the angular distribution of the intensity of the incoherent component of the scattered light at the harmonic frequency displays either well-defined peaks or dips in the retroreflection direction and in the direction normal to the mean plane of the surface. These effects are suppressed by the direct excitation of surface polaritons at the fundamental frequency.

© 1996 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. M. Agranovich, K. I. Grigorishin, Nonlinear Opt. 5, 3 (1993).
  3. A. R. McGurn, T. A. Leskova, V. M. Agranovich, Phys. Rev. B 44, 11441 (1991).
    [CrossRef]
  4. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, London, 1991), p. 39.
  5. F. Toigo, A. Marvin, V. Celli, N. R. Hill, Phys. Rev. B 15, 5618 (1977).
    [CrossRef]
  6. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990).
    [CrossRef]
  7. V. M. Agranovich, S. A. Darmanyan, Pis’ma Zh. Eksp. Teor. Fiz. 35, 68 (1982) [JETP Lett. 35, 80 (1982)].
  8. P. W. Johnson, R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  9. D. Maystre, M. Neviere, R. Reinisch, Appl. Phys. A 32, 115 (1986).
    [CrossRef]
  10. J. L. Coutaz, D. Maystre, M. Neviere, R. Reinisch, J. Appl. Phys. 62, 1529 (1987).
    [CrossRef]
  11. C. S. West, K. A. O’Donnell, J. Opt. Soc. Am. A 12, 390 (1995).
    [CrossRef]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1962), p. 13.
  13. R. T. Deck, R. K. Grygier, Appl. Opt. 23, 3202 (1984).
    [CrossRef] [PubMed]

1995 (1)

1993 (1)

V. M. Agranovich, K. I. Grigorishin, Nonlinear Opt. 5, 3 (1993).

1991 (1)

A. R. McGurn, T. A. Leskova, V. M. Agranovich, Phys. Rev. B 44, 11441 (1991).
[CrossRef]

1990 (1)

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990).
[CrossRef]

1987 (1)

J. L. Coutaz, D. Maystre, M. Neviere, R. Reinisch, J. Appl. Phys. 62, 1529 (1987).
[CrossRef]

1986 (1)

D. Maystre, M. Neviere, R. Reinisch, Appl. Phys. A 32, 115 (1986).
[CrossRef]

1985 (1)

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

1984 (1)

1982 (1)

V. M. Agranovich, S. A. Darmanyan, Pis’ma Zh. Eksp. Teor. Fiz. 35, 68 (1982) [JETP Lett. 35, 80 (1982)].

1977 (1)

F. Toigo, A. Marvin, V. Celli, N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[CrossRef]

1972 (1)

P. W. Johnson, R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, K. I. Grigorishin, Nonlinear Opt. 5, 3 (1993).

A. R. McGurn, T. A. Leskova, V. M. Agranovich, Phys. Rev. B 44, 11441 (1991).
[CrossRef]

V. M. Agranovich, S. A. Darmanyan, Pis’ma Zh. Eksp. Teor. Fiz. 35, 68 (1982) [JETP Lett. 35, 80 (1982)].

Celli, V.

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

F. Toigo, A. Marvin, V. Celli, N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[CrossRef]

Christy, R. W.

P. W. Johnson, R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Coutaz, J. L.

J. L. Coutaz, D. Maystre, M. Neviere, R. Reinisch, J. Appl. Phys. 62, 1529 (1987).
[CrossRef]

Darmanyan, S. A.

V. M. Agranovich, S. A. Darmanyan, Pis’ma Zh. Eksp. Teor. Fiz. 35, 68 (1982) [JETP Lett. 35, 80 (1982)].

Deck, R. T.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1962), p. 13.

Grigorishin, K. I.

V. M. Agranovich, K. I. Grigorishin, Nonlinear Opt. 5, 3 (1993).

Grygier, R. K.

Hill, N. R.

F. Toigo, A. Marvin, V. Celli, N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[CrossRef]

Johnson, P. W.

P. W. Johnson, R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Leskova, T. A.

A. R. McGurn, T. A. Leskova, V. M. Agranovich, Phys. Rev. B 44, 11441 (1991).
[CrossRef]

Maradudin, A. A.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990).
[CrossRef]

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

Marvin, A.

F. Toigo, A. Marvin, V. Celli, N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[CrossRef]

Maystre, D.

J. L. Coutaz, D. Maystre, M. Neviere, R. Reinisch, J. Appl. Phys. 62, 1529 (1987).
[CrossRef]

D. Maystre, M. Neviere, R. Reinisch, Appl. Phys. A 32, 115 (1986).
[CrossRef]

McGurn, A. R.

A. R. McGurn, T. A. Leskova, V. M. Agranovich, Phys. Rev. B 44, 11441 (1991).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990).
[CrossRef]

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

Méndez, E. R.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990).
[CrossRef]

Michel, T.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990).
[CrossRef]

Neviere, M.

J. L. Coutaz, D. Maystre, M. Neviere, R. Reinisch, J. Appl. Phys. 62, 1529 (1987).
[CrossRef]

D. Maystre, M. Neviere, R. Reinisch, Appl. Phys. A 32, 115 (1986).
[CrossRef]

O’Donnell, K. A.

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, London, 1991), p. 39.

Reinisch, R.

J. L. Coutaz, D. Maystre, M. Neviere, R. Reinisch, J. Appl. Phys. 62, 1529 (1987).
[CrossRef]

D. Maystre, M. Neviere, R. Reinisch, Appl. Phys. A 32, 115 (1986).
[CrossRef]

Toigo, F.

F. Toigo, A. Marvin, V. Celli, N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[CrossRef]

West, C. S.

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

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (1)

D. Maystre, M. Neviere, R. Reinisch, Appl. Phys. A 32, 115 (1986).
[CrossRef]

J. Appl. Phys. (1)

J. L. Coutaz, D. Maystre, M. Neviere, R. Reinisch, J. Appl. Phys. 62, 1529 (1987).
[CrossRef]

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

Nonlinear Opt. (1)

V. M. Agranovich, K. I. Grigorishin, Nonlinear Opt. 5, 3 (1993).

Phys. Rev. B (4)

A. R. McGurn, T. A. Leskova, V. M. Agranovich, Phys. Rev. B 44, 11441 (1991).
[CrossRef]

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

F. Toigo, A. Marvin, V. Celli, N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[CrossRef]

P. W. Johnson, R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Pis’ma Zh. Eksp. Teor. Fiz. (1)

V. M. Agranovich, S. A. Darmanyan, Pis’ma Zh. Eksp. Teor. Fiz. 35, 68 (1982) [JETP Lett. 35, 80 (1982)].

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1962), p. 13.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, London, 1991), p. 39.

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Figures (2)

Fig. 1
Fig. 1

Contribution to the mean drc from the incoherent component of the scattered light of frequency 2ω calculated for a surface possessing the power spectrum [Eq. (3)] with H1 = 0, H2 = 1, and δ = 30 nm. (a) θ0 = 0°, (b) θ0 = 3°, and (c) θ0 = 15°. The dashed lines indicate the backscattering direction.

Fig. 2
Fig. 2

Contribution to the mean drc from the incoherent component of the scattered light of (a) frequency ω and (b) frequency 2ω calculated for a surface possessing a rectangular power spectrum [Eq. (3)] with H1 = 0.1, H2 = 0.9, and δ = 30 nm; θ0 = 15°.

Equations (3)

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L ( x 1 2 ω ) - L < ( x 1 2 ω ) ɛ ( 2 ω ) = 2 i c ω d d x 1 × { μ 1 ( ω ) [ ϕ ( x 1 ) d d x 1 H ( x 1 ω ) ] 2 + μ 2 ( ω ) [ ϕ ( x 1 ) L ( x 1 ω ) ] 2 } ,
H ( x 1 2 ω ) - H < ( x 1 2 ω ) = 2 i c ω μ 3 ( ω ) ϕ 2 ( x 1 ) × L ( x 1 ω ) d d x 1 H ( x 1 ω ) ,
g ( k ) = π H 1 Δ k ( ω ) { rect [ k - k sp ( ω ) Δ k ( ω ) ] + rect [ k + k sp ( ω ) Δ k ( ω ) ] } + π H 2 Δ k ( 2 ω ) { rect [ k - k sp ( 2 ω ) Δ k ( 2 ω ) ] + rect [ k + k sp ( 2 ω ) Δ k ( 2 ω ) ] } ,

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