Abstract

A method is proposed for designing a two-dimensional randomly rough Dirichlet surface that, when illuminated at normal incidence, scatters a scalar plane wave with a specified angular distribution of its intensity. The method is validated by computer simulation calculations.

© 2004 Optical Society of America

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References

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  1. E. R. Méndez, E. E. García-Guerrero, H. M. Escamilla, A. A. Maradudin, T. A. Leskova, and A. V. Shchegrov, Appl. Opt. 40, 1098 (2001).
    [CrossRef]
  2. T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, Providence, R.I., 2003), p. 117.
    [CrossRef]
  3. A. A. Maradudin, T. A. Leskova, and E. R. Méndez, Opt. Lett. 28, 72 (2003).
    [CrossRef] [PubMed]
  4. A. A. Maradudin, E. R. Méndez, and T. A. Leskova, SPIE 4780, 51 (2002).
  5. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 281–282.
  6. E. R. Méndez, T. A. Leskova, A. A. Maradudin, M. Leyva-Lucero, and J. Muñoz-Lopez, “The design of two-dimensional random surfaces with specified scattering properties,” J. Opt. A Pure Appl. Opt. (to be published).

2003

2002

A. A. Maradudin, E. R. Méndez, and T. A. Leskova, SPIE 4780, 51 (2002).

2001

Escamilla, H. M.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 281–282.

García-Guerrero, E. E.

Leskova, T. A.

A. A. Maradudin, T. A. Leskova, and E. R. Méndez, Opt. Lett. 28, 72 (2003).
[CrossRef] [PubMed]

A. A. Maradudin, E. R. Méndez, and T. A. Leskova, SPIE 4780, 51 (2002).

E. R. Méndez, E. E. García-Guerrero, H. M. Escamilla, A. A. Maradudin, T. A. Leskova, and A. V. Shchegrov, Appl. Opt. 40, 1098 (2001).
[CrossRef]

T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, Providence, R.I., 2003), p. 117.
[CrossRef]

E. R. Méndez, T. A. Leskova, A. A. Maradudin, M. Leyva-Lucero, and J. Muñoz-Lopez, “The design of two-dimensional random surfaces with specified scattering properties,” J. Opt. A Pure Appl. Opt. (to be published).

Leyva-Lucero, M.

E. R. Méndez, T. A. Leskova, A. A. Maradudin, M. Leyva-Lucero, and J. Muñoz-Lopez, “The design of two-dimensional random surfaces with specified scattering properties,” J. Opt. A Pure Appl. Opt. (to be published).

Maradudin, A. A.

A. A. Maradudin, T. A. Leskova, and E. R. Méndez, Opt. Lett. 28, 72 (2003).
[CrossRef] [PubMed]

A. A. Maradudin, E. R. Méndez, and T. A. Leskova, SPIE 4780, 51 (2002).

E. R. Méndez, E. E. García-Guerrero, H. M. Escamilla, A. A. Maradudin, T. A. Leskova, and A. V. Shchegrov, Appl. Opt. 40, 1098 (2001).
[CrossRef]

T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, Providence, R.I., 2003), p. 117.
[CrossRef]

E. R. Méndez, T. A. Leskova, A. A. Maradudin, M. Leyva-Lucero, and J. Muñoz-Lopez, “The design of two-dimensional random surfaces with specified scattering properties,” J. Opt. A Pure Appl. Opt. (to be published).

Méndez, E. R.

A. A. Maradudin, T. A. Leskova, and E. R. Méndez, Opt. Lett. 28, 72 (2003).
[CrossRef] [PubMed]

A. A. Maradudin, E. R. Méndez, and T. A. Leskova, SPIE 4780, 51 (2002).

E. R. Méndez, E. E. García-Guerrero, H. M. Escamilla, A. A. Maradudin, T. A. Leskova, and A. V. Shchegrov, Appl. Opt. 40, 1098 (2001).
[CrossRef]

T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, Providence, R.I., 2003), p. 117.
[CrossRef]

E. R. Méndez, T. A. Leskova, A. A. Maradudin, M. Leyva-Lucero, and J. Muñoz-Lopez, “The design of two-dimensional random surfaces with specified scattering properties,” J. Opt. A Pure Appl. Opt. (to be published).

Muñoz-Lopez, J.

E. R. Méndez, T. A. Leskova, A. A. Maradudin, M. Leyva-Lucero, and J. Muñoz-Lopez, “The design of two-dimensional random surfaces with specified scattering properties,” J. Opt. A Pure Appl. Opt. (to be published).

T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, Providence, R.I., 2003), p. 117.
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 281–282.

Shchegrov, A. V.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 281–282.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 281–282.

Appl. Opt.

Opt. Lett.

SPIE

A. A. Maradudin, E. R. Méndez, and T. A. Leskova, SPIE 4780, 51 (2002).

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 281–282.

E. R. Méndez, T. A. Leskova, A. A. Maradudin, M. Leyva-Lucero, and J. Muñoz-Lopez, “The design of two-dimensional random surfaces with specified scattering properties,” J. Opt. A Pure Appl. Opt. (to be published).

T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez, in Waves in Periodic and Random Media, P. Kuchment, ed. (American Mathematical Society, Providence, R.I., 2003), p. 117.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Segment of the x1x2 plane showing the equilateral triangles above which the triangular facets are placed that generate the two-dimensional randomly rough surface.

Fig. 2
Fig. 2

Mean differential reflection coefficient R/Ωs for scattering from a two-dimensional randomly rough surface that acts as a band-limited uniform diffuser within a circular domain of scattering angles. Typical cross sections are also presented.

Fig. 3
Fig. 3

Mean differential reflection coefficient R/Ωs for scattering from a two-dimensional randomly rough surface that acts as a band-limited uniform diffuser within a triangular domain of scattering angles. The cross sections corresponding to q1=0 and q2=0 are also presented.

Equations (11)

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

RΩs=1Sω2πc2d2u exp-iq·u×d2xexp-iau·ζx,
RΩs=ωac2f-q1a,-q2a.
fs1,s2=41+s22RΩs-s1,-s2,
fs1=-fs1,s2ds2,
f(s2|s1)=fs1,s2/fs1.
RΩs=AθQ-q12+q221/2,
fs1,s2=1π1+q*2q*2θq*-s1+s22,
fs1=1π1+q*2q*211+s123/2tan-1q*2-s121+s121/2+q*2-s121/21+s121/21+q*2×θq*-s1,
RΩs=3M2θ13M-cωq2-cωq1×θM-cωq2θcωq2.
fs1,s2=43M2θM23+s23-s1×θM2+s2θ-s2,
fs1=12M2M23+s1θM3-s1,

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