Abstract

When a photon flux is incident upon a rough interface that separates media with different refractive indices, the interface roughness influences the angular distribution of the transmitted flux. For the case of very rough surfaces with slopes of the order of unity, we find that a simple facet model is sufficient to describe the main features of the flux-transmission behavior. We demonstrate the effect observed by Nieto-Vesperinas et al. [Opt. Lett. 15, 1261 (1990)] for plane-wave incidence, that the interface roughness tends to suppress the refractive-index contrast. In addition, for cases in which the incident flux is distributed in angle, we find that the direction of maximum transmitted flux can be predicted from the surface roughness.

© 1996 Optical Society of America

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References

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  1. C. M. Lam, A. Ishimaru, IEEE Trans. Antennas Propag. 42, 145 (1994).
    [CrossRef]
  2. A. Dogariu, G. Boreman, M. Dogariu, Opt. Lett. 20, 1665 (1995).
    [CrossRef] [PubMed]
  3. T. J. Farell, M. S. Patterson, B. Wilson, Med. Phys. 19, 879 (1992).
    [CrossRef]
  4. A. Dogariu, J. Uozumi, T. Asakura, Part. Part. Syst. Charact. 2, 250 (1994).
    [CrossRef]
  5. M. Nieto-Vesperinas, J. A. Sanchez-Gil, A. J. Sant, J. C. Dainty, Opt. Lett. 15, 1261 (1990).
    [CrossRef] [PubMed]
  6. J. A. Sanchez-Gil, M. Nieto-Vesperinas, J. Opt. Soc. Am. A 8, 1270 (1991).
    [CrossRef]
  7. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech, Norwood, Mass., 1987).
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

1995

1994

A. Dogariu, J. Uozumi, T. Asakura, Part. Part. Syst. Charact. 2, 250 (1994).
[CrossRef]

C. M. Lam, A. Ishimaru, IEEE Trans. Antennas Propag. 42, 145 (1994).
[CrossRef]

1992

T. J. Farell, M. S. Patterson, B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef]

1991

1990

Asakura, T.

A. Dogariu, J. Uozumi, T. Asakura, Part. Part. Syst. Charact. 2, 250 (1994).
[CrossRef]

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech, Norwood, Mass., 1987).

Boreman, G.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

Dainty, J. C.

Dogariu, A.

A. Dogariu, G. Boreman, M. Dogariu, Opt. Lett. 20, 1665 (1995).
[CrossRef] [PubMed]

A. Dogariu, J. Uozumi, T. Asakura, Part. Part. Syst. Charact. 2, 250 (1994).
[CrossRef]

Dogariu, M.

Farell, T. J.

T. J. Farell, M. S. Patterson, B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef]

Ishimaru, A.

C. M. Lam, A. Ishimaru, IEEE Trans. Antennas Propag. 42, 145 (1994).
[CrossRef]

Lam, C. M.

C. M. Lam, A. Ishimaru, IEEE Trans. Antennas Propag. 42, 145 (1994).
[CrossRef]

Nieto-Vesperinas, M.

Patterson, M. S.

T. J. Farell, M. S. Patterson, B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef]

Sanchez-Gil, J. A.

Sant, A. J.

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech, Norwood, Mass., 1987).

Uozumi, J.

A. Dogariu, J. Uozumi, T. Asakura, Part. Part. Syst. Charact. 2, 250 (1994).
[CrossRef]

Wilson, B.

T. J. Farell, M. S. Patterson, B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

IEEE Trans. Antennas Propag.

C. M. Lam, A. Ishimaru, IEEE Trans. Antennas Propag. 42, 145 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Med. Phys.

T. J. Farell, M. S. Patterson, B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef]

Opt. Lett.

Part. Part. Syst. Charact.

A. Dogariu, J. Uozumi, T. Asakura, Part. Part. Syst. Charact. 2, 250 (1994).
[CrossRef]

Other

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech, Norwood, Mass., 1987).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

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Figures (3)

Fig. 1
Fig. 1

Transmission geometry through a rough interface h(x) having facets of length L. The local normal n is rotated with an angle s with respect to the average normal z.

Fig. 2
Fig. 2

(a) Angular dependence of the transmitted photon flux corresponding to plane waves with different angles of incidence for a rough interface with L/σ = 1.5 and n1/n2 = 1.5. (b) Angular dependence of the transmitted photon flux corresponding to a plane wave incident at 20° upon interfaces with n1/n2 = 1.5 and roughness parameters as indicated.

Fig. 3
Fig. 3

(a) Polar plot of the transmitted photon flux corresponding to an angularly uniform incident flux, n1/n2 = 1.5, and roughness parameters as indicated. (b) Polar plot of the transmitted photon flux corresponding to a cosine distribution of the incident flux, n1/n2 = 1.5, and roughness parameters as indicated.

Equations (3)

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s = tan - 1 [ h ( x ) - h ( x + L ) L ] .
P s ( s ) = L 2 π cos 2 ( s ) exp [ - ( L tan  s ) 2 4 σ 2 ] .
J ( θ ) = - π / 2 π / 2 J 0 ( θ 0 ) T ( s - θ 0 ) P ( s ) d s ,

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