Abstract

A physical mechanism is proposed for the explanation of the angular shift of the Brewster angle induced by a rough surface as recently discovered by Saillard and Maystre [J. Opt. Soc. Am. A 7, 982 (1990)]. An explicit formula giving the angular shift as a function of the correlation length σ and the mean-square departure from the flat surface δ is derived. It is shown that in the case of a rough surface, a minimum rather than a true zero is obtained for the reflection factor.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Saillard, D. Maystre, J. Opt. Soc. Am. A 7, 982 (1990).
    [CrossRef]
  2. J. A. DeSanto, G. S. Brown, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1986), pp. 1–62.
    [CrossRef]
  3. D. Winnebrener, A. Ishimaru, Radio Sci. 20, 161 (1985).
    [CrossRef]
  4. G. S. Brown, IEEE Trans. Antennas Propag. AP-26, 472 (1978).
    [CrossRef]
  5. J.-J. Greffet, Phys. Rev. B 37, 6436 (1988).
    [CrossRef]
  6. A. A. Maradudin, J. Opt. Soc. Am. 73, 759 (1983).
    [CrossRef]
  7. P. Tran, V. Celli, J. Opt. Soc. Am. A 5, 1635 (1988).
    [CrossRef]

1990 (1)

1988 (2)

1985 (1)

D. Winnebrener, A. Ishimaru, Radio Sci. 20, 161 (1985).
[CrossRef]

1983 (1)

1978 (1)

G. S. Brown, IEEE Trans. Antennas Propag. AP-26, 472 (1978).
[CrossRef]

Brown, G. S.

G. S. Brown, IEEE Trans. Antennas Propag. AP-26, 472 (1978).
[CrossRef]

J. A. DeSanto, G. S. Brown, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1986), pp. 1–62.
[CrossRef]

Celli, V.

DeSanto, J. A.

J. A. DeSanto, G. S. Brown, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1986), pp. 1–62.
[CrossRef]

Greffet, J.-J.

J.-J. Greffet, Phys. Rev. B 37, 6436 (1988).
[CrossRef]

Ishimaru, A.

D. Winnebrener, A. Ishimaru, Radio Sci. 20, 161 (1985).
[CrossRef]

Maradudin, A. A.

Maystre, D.

Saillard, M.

Tran, P.

Winnebrener, D.

D. Winnebrener, A. Ishimaru, Radio Sci. 20, 161 (1985).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

G. S. Brown, IEEE Trans. Antennas Propag. AP-26, 472 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Phys. Rev. B (1)

J.-J. Greffet, Phys. Rev. B 37, 6436 (1988).
[CrossRef]

Radio Sci. (1)

D. Winnebrener, A. Ishimaru, Radio Sci. 20, 161 (1985).
[CrossRef]

Other (1)

J. A. DeSanto, G. S. Brown, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1986), pp. 1–62.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Mechanism of the Brewster-angle shift. The solid curve is the zero-order reflected field (i.e., the Fresnel reflection factor, which is real). The dashed curve is the real part of the second-order average coherent field, and the dotted curve is the modulus of the sum of the two components. δ = λ/10, σ = 2λ, = 2.25, and θB = 56.31°.

Fig. 2
Fig. 2

Same as in Fig. 1, except σ = λ/2.

Fig. 3
Fig. 3

Angular shift δθ as a function of δ.

Fig. 4
Fig. 4

Angular shift δθ as a function of σ.

Equations (20)

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

H ( x , z ) = A ( k ) exp ( i k x i α z ) d k , α = ( ω 2 c 2 k 2 ) 1 / 2 , Im ( α ) > 0 ,
S ( x ) = 0 ,
S ( x ) S ( x ) = δ 2 exp ( | x x | 2 / σ 2 ) .
A = A ( 0 ) + A ( 1 ) + A ( 2 ) + .
A = A ( 0 ) + A ( 2 ) + .
| A ( k ) | 2 δ k = 0 ,
A ( k ) = A ( 0 ) ( k ) + A ( 2 ) ( k ) .
Re [ A * ( k ) A ( k ) ] = 0 ,
δ k = k k B = Re [ A * ( k B ) A ( k B ) ] Re [ A * ( k B ) A ( k B ) + | A ( k B ) | 2 ] = ω c cos θ B δ θ .
S ( x ) = n = S n exp ( i n 2 π a x ) ,
S n = 0 ,
S n S m = δ 2 a g ( n 2 π a ) δ n , m ,
H ( x , z ) = exp ( i k x i α 0 z ) + p = A p exp ( i k p x + i α p z ) ,
k p = k + p 2 π a ,
k = ( ω / c ) sin θ ,
α p = ( ω 2 c 2 k p 2 ) 1 / 2 , Im ( α p ) > 0 .
A 0 ( 0 ) = α 0 β 0 α 0 + β 0 ,
A 0 ( 2 ) = p = δ 2 g ( p 2 π a ) f p ,
f p = 1 a 2 α 0 ( ε 1 ) ( ε α 0 + β 0 ) 2 [ β 0 ( β 0 2 k 2 ) + ε β 0 ( α 0 2 k 2 ) 2 ( ε 1 ) ε α p + β p ( β 0 β p ε k k p ) ( β 0 α p + k k p ) ] ,
β p = ( ε ω 2 c 2 k p 2 ) 1 / 2 , Im ( β p ) > 0 .

Metrics