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  1. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963).
  2. A. Andronow, M. Leontowicz, Ann. Phys. 38, 485 (1926).
  3. A. Vrij, J. Colloid Sci. 19, 1 (1964).
    [CrossRef]
  4. G. W. Stroke, in Handbuch der Physik (Springer-Verlag, Berlin, 1967), Vol. 29, p. 426.
    [CrossRef]
  5. P. Bousquet, Rev. Opt. 41, 277 (1962); P. Bousquet, R. Deleuil, Compt. Rend. Acad. Sci. Paris 256, 1461 (1963).
  6. R. Petit, Compt. Rend. Acad. Sci. Paris 257, 2018 (1963); Compt. Rend. Acad. Sci. Paris 261, 4677, (1965); A. Wirgin, Rev. Opt. 43, 669 (964); Rev. Opt. 44, 20 (1965).
  7. The assumption k/p < 1 does not imply necessarily, as Bousquet and Deleuil1 assumed that the ampitudes of the diffracted waves can be neglected.

1964 (1)

A. Vrij, J. Colloid Sci. 19, 1 (1964).
[CrossRef]

1963 (1)

R. Petit, Compt. Rend. Acad. Sci. Paris 257, 2018 (1963); Compt. Rend. Acad. Sci. Paris 261, 4677, (1965); A. Wirgin, Rev. Opt. 43, 669 (964); Rev. Opt. 44, 20 (1965).

1962 (1)

P. Bousquet, Rev. Opt. 41, 277 (1962); P. Bousquet, R. Deleuil, Compt. Rend. Acad. Sci. Paris 256, 1461 (1963).

1926 (1)

A. Andronow, M. Leontowicz, Ann. Phys. 38, 485 (1926).

Andronow, A.

A. Andronow, M. Leontowicz, Ann. Phys. 38, 485 (1926).

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963).

Bousquet, P.

P. Bousquet, Rev. Opt. 41, 277 (1962); P. Bousquet, R. Deleuil, Compt. Rend. Acad. Sci. Paris 256, 1461 (1963).

Leontowicz, M.

A. Andronow, M. Leontowicz, Ann. Phys. 38, 485 (1926).

Petit, R.

R. Petit, Compt. Rend. Acad. Sci. Paris 257, 2018 (1963); Compt. Rend. Acad. Sci. Paris 261, 4677, (1965); A. Wirgin, Rev. Opt. 43, 669 (964); Rev. Opt. 44, 20 (1965).

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963).

Stroke, G. W.

G. W. Stroke, in Handbuch der Physik (Springer-Verlag, Berlin, 1967), Vol. 29, p. 426.
[CrossRef]

Vrij, A.

A. Vrij, J. Colloid Sci. 19, 1 (1964).
[CrossRef]

Ann. Phys. (1)

A. Andronow, M. Leontowicz, Ann. Phys. 38, 485 (1926).

Compt. Rend. Acad. Sci. Paris (1)

R. Petit, Compt. Rend. Acad. Sci. Paris 257, 2018 (1963); Compt. Rend. Acad. Sci. Paris 261, 4677, (1965); A. Wirgin, Rev. Opt. 43, 669 (964); Rev. Opt. 44, 20 (1965).

J. Colloid Sci. (1)

A. Vrij, J. Colloid Sci. 19, 1 (1964).
[CrossRef]

Rev. Opt. (1)

P. Bousquet, Rev. Opt. 41, 277 (1962); P. Bousquet, R. Deleuil, Compt. Rend. Acad. Sci. Paris 256, 1461 (1963).

Other (3)

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963).

G. W. Stroke, in Handbuch der Physik (Springer-Verlag, Berlin, 1967), Vol. 29, p. 426.
[CrossRef]

The assumption k/p < 1 does not imply necessarily, as Bousquet and Deleuil1 assumed that the ampitudes of the diffracted waves can be neglected.

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Figures (1)

Fig. 1
Fig. 1

Wavefronts for successive diffraction orders in a lattice of spacing 2p (left side, X) and p (right side, O).

Equations (20)

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z = ζ ρ exp ( i ρ p x ) ,
E = A exp [ i k ( u 0 x + w 0 z ) ] ,
E ρ r = m = - + E m , ρ r = m = - + A m , ρ r exp [ i k ( u m , ρ r x + w m , ρ r z ) ] in medium 1 and E ρ t = m = - + E m , ρ t = m = - + A m , ρ t exp [ i k ( u m , ρ t x + w m , ρ t z ) ]
u m , ρ t = u 0 - m ( ρ p / k ) = sin θ = u m , ρ r w m , ρ r = [ 1 - ( u m , ρ r 2 ) ] 1 2 and w m , ρ t = [ n 2 - ( u m , ρ t ) 2 ] 1 2 = [ n 2 - n 2 sin θ ] 1 2 = n cos θ ,
z = ζ ρ 1 exp ( i ρ 1 ρ ) + ζ ρ 2 exp ( i ρ 2 p ) .
E ρ 1 , ρ 2 r m = - + A m , ρ 1 r exp [ i k ( u r m , ρ 1 x + w m , ρ 1 r z ) + m = - + A m , ρ 2 r × exp [ i k ( u m , ρ 2 r x + w m , ρ 2 r z ) ]
u m , ρ 1 r = u 0 - m ( ρ 1 p / k ) and u m , ρ 2 r = u 0 - m ( ρ 2 p / k ) .
z ( x , y ) = ρ , σ = - + ζ ρ , σ exp [ i p ( ρ x + σ y ) ] .
z ( x , y ) = ρ = - + ζ ρ exp ( i p ρ x ) .
E r = ρ = - + m = - + A m , ρ r exp [ i k ( u m , ρ r x + w m , ρ r z ) ]
u m , ρ r = u 0 - m ρ ( p / k )
w m , ρ r = [ 1 - ( u m , ρ r ) 2 ] 1 2 .
E r = λ = - + A λ r exp [ i k ( u λ r x + w λ r z ) ]
λ = ± 1 , ± 2 ,
u λ r = u 0 - λ ( p / k ) ,
w λ r = [ 1 - ( u λ r ) 2 ] 1 2 .
E 1 r = ρ = - + A 1 , ρ r exp [ i k ( u 1 , ρ r x + w 1 , ρ r z ) ]
A 1 , ρ r = A 1 , ρ t = ( - i ) [ ( 1 - n ) / ( w 1 , ρ t + w 1 , ρ r ) ] k ζ ρ ,
A 1 , ρ r = A 1 , ρ t = i [ ( n - 1 ) / ( cos θ + n cos θ ) k ζ ρ ,
E r = i ( n - 1 ) k ρ = - + [ ζ ρ / ( w 1 , ρ r + w 1 , ρ t ) ] × exp [ i k ( u 1 , ρ t x + w 1 , ρ t z ) ] .

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