Abstract

An analytical series solution is derived within the Rayleigh hypothesis to compute the efficiencies of a crossed grating illuminated by an arbitrary polarized beam. A comparison with previously reported numerical results for a dielectric crossed grating illuminated by a plane wave shows good agreement. The formulas given can be directly implemented on a personal computer.

© 1992 Optical Society of America

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References

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  1. R. C. McPhedran, G. H. Derrick, L. C. Botten, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1981), p. 227.
  2. P. Vincent, Opt. Commun. 26, 293 (1978).
    [CrossRef]
  3. D. Maystre, M. Nevière, J. Opt. (Paris) 9, 301 (1978).
    [CrossRef]
  4. G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, Appl. Phys. 18, 39 (1979).
    [CrossRef]
  5. M. Saillard, D. Maystre, J. Opt. Soc. Am. A 7, 982 (1990).
    [CrossRef]
  6. J. A. Sanchez-Gil, M. Nieto-Vesperinas, J. Opt. Soc. Am. A 8, 1270 (1991).
    [CrossRef]
  7. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, Ann. Phys. (N.Y.) 203, 255 (1990).
    [CrossRef]
  8. E. I. Thorsos, J. Acoust. Soc. Am. 83, 78 (1988).
    [CrossRef]
  9. J. C. Dainty, N. C. Bruce, A. J. Sant, Waves Random Media 1, S29 (1991).
    [CrossRef]
  10. K. A. O'Donnell, E. R. Mendez, J. Opt. Soc. Am. A 4, 1194 (1987).
    [CrossRef]
  11. E. R. Mendez, K. A. O'Donnell, Opt. Commun. 61, 91 (1987).
    [CrossRef]
  12. P. Tran, A. A. Maradudin, Phys. Rev. B 45, 3936 (1992).
    [CrossRef]
  13. K. A. O'Donnell, M. E. Knotts, J. Opt. Soc. Am. A 8, 1126 (1991).
    [CrossRef]
  14. T. R. Michel, M. E. Knotts, K. A. O'Donnell, J. Opt. Soc. Am. A 9, 585 (1992).
    [CrossRef]
  15. J.-J. Greffet, Phys. Rev. B 37, 6436 (1988).
    [CrossRef]
  16. E. Lalor, E. Wolf, J. Opt. Soc. Am. 62, 1165 (1972).
    [CrossRef]
  17. J.-J. Greffet, Z. Maassarani, J. Opt. Soc. Am. A 7, 1483 (1990).
    [CrossRef]

1992 (2)

1991 (3)

1990 (3)

1988 (2)

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

E. I. Thorsos, J. Acoust. Soc. Am. 83, 78 (1988).
[CrossRef]

1987 (2)

K. A. O'Donnell, E. R. Mendez, J. Opt. Soc. Am. A 4, 1194 (1987).
[CrossRef]

E. R. Mendez, K. A. O'Donnell, Opt. Commun. 61, 91 (1987).
[CrossRef]

1979 (1)

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, Appl. Phys. 18, 39 (1979).
[CrossRef]

1978 (2)

P. Vincent, Opt. Commun. 26, 293 (1978).
[CrossRef]

D. Maystre, M. Nevière, J. Opt. (Paris) 9, 301 (1978).
[CrossRef]

1972 (1)

Botten, L. C.

R. C. McPhedran, G. H. Derrick, L. C. Botten, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1981), p. 227.

Bruce, N. C.

J. C. Dainty, N. C. Bruce, A. J. Sant, Waves Random Media 1, S29 (1991).
[CrossRef]

Dainty, J. C.

J. C. Dainty, N. C. Bruce, A. J. Sant, Waves Random Media 1, S29 (1991).
[CrossRef]

Derrick, G. H.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, Appl. Phys. 18, 39 (1979).
[CrossRef]

R. C. McPhedran, G. H. Derrick, L. C. Botten, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1981), p. 227.

Greffet, J.-J.

Knotts, M. E.

Lalor, E.

Maassarani, Z.

Maradudin, A. A.

P. Tran, A. A. Maradudin, Phys. Rev. B 45, 3936 (1992).
[CrossRef]

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

Maystre, D.

M. Saillard, D. Maystre, J. Opt. Soc. Am. A 7, 982 (1990).
[CrossRef]

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, Appl. Phys. 18, 39 (1979).
[CrossRef]

D. Maystre, M. Nevière, J. Opt. (Paris) 9, 301 (1978).
[CrossRef]

McGurn, A. R.

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

McPhedran, R. C.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, Appl. Phys. 18, 39 (1979).
[CrossRef]

R. C. McPhedran, G. H. Derrick, L. C. Botten, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1981), p. 227.

Mendez, E. R.

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

K. A. O'Donnell, E. R. Mendez, J. Opt. Soc. Am. A 4, 1194 (1987).
[CrossRef]

E. R. Mendez, K. A. O'Donnell, Opt. Commun. 61, 91 (1987).
[CrossRef]

Michel, T.

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

Michel, T. R.

Nevière, M.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, Appl. Phys. 18, 39 (1979).
[CrossRef]

D. Maystre, M. Nevière, J. Opt. (Paris) 9, 301 (1978).
[CrossRef]

Nieto-Vesperinas, M.

O'Donnell, K. A.

Saillard, M.

Sanchez-Gil, J. A.

Sant, A. J.

J. C. Dainty, N. C. Bruce, A. J. Sant, Waves Random Media 1, S29 (1991).
[CrossRef]

Thorsos, E. I.

E. I. Thorsos, J. Acoust. Soc. Am. 83, 78 (1988).
[CrossRef]

Tran, P.

P. Tran, A. A. Maradudin, Phys. Rev. B 45, 3936 (1992).
[CrossRef]

Vincent, P.

P. Vincent, Opt. Commun. 26, 293 (1978).
[CrossRef]

Wolf, E.

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

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

Appl. Phys. (1)

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Nevière, Appl. Phys. 18, 39 (1979).
[CrossRef]

J. Acoust. Soc. Am. (1)

E. I. Thorsos, J. Acoust. Soc. Am. 83, 78 (1988).
[CrossRef]

J. Opt. (Paris) (1)

D. Maystre, M. Nevière, J. Opt. (Paris) 9, 301 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

Opt. Commun. (2)

P. Vincent, Opt. Commun. 26, 293 (1978).
[CrossRef]

E. R. Mendez, K. A. O'Donnell, Opt. Commun. 61, 91 (1987).
[CrossRef]

Phys. Rev. B (2)

P. Tran, A. A. Maradudin, Phys. Rev. B 45, 3936 (1992).
[CrossRef]

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

Waves Random Media (1)

J. C. Dainty, N. C. Bruce, A. J. Sant, Waves Random Media 1, S29 (1991).
[CrossRef]

Other (1)

R. C. McPhedran, G. H. Derrick, L. C. Botten, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1981), p. 227.

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Tables (1)

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Table 1 Comparison among Different Methods

Equations (23)

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S ( x , y ) = a , b J a , b 4 π 2 exp [ i ( a 2 π d x x + 2 π d y y ) ] ,
S ( n ) ( k x , k y ) = d x d y S n ( x , y ) exp [ i ( k x x + k y y ) ] ,
s ( n ) ( k x , k y ) = 4 π 2 TF [ S n ( x , y ) ] .
S ( 0 ) ( k ) = 4 π 2 δ ( k ) ,
S ( 1 ) ( k ) = a , b J a , b δ ( k a 2 π d x u x b 2 π d y u y ) ,
S ( p ) ( k ) = a , b J a , b ( p ) δ ( k a 2 π d x u x b 2 π d y u y ) ,
J a , b ( p ) = u , υ 1 4 π 2 J u , υ J a u , b υ ( p 1 ) ,
E t ( r ) = d k e t ( k ) exp [ i ( k r γ t z ) ] ,
e t ( k ) = a , b e t ( k a , b ) δ ( k k a , b ) , k a , b = k inc + a 2 π d x u x + b 2 π d y u y .
E r ( r ) = d k e r ( k ) exp [ i ( k r + γ r Z ) ] ,
e r ( k ) = a , b e r ( k a , b ) δ ( k k a , b ) .
e r ( k ) = e r , s ( k ) a r , s ( k ) + e r , p ( k ) a r , p ( k ) ,
e t ( k ) = e t , s ( k ) a t , s ( k ) + e t , p ( k ) a t , p ( k ) ,
a r , s ( k ) = u z × k / | k | , a t , s ( k ) = u z × k / | k | ,
a r , p ( k ) = a r , s ( k ) × k + γ r u z k 0 , a t , p ( k ) = a t , s ( k ) × k γ t u z n k 0 ,
e t ( k a , b ) = n = 0 e t ( n ) ( k a , b ) n ! , e r ( k a , b ) = n = 0 e r ( n ) ( k a , b ) n ! .
[ e t , s ( 0 ) ( k inc ) e t , p ( 0 ) ( k inc ) ] = [ 2 γ r γ r + γ t 0 0 2 n γ r γ r + γ t ] × [ e t , s inc ( k inc ) e t , p inc ( k inc ) ] ,
[ e t , s ( n ) ( k a , b ) e t , p ( n ) ( k a , b ) ] = γ t ( k a , b ) γ r ( k a , b ) 4 π 2 R 1 ( k a , b , k a , b ) × u , υ R ( k a , b , k u , υ ) m = 1 n n ! m ! ( n m ) ! × i m [ γ r ( k a , b ) γ t ( k u , υ ) ] m 1 × J u a , υ b ( m ) [ e t , s ( n m ) ( k u , υ ) e t , p ( n m ) ( k u , υ ) ] ,
[ e t , s ( n ) ( k a , b ) e t , p ( n ) ( k a , b ) ] = 1 4 π 1 2 π γ r ( k a , b ) u , υ P ( k a , b , k u , υ ) × m = 0 n n ! m ! ( n m ) ! ( i ) n m × [ γ r ( k a , b ) + γ t ( k u , υ ) ] n m 1 × J u a , υ b ( n m ) [ e t , s ( n m ) ( k u , υ ) e t , p ( n m ) ( k u , υ ) ] .
R ( k , k ) = ω 2 c 2 [ k ^ k ^ γ t ( k ) n ω / c k ^ ( u z × k ^ ) γ r ( k ) ω / c k ^ ( u z × k ^ ) γ t ( k ) γ r ( k ) ( k ^ k ^ ) + | k | | k ^ | n ω 2 / c 2 ] ,
P ( k , k ) = ω 2 c 2 [ k ^ k ^ γ t ( k ) n ω 2 / c 2 k ^ ( u z × k ^ ) γ r ( k ) ω / c k ^ ( u z × k ^ ) γ t ( k ) γ r ( k ) ( k ^ k ^ ) + | k | | k ^ | n ω 2 / c 2 ] ,
T ( a , b ) = | e t ( k a , b ) | 2 Re [ γ t ( k a , b ) ] | e inc | 2 ω c cos θ i , R ( a , b ) = | e r ( k a , b ) | 2 Re [ γ r ( k a , b ) ] | e inc | 2 ω c cos θ i .
a , b [ T ( a , b ) + R ( a , b ) ] = 1 .

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