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  1. R. K. Luneberg, Mathematical Theory of Optics (Brown University Press, Providence, Rhode Island, 1944), p. 359.
  2. M. Severin, Physik. Z. 123, 426 (1951).
    [Crossref]
  3. J. P. Vasseur, Ann. Phys. (Paris) 7, 506 (1952).
  4. P. Young, Phil. Trans. Roy. Soc. (London) 20, 26 (1802).
  5. E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 52, 765 (1962).
    [Crossref]

1962 (1)

E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 52, 765 (1962).
[Crossref]

1952 (1)

J. P. Vasseur, Ann. Phys. (Paris) 7, 506 (1952).

1951 (1)

M. Severin, Physik. Z. 123, 426 (1951).
[Crossref]

1802 (1)

P. Young, Phil. Trans. Roy. Soc. (London) 20, 26 (1802).

Luneberg, R. K.

R. K. Luneberg, Mathematical Theory of Optics (Brown University Press, Providence, Rhode Island, 1944), p. 359.

Marchand, E. W.

E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 52, 765 (1962).
[Crossref]

Severin, M.

M. Severin, Physik. Z. 123, 426 (1951).
[Crossref]

Vasseur, J. P.

J. P. Vasseur, Ann. Phys. (Paris) 7, 506 (1952).

Wolf, E.

E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 52, 765 (1962).
[Crossref]

Young, P.

P. Young, Phil. Trans. Roy. Soc. (London) 20, 26 (1802).

Ann. Phys. (Paris) (1)

J. P. Vasseur, Ann. Phys. (Paris) 7, 506 (1952).

J. Opt. Soc. Am. (1)

E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 52, 765 (1962).
[Crossref]

Phil. Trans. Roy. Soc. (London) (1)

P. Young, Phil. Trans. Roy. Soc. (London) 20, 26 (1802).

Physik. Z. (1)

M. Severin, Physik. Z. 123, 426 (1951).
[Crossref]

Other (1)

R. K. Luneberg, Mathematical Theory of Optics (Brown University Press, Providence, Rhode Island, 1944), p. 359.

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Figures (1)

Fig. 1
Fig. 1

Illustrating notation used in one-side boundary value problem.

Equations (22)

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E x ( P ) = 1 2 π A E x ( i ) z Q G d S ,
E y ( P ) = 1 2 π A E y ( i ) z Q G d S ,
E z ( P ) = 1 2 π A ( E x ( i ) x Q G + E y ( i ) y Q G ) d S ,
E x ( P ) = 1 2 π A E x ( i ) Q G · n d S ,
1 2 π E x ( i ) Q G = Q × [ W ( 1 ) ( P , Q ) W ( 1 ) ( P * , Q ) ] ,
W ( 1 ) ( P , Q ) = 1 4 π exp ( i k s ) s s ˆ × 0 exp ( i k μ ) E x ( i ) · ( r + μ s ˆ ) d μ + W ( 1 ) ( P , A ) .
( 1 / 2 π ) E y ( i ) Q G = Q × [ W ( 2 ) ( P , Q ) W ( 2 ) ( P * , Q ) ] ,
W ( 2 ) ( P , Q ) = 1 4 π exp ( i k s ) s s ˆ × 0 exp ( i k μ ) E y ( i ) · ( r + μ s ˆ ) d μ + W ( 2 ) ( P , A ) .
E x ( P ) = A Q × [ W ( 1 ) ( P , Q ) W ( 1 ) ( P * , Q ) ] · n d S ,
E y ( P ) = A Q × [ W ( 2 ) ( P , Q ) W ( 2 ) ( P * , Q ) ] · n d S .
E z ( P ) = 1 2 π A ( E x ( i ) x Q G + E y ( i ) y Q G ) d S , = 1 2 π A [ x Q ( G E x i ) + y Q ( G E y i ) ] d S + 1 2 π A ( G x Q E x ( i ) + G y Q E y ( i ) + G z Q E z ( i ) ) d S 1 2 π A G z Q E z ( i ) d S .
E z ( P ) = 1 2 π A [ x Q ( G E x ( i ) ) + y Q ( G E y ( i ) ) ] d S + 1 2 π A G z Q E z ( i ) d S .
A x Q ( G E x ( i ) ) d S = c G E x ( i ) d y ,
A y Q ( G E y ( i ) ) d S = c G E y ( i ) d x .
1 2 π G Q E z ( i ) = Q × [ W ( 3 ) ( P , Q ) + W ( 3 ) ( P * , Q ) ] ,
W ( 3 ) ( P , Q ) = 1 4 π exp ( i k s ) s s ˆ × 0 exp ( i k μ ) E z ( i ) · ( r + μ s ˆ ) d μ + W ( 3 ) ( P , A ) .
E x ( P ) = A Q × [ W ( 1 ) ( P , Q ) W ( 1 ) ( P * , Q ) ] · n d S ,
E y ( P ) = A Q × [ W ( 2 ) ( P , Q ) W ( 2 ) ( P * , Q ) ] · n d S ,
E z ( P ) = A Q × [ W ( 3 ) ( P , Q ) + W ( 3 ) ( P * , Q ) ] · n d S + 1 2 π c ( G E x ( i ) d y G E y ( i ) d x ) .
E x ( P ) = c [ W ( 1 ) ( P , Q ) W ( 1 ) ( P * , Q ) ] d t + j F x j ,
E y ( P ) = c [ W ( 2 ) ( P , Q ) W ( 2 ) ( P * , Q ) ] d t + j F y j ,
E z ( P ) = c [ W ( 3 ) ( P , Q ) W ( 3 ) ( P * , Q ) ] d t + F z j 1 2 π c ( G E x ( i ) d y G E y ( i ) d x )