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References

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  1. Born and Wolf, Principles of Optics (Pergamon Press, New York, 1959), Chap. X.
  2. P. Roman and E. Wolf, Nuovo cimento 17, 461, 477 (1960).
  3. After this work was completed the authors discovered that P. Roman has developed a similar set of equations.

1960 (1)

P. Roman and E. Wolf, Nuovo cimento 17, 461, 477 (1960).

Born,

Born and Wolf, Principles of Optics (Pergamon Press, New York, 1959), Chap. X.

Roman, P.

P. Roman and E. Wolf, Nuovo cimento 17, 461, 477 (1960).

Wolf,

Born and Wolf, Principles of Optics (Pergamon Press, New York, 1959), Chap. X.

Wolf, E.

P. Roman and E. Wolf, Nuovo cimento 17, 461, 477 (1960).

Nuovo cimento (1)

P. Roman and E. Wolf, Nuovo cimento 17, 461, 477 (1960).

Other (2)

After this work was completed the authors discovered that P. Roman has developed a similar set of equations.

Born and Wolf, Principles of Optics (Pergamon Press, New York, 1959), Chap. X.

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Equations (18)

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j k l k ( 1 ) E l ( x 1 , t 1 ) = - t 1 H j ( x 1 , t 1 )
j k l k ( 1 ) H l ( x 1 , t 1 ) - t 1 E j ( x 1 , t 1 ) = j j ( x 1 , t 1 ) ,
E j k ( x 1 , x 2 , t 1 , t 2 ) = { E j ( x 1 , t 1 ) E k ( x 2 , t 2 ) } ; j k ( x 1 , x 2 , t 1 , t 2 ) = { H j ( x 1 , t 1 ) H k ( x 2 , t 2 ) } ,
j k l m n p k ( 1 ) n ( 2 ) E l ( x 1 , t 1 ) E p ( x 2 , t 2 ) = t 1 t 2 H j ( x 1 , t 1 ) H m ( x 2 , t 2 ) .
j k l m n p k ( 1 ) n ( 2 ) E l p ( x 1 , x 2 , t 1 , t 2 ) = t 1 t 2 j m ( x 1 , x 2 , t 1 , t 2 ) .
j k l m n p k ( 1 ) n ( 2 ) l p ( x 1 , x 2 , t 1 , t 2 ) + t 1 t 2 E j m ( x 1 , x 2 , t 1 , t 2 ) - j k l k ( 1 ) t 2 { H l ( x 1 , t 1 ) E m ( x 2 , t 2 ) } - m n p n ( 2 ) t 1 { E j ( x 1 , t 1 ) H p ( x 2 , t 2 ) } = J j m ( x 1 , x 2 , t 1 , t 2 ) ,
{ H l ( x 1 , t 1 ) E m ( x 2 , t 2 ) }
{ E j ( x 1 , t 1 ) H p ( x 2 , t 2 ) }
( / t 1 ) { H l ( x 1 , t 1 ) E m ( x 2 , t 2 ) }
( / t 2 ) { E j ( x 1 , t 1 ) H p ( x 2 , t 2 ) } ,
j k l m n p l a b p c d a ( 1 ) k ( 1 ) c ( 2 ) n ( 2 ) E b d ( x 1 , x 2 , t 1 , t 2 ) + t 1 2 2 t 2 2 E j m ( x 1 , x 2 , t 1 , t 2 ) + j k l l r s k ( 1 ) r ( 1 ) 2 t 2 2 E s m ( x 1 , x 2 , t 1 , t 2 ) + m n p p u v n ( 2 ) u ( 2 ) 2 t 1 2 E j v ( x 1 , x 2 , t 1 , t 2 ) = t 1 t 2 J j m ( x 1 , x 2 , t 1 , t 2 ) .
j k l m n p r q m k ( 1 ) s ( 1 ) q ( 2 ) n ( 2 ) l p ( x 1 , x 2 , t 1 , t 2 ) + r q m u s j t 1 t 2 s ( 1 ) q ( 2 ) E j m ( x 1 , x 2 , t 1 , t 2 ) + j k l u s j 2 t 2 2 k ( 1 ) s ( 2 ) l r ( x 1 , x 2 , t 1 , t 2 ) + m n p r q m 2 t 1 2 n ( 2 ) q ( 2 ) u p ( x 1 , x 2 , t 1 , t 2 ) = r q m u s j s ( 1 ) q ( 2 ) J j m ( x 1 , x 2 , t 1 , t 2 ) ,
j ( 1 ) E j ( x 1 , t 1 ) = ρ ( x 1 , t 1 ) .
j ( 1 ) t ( 2 ) E j l ( x 1 , x 2 , t 1 , t 2 ) = P ( x 1 , x 2 , t 1 , t 2 ) ,
t 1 t 2 P ( x 1 , x 2 , t 1 , t 2 ) = k ( 1 ) l ( 2 ) J k l ( x 1 , x 2 , t 1 , t 2 ) .
j k l m n p l a b p c d a ( 1 ) k ( 1 ) c ( 2 ) n ( 2 ) E b d ( x 1 , x 2 , τ ) + 4 τ 4 E j m ( x 1 , x 2 , τ ) + j k l l r s k ( 1 ) r ( 1 ) 2 τ 2 E s m ( x 1 , x 2 , τ ) + m n p p u v n ( 2 ) u ( 2 ) 2 τ 2 E j v ( x 1 , x 2 , τ ) = - τ 2 J j m ( x 1 , x 2 , τ )
j k l m n p k ( 1 ) n ( 2 ) E l p ( x 1 , x 2 , τ ) = - τ 2 j m ( x 1 , x 2 , τ )
j k l m n p k ( 1 ) n ( 2 ) l p ( x 1 , x 2 m τ ) - τ 2 E j m ( x 1 , x 2 , τ ) - j k l l q r k ( 1 ) q ( 1 ) E r m ( x 1 , x 2 , τ ) - m n p p r s n ( 2 ) r ( 2 ) E j s ( x 1 , x 2 , τ ) = J j m ( x 1 , x 2 , τ ) .