Abstract

The propagation of a complex amplitude distribution in quadratix-index material is studied by the characteristic point function, and we determine the maximum distance for which an optical image and transform can be transmitted without estimable loss of information due to modal dispersion.

© 1983 Optical Society of America

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References

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  1. C. Gómez-Reino, E. Larrea, Appl. Opt. 21, 4271 (1982);Appl. Opt. 22, 387, 970 (1983).
    [CrossRef] [PubMed]
  2. C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982).
    [CrossRef]
  3. A. Yariv, J. Opt. Soc. Am. 66, 301 (1976).
    [CrossRef]
  4. C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 45, 372 (1983).
    [CrossRef]
  5. E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), Chap. 5.
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chaps. 3 and 4.
  7. C. Gómez-Reino, E. Larrea, Opt. Acta 29, 691 (1982).
    [CrossRef]

1983

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 45, 372 (1983).
[CrossRef]

1982

C. Gómez-Reino, E. Larrea, Opt. Acta 29, 691 (1982).
[CrossRef]

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982).
[CrossRef]

C. Gómez-Reino, E. Larrea, Appl. Opt. 21, 4271 (1982);Appl. Opt. 22, 387, 970 (1983).
[CrossRef] [PubMed]

1976

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chaps. 3 and 4.

Gómez-Reino, C.

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 45, 372 (1983).
[CrossRef]

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982).
[CrossRef]

C. Gómez-Reino, E. Larrea, Opt. Acta 29, 691 (1982).
[CrossRef]

C. Gómez-Reino, E. Larrea, Appl. Opt. 21, 4271 (1982);Appl. Opt. 22, 387, 970 (1983).
[CrossRef] [PubMed]

Larrea, E.

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 45, 372 (1983).
[CrossRef]

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982).
[CrossRef]

C. Gómez-Reino, E. Larrea, Appl. Opt. 21, 4271 (1982);Appl. Opt. 22, 387, 970 (1983).
[CrossRef] [PubMed]

C. Gómez-Reino, E. Larrea, Opt. Acta 29, 691 (1982).
[CrossRef]

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), Chap. 5.

Pérez, M. V.

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 45, 372 (1983).
[CrossRef]

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chaps. 3 and 4.

Yariv, A.

Appl. Opt.

J. Opt. Soc. Am.

Opt. Acta

C. Gómez-Reino, E. Larrea, Opt. Acta 29, 691 (1982).
[CrossRef]

Opt. Commun.

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982).
[CrossRef]

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 45, 372 (1983).
[CrossRef]

Other

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), Chap. 5.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chaps. 3 and 4.

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Equations (39)

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n 2 ( r ) = n 0 2 ( 1 g 2 r 2 ) ,
n z = 0 ,
l 0 = n z = const ,
r ¨ + ( n 0 g l 0 ) 2 r = 0 ,
x = x 0 cos z ̅ + p 0 n 0 g sin z ̅
y = y 0 cos z ̅ + q 0 n 0 g sin z ̅ ,
z ̅ = n 0 g l 0 z .
p = n x = l 0 x ˙ ,
q = n y = l 0 y ˙ ,
l = l 0 ,
p 2 + q 2 + l 0 2 = n 2 .
1 2 d 2 r 2 d z 2 = d d z ( r r ˙ ) = r r ¨ + ( r ˙ ) 2 .
( r ˙ ) 2 = ( n l 0 ) 2 1 ,
d d z ( r r ˙ ) = 1 l 0 2 ( 2 n 2 n 0 2 l 0 2 ) .
V = 0 s nds .
V = 0 s n s ˙ d z = 1 l 0 0 z n 2 d z .
V = l 0 2 ( r r ˙ r 0 r ˙ 0 ) + 1 2 l 0 ( n 0 2 + l 0 2 ) z .
r r ˙ = 1 2 l 0 [ 2 ( x 0 p 0 + y 0 q 0 ) cos 2 z ̅ + p 0 2 + q 0 2 ( n 0 g r 0 ) 2 n 0 g sin 2 z ̅ ] ,
V = 1 4 p 0 2 + q 0 2 ( n 0 g r 0 ) 2 n 0 g sin 2 z ̅ ( x 0 p 0 + y 0 p 0 ) × sin 2 z ̅ + 1 2 l 0 ( n 0 2 + l 0 2 ) z .
V ( r , r 0 ; z ) = n 0 g 2 sin z ̅ [ ( r 2 + r 0 2 ) cos z ̅ 2 r r 0 ] + 1 2 l 0 ( n 0 2 + l 0 2 ) z .
r 2 2 r r 0 cos z ̅ = r 0 2 cos 2 z ̅ + p 0 2 + q 0 2 ( n 0 g ) 2 sin 2 z ̅ ,
l 0 2 = n 0 2 ( 1 g 2 r 0 2 ) ( p 0 2 + q 0 2 ) ,
l 0 2 = n 0 2 [ 1 g 2 sin 2 z ̅ ( r 0 2 + r 2 2 r r 0 cos z ̅ ) ] .
l 0 2 ( 1 g 2 r 0 2 ) n 0 2 .
( g r 0 ) 2 1 .
V p a ( r , r 0 ; z ) n 0 g 2 tan g ( g z ) [ r 2 + r 0 2 2 r r 0 cos ( g z ) ] + n 0 z .
2 a + k 2 n 2 a = 0 ,
a ( r , z ) = a ( r 0 ) exp ( 1 2 l 0 z 2 Vdz ) exp ( ikV ) ,
( V ) 2 = n 2 .
a ( r , d ) = c R 2 a ( r 0 ) exp ( 1 2 l 0 d 2 Vdz ) exp ( ikV ) d r 0 ,
a ( r , 0 ) = a ( r 0 ) .
2 V = 2 n 0 g cotan g z ̅ ,
a ( r , d ) = c R 2 a ( r 0 ) sin d ̅ exp [ ikV ( r , r 0 ; d ) ] d r 0 ,
d ̅ = n 0 g l 0 d .
c = i k n 0 g 2 π
a ( r , d ) = i k n 0 g 2 π R 2 a ( r 0 ) sin d ̅ exp [ ikV ( r , r 0 ; d ) ] d r 0 .
a ( r , d ) = i k n 0 g exp ( i k n 0 d ) 2 π sin ( g d ) R 2 a ( r 0 ) exp { i k n 0 g 2 tan g ( g d ) [ r 2 + r 0 2 2 r r 0 cos ( g d ) ] } d r 0 ,
( n 0 2 + l 0 2 2 l 0 n 0 ) k L π or ( n 0 l 0 1 ) 2 L λ ,
L max 4 λ ( g r 0 m ) 4

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