Abstract

In this paper we determine the image planes and the transmittance function for a conical gradient-index (GRIN) rod, and we consider the problem of modal propagation.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Gómez-Reino, E. Larrea, Appl. Opt. 21, 4271 (1982); Appl. Opt. 22, 387 (1983).
    [CrossRef] [PubMed]
  2. C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982); Opt. Commun. 45, 372 (1983).
    [CrossRef]
  3. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), Sec. 16.
  4. S. J. S. Brown, Appl. Opt. 19, 1056 (1980).
    [CrossRef] [PubMed]
  5. A. Yariv, J. Opt. Soc. Am. 66, 301 (1976).
    [CrossRef]

1982

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982); Opt. Commun. 45, 372 (1983).
[CrossRef]

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

1980

1976

Brown, S. J. S.

Gómez-Reino, C.

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982); Opt. Commun. 45, 372 (1983).
[CrossRef]

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

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), Sec. 16.

Larrea, E.

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

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982); Opt. Commun. 45, 372 (1983).
[CrossRef]

Pérez, M. V.

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982); Opt. Commun. 45, 372 (1983).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), Sec. 16.

Yariv, A.

Appl. Opt.

J. Opt. Soc. Am.

Opt. Commun.

C. Gómez-Reino, M. V. Pérez, E. Larrea, Opt. Commun. 44, 8 (1982); Opt. Commun. 45, 372 (1983).
[CrossRef]

Other

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), Sec. 16.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Conical GRIN rod.

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

n 2 ( x , y , z ) = n 0 2 [ 1 - g 2 ( z ) ( x 2 + y 2 ) ] ,
g ( z ) = g 0 1 - z l = g 0 t ( z ) ,
H ¨ 1 , 2 ( z ) + g 2 ( z ) H 1 , 2 ( z ) = 0 ,
H 1 ( o ) = H ˙ 2 ( o ) = 0 ,
H ˙ 1 ( o ) = H 2 ( o ) = 1 ,
H ˙ 1 ( z ) H 2 ( z ) - H 1 ( z ) H ˙ 2 ( z ) = 1 ,
H 1 ( z ) = - L b t ( z ) sin [ b ln t ( z ) ] ,
H 2 ( z ) = t ( z ) { cos [ b ln t ( z ) ] - sin [ b ln t ( z ) ] 2 b } ,
b 2 = ( g 0 L ) 2 - ¼ .
sin [ b ln t ( z m ) ] = 0 ,
t ( z m ) = 1 - z m L = exp ( - m π b ) ,
z m = L [ 1 - exp ( - m π b ) ] ,
M = H 2 ( z m ) = ( - 1 ) m t ( z m ) = ( - 1 ) m exp ( - m π 2 b ) ,
t ( z ) = ρ ( z ) ρ 1 ,
ρ ( z m ) = ρ 1 exp ( - m π b ) .
t ( x , y , d ) = exp ( i k n 0 d ) H 2 ( d ) exp [ i k n 0 H ˙ 2 ( d ) 2 H 2 ( d ) ( x 2 + y 2 ) ] ,
f = H 2 ( d ) n 0 H ˙ 2 ( d ) ,
H ˙ 2 ( z ) = ρ 1 ρ ( z ) ( g 0 L ) 2 b L sin [ b ln ρ ( z ) ρ 1 ] ,
f = - L ρ 2 2 n 0 ρ 1 ( g 0 L ) 2 [ 1 - 2 b tan ( b ln ρ 2 ρ 1 ) ] ,
β p q = k n 0 - 1 z [ b g 0 L 0 z g ( z ) d z ] ( p + q + 1 ) ,
b g 0 L 0 z g ( z ) d z = - b ln t ( z ) ,
β p q = k n 0 + ( p + q + 1 ) b ln t ( z ) z .
b g 0 L 0 z m g ( z ) d z = - b ln t ( z m ) = m π ;             m = 0 , 1 , 2 ,
β p q = k n 0 { 1 - 2 ( p + q + 1 ) k n 0 z [ b g 0 L 0 z g ( z ) d z ] } 1 / 2 = k n 0 [ 1 + 2 ( p + q + 1 ) b ln t ( z ) k n 0 z ] 1 / 2 .
β p q = β p q - ( p + q + 1 ) 2 b 2 ln 2 t ( z ) 2 k n 0 z 2 + ,
β p q - β p q z π .
b 2 ln t ( z max ) z max 4 π 2 n 0 λ ( p max + q max + 1 ) 2 .
z max m max 2 λ ( p max + q max + 1 ) 2 4 n 0

Metrics