Abstract

Similarities between two papers on Luneburg lenses published previously are pointed out.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Sochacki, “Exact analytical solution of the generalized Luneburg lens problem,” J. Opt. Soc. Am. 73, 789–795 (1983).
    [Crossref]
  2. E. Colombini, “Index-profile computation for the generalized Luneburg lens,” J. Opt. Soc. Am. 71, 1403–1405 (1981).
  3. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, Calif., 1966), p. 187.
  4. S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys.,  29, 1358–1368 (1958).
    [Crossref]
  5. W. H. Southwell, “Index profiles for generalized Luneburg lenses and their use in planar optical waveguides,” J. Opt. Soc. Am. 67, 1010–1014 (1977).
    [Crossref]

1983 (1)

1981 (1)

1977 (1)

1958 (1)

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys.,  29, 1358–1368 (1958).
[Crossref]

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.


Equations (7)

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

ω ( ρ , f ) = ( 1 - ρ 2 ) 1 / 2 π m = 0 a m f - ( 2 m + 1 ) r = 0 m b r ρ 2 ( m - r ) ,
ω ( ρ , f ) = ( 1 - ρ 2 ) 1 / 2 π k = 0 s k ( f ) ρ 2 k ,
s k ( f ) = l = 0 ( 2 l ) ! ( 2 l l ! ) 2 [ 2 ( k + l ) + 1 ] 2 f 2 ( k + l ) + 1
k = 0 s k ( f ) = arcsin 1 / f , π
lim p 1 ω ( ρ , f ) = arcsin 1 / f π ( 1 - ρ 2 ) 1 / 2 2 arcsin 1 / f π ( 1 - ρ ) 1 / 2 .
Ω ( ρ , f ) = 1 π k = 0 s k ( f ) ρ 2 k ,
Ω ( 0 , 2 ) = 0.1615329 ,             Ω ( 1 , 2 ) = arcsin ½ π = 0.1666666 , Ω ( 0 , 3 ) = 0.1067789 ,             Ω ( 1 , 3 ) = arcsin π = 0.1081734 , Ω ( 0 , 4 ) = 0.0798586 ,             Ω ( 1 , 4 ) = arcsin ¼ π = 0.0804306.