Numerical evaluation of the Luneburg integral and ray tracing

Applied Optics

Volumn 35, Issue 7, 1996, Pages 1011-1014

  Beliakov, Gleb ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Luneburg integral; Luneburg lens; Numerical integration; Ray tracing; Splines

Indexed keywords

EID: 5944222293     PISSN: 1559128X     EISSN: 21553165     Source Type: Journal    
DOI: 10.1364/AO.35.001011     Document Type: Article

References (15)

1. S. Doric and E. Munro, “General solution of the nonfull-aperture Luneburg lens problem,” J. Opt. Soc. Am. 73, 1083-1086 (1983).
2. J. Sochacki and C. Gomez-Reino, “Nonfull-aperture Luneburg lenses: a novel solution,”Appl. Opt. 24, 1371-1373 (1985).
3. W. H. Southwell, “Ray tracing in gradient-index media,” J. Opt. Soc. Am. 72, 908-911 (1982).
4. G. Beliakov, “Reconstruction of optical characteristics of waveguide lenses by the use of ray tracing,” Appl. Opt. 33, 3401-3404 (1994).
5. G. Beliakov, “Study of mathematical model of the refractive index reconstruction of a smooth thin film waveguide by the use of ray tracing,” Ph.D. dissertation (Russian Peoples’ Friendship University, Moscow, 1992), in Russian.
6. L. Montagnino, “Ray tracing in inhomogeneous media,” J. Opt. Soc. Am. 58, 1667-1668 (1968).
7. A. Sharma, D. V. Kumar, and A. K. Ghatak, “Tracing rays through graded-index media: a new method,”Appl. Opt. 21, 984-987 (1982).
8. S. Doric and E. Munro, “Improvements of the ray trace through the generalized Luneburg lens,” Appl. Opt. 22, 443-445 (1983).
9. J. Sochacki, D. Rogus, and C. Gomez-Reino, “Paraxial design-ing of planar waveguide. Variable-index focusing elements: Part 1. Lenses of circular symmetry,” Fiber Integr. Opt. 8, 121-127 (1989).
10. J. Sochacki, “Functional approach to the Luneburg’s integral for the planar Luneburg lenses design,” IEEE J. Lightwave Technol. LT-3, 684-687 (1985).
11. J. Sochacki, J. R. Flores, R. Staronski, and C. Gomez-Reino, “Improvements in the computation of refractive-index profiles for the generalized Luneburg lens,” J. Opt. Soc. Am. A 8, 1248-1255 (1991).
12. E. Colombini, “Index-profile computation for the generalized Luneburg lens,”J. Opt. Soc. Am. 71, 1403-1405 (1981).
13. W. H. Southwell, “Index profiles for generalized Luneburg lenses and their use in planar optical waveguides,” J. Opt. Soc. Am. 67, 1010-1014 (1977).
14. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1989), p. 122.
15. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Vol. 55 of the Appl. Math. Ser. (Dover, New York, 1972), p. 916.