OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 16 — Aug. 1, 2011
  • pp: 15584–15595

Gradient-index lenses for near-ideal imaging and concentration with realistic materials

Panagiotis Kotsidas, Vijay Modi, and Jeffrey M. Gordon  »View Author Affiliations

Optics Express, Vol. 19, Issue 16, pp. 15584-15595 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (1184 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Fundamentally new classes of spherical gradient-index lenses with imaging and concentration properties that approach the fundamental limits are derived. These analytic solutions admit severely constrained maximum and minimum refractive indices commensurate with existing manufacturable materials, for realistic optical and solar lenses.

© 2011 OSA

OCIS Codes
(110.2760) Imaging systems : Gradient-index lenses
(350.6050) Other areas of optics : Solar energy

ToC Category:
Imaging Systems

Original Manuscript: June 16, 2011
Manuscript Accepted: July 20, 2011
Published: July 28, 2011

Panagiotis Kotsidas, Vijay Modi, and Jeffrey M. Gordon, "Gradient-index lenses for near-ideal imaging and concentration with realistic materials," Opt. Express 19, 15584-15595 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. K. Luneburg, The Mathematical Theory of Optics (U. California Press, Berkeley, 1964).
  2. S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29(9), 1358–1368 (1958). [CrossRef]
  3. J. Sochacki, J. R. Flores, and C. Gómez-Reino, “New method for designing the stigmatically imaging gradient-index lenses of spherical symmetry,” Appl. Opt. 31(25), 5178–5183 (1992). [CrossRef] [PubMed]
  4. Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci. 103(3), 1834–1841 (2007). [CrossRef]
  5. G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008). [PubMed]
  6. M. Ponting, A. Hiltner, and E. Baer, “Polymer nanostructures by forced assembly: process, structure and properties,” Macromol. Symp. 294(1), 19–32 (2010). [CrossRef]
  7. R. Winston, P. Benítez, and J. C. Miñano, with contributions from N. Shatz and J. Bortz, Nonimaging Optics (Elsevier, Oxford, 2005).
  8. J. M. Gordon, “Spherical gradient-index lenses as perfect imaging and maximum power transfer devices,” Appl. Opt. 39(22), 3825–3832 (2000). [CrossRef] [PubMed]
  9. A. Goldstein and J. M. Gordon, “Tailored solar optics for maximal optical tolerance and concentration,” Sol. Energy Mater. Sol. Cells 95(2), 624–629 (2011). [CrossRef]
  10. P. Kotsidas, V. Modi, and J. M. Gordon, “Nominally stationary high-concentration solar optics by gradient-index lenses,” Opt. Express 19(3), 2325–2334 (2011). [CrossRef] [PubMed]
  11. A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, 2nd Ed. (Chapman and Hall/CRC Press, Boca Raton, 2008).
  12. C. T. H. Baker, The Numerical Treatment of Integral Equations (Clarendon Press, Oxford, 1977).
  13. R. Estrada and R. P. Kanwal, Singular Integral Equations (Birkhäuser, Boston, 2000).
  14. L. N. Trefethen, Spectral Methods in Matlab (S.I.A.M., Philadelphia, 2000).
  15. S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature,” J. ACM 10(1), 97–101 (1963). [CrossRef]
  16. D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. ACM 9(1), 84–97 (1962). [CrossRef]
  17. Matlab v. 7.9 and online documentation: http://www.mathworks.com/help/techdoc/ref/quadgk.html (MathWorks Inc., Natick, MA, 2003).
  18. J. M. Gordon, D. Babai, and D. Feuermann, “A high-irradiance solar furnace for photovoltaic characterization and nanomaterial synthesis,” Sol. Energy Mater. Sol. Cells 95(3), 951–956 (2011). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited