OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 21 — Oct. 16, 2006
  • pp: 9627–9635

Perfect imaging in a homogeneous three-dimensional region

Juan C. Miñano  »View Author Affiliations

Optics Express, Vol. 14, Issue 21, pp. 9627-9635 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (259 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We introduce a family of spherically symmetric gradient-index lenses forming a perfect (sharp) image of any point of the space in three dimensions, including the points of a homogeneous (constant refractive index) region. The only previously known example of an optical instrument with such properties is the plane mirror (or combinations thereof).

© 2006 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design

Original Manuscript: September 5, 2006
Manuscript Accepted: September 26, 2006
Published: October 16, 2006

Juan C. Miñano, "Perfect imaging in a homogeneous threedimensional region," Opt. Express 14, 9627-9635 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Born, E. Wolf, Principles of Optics, (Pergamon, Oxford, 1989).
  2. G. W. Forbes and J. K. Wallace, "Can the bounds to system performance in geometrical optics be attained?," J. Opt. Soc. Am. A 12, 2064-2071 (1995) http://www.opticsinfobase.org/abstract.cfm?URI=josaa-12-9-2064 [CrossRef]
  3. M. Herzberger, Modern Geometrical Optics, (Interscience, New York, 1958).
  4. S. Cornbleet, Microwave and Geometrical Optics (Academic, 1994).
  5. R.K. Luneburg, Mathematical Theory of Optics, (University of California Press, Los Angeles 1964).
  6. E. Kreyszig, Differential Geometry, (Dover, New York, 1991).
  7. D.J. Struik, Lectures on Classical Differential Geometry, (Dover, New York, 1988).
  8. J. Eaton, "On spherically symmetric lenses," IRE Transactions on Antennas and Propagation, 4, 66-71 (1952), http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=25697&arnumber=1144350&count=27&index=14
  9. A.F. Kay, "Spherically Symmetric Lenses," IRE Transactions on Antennas and Propagation, 7, 32-38, (1959), http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=1144648 [CrossRef]
  10. S.P. Morgan, "Generalizations of Spherically Symmetric Lenses," IRE Transactions on Antennas and Propagation, 7, 342-345 (1959), http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=1144697 [CrossRef]
  11. J.C. Miñano, P. Benítez, A. Santamaría, "Hamilton-Jacobi equation in momentum space," Opt. Express 14, 9083-9092 (2006). [CrossRef] [PubMed]
  12. P. Uslenghi, "Electromagnetic and Optical Behavior of Two Classes of Dielectric Lenses," IEEE Transactions on Antennas and Propagation, 17, 235-236 (1969), http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=1139390 [CrossRef]
  13. U. Leonhardt, "Optical Conformal Mapping", Science,  312, 1777-1780 (2006), http://www.sciencemag.org/cgi/rapidpdf/1126493?ijkey=afgHAtDOTcMj.&keytype=ref&siteid=sci [CrossRef] [PubMed]
  14. U. Leonhardt, "Notes on Conformal Invisibility Devices", New Journal of Physics 8, 118 (2006), http://stacks.iop.org/1367-2630/8/118 [CrossRef]
  15. M. Kerker, "Invisible bodies," J. Opt. Soc. Am. 65, 376- (1975) http://www.opticsinfobase.org/abstract.cfm?URI=josa-65-4-376 [CrossRef]
  16. G. Gbur, "Nonradiating sources and other 'invisible' objects", in E. Wolf (Ed.), Prog. in Optics, vol. 45 (Elsevier, Amsterdam, 2003), p. 273. [CrossRef]
  17. E. Wolf, T. Habashy, "Invisible bodies and uniqueness of the inverse scattering problem," J. of Modern Optics,  40, 785-792 (1993) http://taylorandfrancis.metapress.com/openurl.asp?genre=article&issn=0950-0340&volume=40&issue=5&spage=785. [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