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Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Vol. 36, Iss. 9 — May. 1, 2011
  • pp: 1701–1703

Two Lagrange-like optical invariants and some applications

Fabio Corrente and Pasquale Onorato  »View Author Affiliations


Optics Letters, Vol. 36, Issue 9, pp. 1701-1703 (2011)
http://dx.doi.org/10.1364/OL.36.001701


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Abstract

Geometric optics can be completely derived from Fermat’s principle, as classical mechanics can be obtained by the application of the Hamilton principle. In Lagrangian optics, for optical systems with rotational symmetry, is known the invariant L 3 , the Lagrange optical invariant. For systems built only with spherical lenses, we demonstrate there are two other optical invariants, L 1 and L 2 , analogous to L 3 . A proof based on Snell’s law, the Weierstrass–Erdman jump condition, and the expression of the ray between two optical surfaces in the Hamiltonian formalism is reported. The presence of a conserved vector, L, allows us to write the equation of an emerging ray without any approximation.

© 2011 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(080.0080) Geometric optics : Geometric optics
(220.3630) Optical design and fabrication : Lenses

History
Original Manuscript: February 2, 2011
Manuscript Accepted: March 22, 2011
Published: April 29, 2011

Citation
Fabio Corrente and Pasquale Onorato, "Two Lagrange-like optical invariants and some applications," Opt. Lett. 36, 1701-1703 (2011)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-9-1701


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References

  1. R. Feynman, R. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 1963).
  2. A. Marasco and A. Romano, Il Nuovo Cimento B 121, 91(2006).
  3. M. S. Mahoney, The Mathematical Career of Pierre de Fermat, 1601-1665, 2nd ed. (Princeton U. Press, 1994).
  4. A. Romano, Geometric Optics (Springer, 2010). [CrossRef]
  5. V. Lakshminarayanan, A. Ghatak, and K. Thyagarajan, Lagrangian Optics (Springer, 2001). [CrossRef]
  6. D. J. Gross, Proc. Natl. Acad. Sci. USA 93, 14256 (1996). [CrossRef] [PubMed]
  7. F. Corrente, “Questioni di Ottica Geometrica,” Master’sthesis (Università degli studi di Napoli Federico II, 2005).
  8. L. P. Lebedev and M. J. Cloud, The Calculus of Variations and Functional Analysis: With Optimal Control and Applications in Mechanics (World Scientific, 2003). [CrossRef] [PubMed]
  9. R. K. Luneburg, Mathematical Theory of Optics (U. of California Press, 1964).
  10. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, 1970).

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