OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 12 — Dec. 1, 2004
  • pp: 2386–2391

Vectorlike representation of multilayers

Alberto G. Barriuso, Juan J. Monzón, Luis L. Sánchez-Soto, and José F. Cariñena  »View Author Affiliations

JOSA A, Vol. 21, Issue 12, pp. 2386-2391 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (311 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We use the concept of turns to provide a geometrical representation of the action of any lossless multilayer, which can be considered to be analogous in the unit disk to sliding vectors in Euclidean geometry. This construction clearly shows the peculiar effects arising in the composition of multilayers. A simple optical experiment revealing the appearance of the Wigner angle is analyzed in this framework.

© 2004 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(120.5700) Instrumentation, measurement, and metrology : Reflection
(120.7000) Instrumentation, measurement, and metrology : Transmission
(230.4170) Optical devices : Multilayers

Original Manuscript: March 29, 2004
Revised Manuscript: June 2, 2004
Manuscript Accepted: June 2, 2004
Published: December 1, 2004

Alberto G. Barriuso, Juan J. Monzón, Luis L. Sánchez-Soto, and José F. Cariñena, "Vectorlike representation of multilayers," J. Opt. Soc. Am. A 21, 2386-2391 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. W. R. Hamilton, Lectures on Quaternions (Hodges & Smith, Dublin, 1853).
  2. L. C. Biedenharn, J. D. Louck, Angular Momentum in Quantum Physics (Addison-Wesley, Reading, Mass., 1981).
  3. J. J. Monzón, L. L. Sánchez-Soto, “Lossless multilayers and Lorentz transformations: more than an analogy,” Opt. Commun. 162, 1–6 (1999). [CrossRef]
  4. J. J. Monzón, L. L. Sánchez-Soto, “Fully relativisticlike formulation of multilayer optics,” J. Opt. Soc. Am. A 16, 2013–2018 (1999). [CrossRef]
  5. M. Juárez, M. Santander, “Turns for the Lorentz group,” J. Phys. A 15, 3411–3424 (1982). [CrossRef]
  6. R. Simon, N. Mukunda, E. C. G. Sudarshan, “Hamilton’s theory of turns generalized to Sp(2, R),” Phys. Rev. Lett. 62, 1331–1334 (1989). [CrossRef] [PubMed]
  7. R. Simon, N. Mukunda, E. C. G. Sudarshan, “The theory of screws: a new geometric representation for the group SU(1, 1),” J. Math. Phys. 30, 1000–1006 (1989). [CrossRef]
  8. H. A. Macleod, Thin-Film Optical Filters (Hilger, Bristol, UK, 1986).
  9. J. H. Apfel, “Graphics in optical coating design,” Appl. Opt. 11, 1303–1312 (1972). [CrossRef] [PubMed]
  10. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1991).
  11. L. M. Brekovskikh, Waves in Layered Media (Academic, New York, 1960).
  12. J. Lekner, Theory of Reflection (Martinus Nijhoff, Dordrecht, The Netherlands, 1987).
  13. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  14. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  15. F. Abelès, “Sur la propagation des ondes electromagnétiques dans les milieux stratifiés,” Ann. Phys. (Paris) 3, 504–520 (1948).
  16. P. C. S. Hayfield, G. W. T. White, “An assessment of the stability of the Drude–Tronstad polarized light method forthe study of film growth on polycrystalline metals,” in Ellipsometry in the Measurements of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, J. Kruger, eds., Natl. Bur. Stand. Misc. Publ. 256 (U.S. Government Printing Office, Washington, D.C., 1964), pp. 157–200. For a more recent review of the model see Ref. 13, Sec. 4.6.
  17. T. Yonte, J. J. Monzón, L. L. Sánchez-Soto, J. F. Cariñena, C. López-Lacasta, “Understanding multilayers from a geometrical viewpoint,” J. Opt. Soc. Am. A 19, 603–609 (2002). [CrossRef]
  18. I. Ohlı́dal, D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics, Vol. 41, E. Wolf, ed. (Elsevier, North-Holland, Amsterdam, 2000), pp. 181–282.
  19. J. J. Monzón, T. Yonte, L. L. Sánchez-Soto, J. F. Cariñena, “Geometrical setting for the classification of multilayers,” J. Opt. Soc. Am. A 19, 985–991 (2002). [CrossRef]
  20. L. L. Sánchez-Soto, J. J. Monzón, T. Yonte, J. F. Cariñena, “Simple trace criterion for classification of multilayers,” Opt. Lett. 26, 1400–1402 (2001). [CrossRef]
  21. A. F. Beardon, The Geometry of Discrete Groups (Springer, New York, 1983), Chap. 7.
  22. A. Ben-Menahem, “Wigner’s rotation revisited,” Am. J. Phys. 53, 62–66 (1985). [CrossRef]
  23. D. A. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  24. A. A. Ungar, “The relativistic velocity composition paradox and the Thomas rotation,” Found. Phys. 19, 1385–1396 (1989). [CrossRef]
  25. J. J. Monzón, L. L. Sánchez-Soto, “Origin of the Thomas rotation that arises in lossless multilayers,” J. Opt. Soc. Am. A 16, 2786–2792 (1999). [CrossRef]
  26. J. J. Monzón, L. L. Sánchez-Soto, “A simple optical demonstration of geometric phases from multilayer stacks: the Wigner angle as an anholonomy,” J. Mod. Opt. 48, 21–34 (2001). [CrossRef]
  27. A. Shapere, F. Wilczek, eds. Geometric Phases in Physics (World Scientific, Singapore, 1989).
  28. P. K. Aravind, “The Wigner angle as an anholonomy in rapidity space,” Am. J. Phys. 65, 634–636 (1997). [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