OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 2 — Feb. 1, 2002
  • pp: 378–384

Hyperbolic representation of light propagation in a multilayer medium

Remo Giust and Jean-Marie Vigoureux  »View Author Affiliations

JOSA A, Vol. 19, Issue 2, pp. 378-384 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (275 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



By analogy with the representation of the polarization of light on the Poincaré sphere, we describe the propagation and the reflection/transmission of light in a multilayer on a hyperbolic surface. We show that the propagation of light corresponds to a classical rotation on this surface and that its reflection/transmission corresponds to a hyperbolic rotation.

© 2002 Optical Society of America

OCIS Codes
(120.5700) Instrumentation, measurement, and metrology : Reflection
(120.5710) Instrumentation, measurement, and metrology : Refraction
(120.7000) Instrumentation, measurement, and metrology : Transmission
(230.4170) Optical devices : Multilayers

Original Manuscript: February 15, 2001
Revised Manuscript: June 21, 2001
Manuscript Accepted: June 21, 2001
Published: February 1, 2002

Remo Giust and Jean-Marie Vigoureux, "Hyperbolic representation of light propagation in a multilayer medium," J. Opt. Soc. Am. A 19, 378-384 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. C. Jones, “A new calculus for treatment of optical system: I. Description and discussion of the calculus,” J. Opt. Soc. Am. 31, 488–493 (1941). [CrossRef]
  2. H. Hurwitz, R. C. Jones, “A new calculus for treatment of optical system: II. Proof of three general equivalence theorems,” J. Opt. Soc. Am. 31, 493–499 (1941). [CrossRef]
  3. R. C. Jones, “A new calculus for treatment of optical system: III. The Sohncke theory of optical activity,” J. Opt. Soc. Am. 31, 500–503 (1941). [CrossRef]
  4. F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoı̈dales dans les milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris) 5, 596–640 (1950).
  5. J.-M. Vigoureux, “A geometric phase in optical multilayers,” J. Mod. Opt. 45, 2409–2416 (1998). [CrossRef]
  6. M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987). [CrossRef]
  7. M. V. Berry, S. Klein, “Geometric phases from stacks of crystal plates,” J. Mod. Opt. 43, 165–180 (1996). [CrossRef]
  8. J. J. Monzon, L. L. Sanchez-Soto, “Fully relativisticlike formulation of multilayer optics,” J. Opt. Soc. Am. A 16, 2013–2018 (1999). [CrossRef]
  9. J. J. Monzon, L. L. Sanchez-Soto, “Fresnel formulas as Lorentz transformations,” J. Opt. Soc. Am. A 17, 1475–1481 (2000). [CrossRef]
  10. J.-M. Vigoureux, R. Giust, “The use of hyperbolic plane in studies of multilayers,” Opt. Commun. 186, 231–236 (2000). [CrossRef]
  11. N. Ya. Vilenkin, Fonctions spéciales et théorie de la représentation des groups (Dunod, Paris, 1969), Chap. VI.

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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited