OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 11 — Nov. 1, 1999
  • pp: 2786–2792

Origin of the Thomas rotation that arises in lossless multilayers

J. J. Monzón and L. L. Sánchez-Soto  »View Author Affiliations


JOSA A, Vol. 16, Issue 11, pp. 2786-2792 (1999)
http://dx.doi.org/10.1364/JOSAA.16.002786


View Full Text Article

Enhanced HTML    Acrobat PDF (304 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

From the basic fact that the matrix that describes a lossless multilayer belongs to the group SU(1, 1), which is locally isomorphic to the (2+1)-dimensional Lorentz group SO(2, 1), we present a natural identification of the parameters of the multilayer with those of a Lorentz transformation. We show that the phase that appears when one is studying the reflection and transmission of light on a compound multilayer is simply the relativistic Thomas rotation. We propose a simple optical experiment to determine the angle of this rotation.

© 1999 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

History
Original Manuscript: April 1, 1999
Revised Manuscript: June 14, 1999
Manuscript Accepted: June 14, 1999
Published: November 1, 1999

Citation
J. J. Monzón and L. L. Sánchez-Soto, "Origin of the Thomas rotation that arises in lossless multilayers," J. Opt. Soc. Am. A 16, 2786-2792 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-11-2786


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Y. S. Kim, M. E. Noz, Theory and Applications of the Poincaré Group (Reidel, Dordrecht, The Netherlands, 1986).
  2. V. Guillemin, S. Sternberg, Symplectic Techniques in Physics (Cambridge U. Press, London, 1984).
  3. J. Sánchez-Mondragón, K. B. Wolf, Lie Methods in Optics, Vol. 250 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1986).
  4. K. B. Wolf, Lie Methods in Optics II, Vol. 352 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1989). [CrossRef]
  5. A. J. Dragt, “Lie algebraic theory of geometrical optics and optical aberrations,” J. Opt. Soc. Am. 72, 372–379 (1982). [CrossRef]
  6. K. B. Wolf, “Symmetry in Lie optics,” Ann. Phys. (New York) 172, 1–25 (1986). [CrossRef]
  7. J. F. Cariñena, J. Nasarre, “On the symplectic structures arising in geometric optics,” Fortschr. Phys. 44, 181–198 (1996). [CrossRef]
  8. A. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986).
  9. J. M. Vigoureux, “Polynomial formulation of reflection and transmission by stratified planar structures,” J. Opt. Soc. Am. A 8, 1697–1701 (1991). [CrossRef]
  10. J. M. Vigoureux, “Use of Einstein’s addition law in studies of reflection by stratified planar structures,” J. Opt. Soc. Am. A 9, 1313–1319 (1992). [CrossRef]
  11. J. M. Vigoureux, Ph. Grossel, “A relativistic-like presentation of optics in stratified planar media,” Am. J. Phys. 61, 707–712 (1993). [CrossRef]
  12. J. J. Monzón, L. L. Sánchez-Soto, “Lossless multilayers and Lorentz transformations: more than an analogy,” Opt. Commun. 162, 1–6 (1999). [CrossRef]
  13. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981). [CrossRef]
  14. M. D. Reid, D. F. Walls, “Generation of squeezed states in degenerate four-wave mixing,” Phys. Rev. A 31, 1622–1635 (1985). [CrossRef] [PubMed]
  15. J. R. Klauder, S. L. McCall, B. Yurke, “Squeezed states from nondegenerate four-wave mixing,” Phys. Rev. A 33, 3204–3209 (1986). [CrossRef] [PubMed]
  16. D. Han, E. E. Hardekopf, Y. S. Kim, “Thomas precession and squeezed states of light,” Phys. Rev. A 39, 1269–1276 (1989). [CrossRef] [PubMed]
  17. A. Ben-Menahem, “Wigner’s rotation revisited,” Am. J. Phys. 53, 62–66 (1985). [CrossRef]
  18. A. C. Hirshfeld, F. Metzger, “A simple formula for combining rotations and Lorentz boosts,” Am. J. Phys. 54, 550–552 (1986). [CrossRef]
  19. J. M. Vigoureux, “The reflection of light by planar stratified media: the grupoid of amplitudes and a phase ‘Thomas precession,’ ” J. Phys. A 26, 385–393 (1993). [CrossRef]
  20. J. M. Vigoureux, D. V. Labeke, “A geometric phase in optical multilayers,” J. Mod. Opt. 45, 2409–2416 (1998). [CrossRef]
  21. J. Lekner, Theory of Reflection (Kluwer Academic, Dordrecht, The Netherlands, 1987).
  22. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  23. A. O. Barut, R. Ra̧czka, Theory of Group Representations and Applications (PWN-Polish Scientific, Warsaw, 1977).
  24. E. P. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (Academic, New York, 1959).
  25. D. A. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  26. J. J. Monzón, L. L. Sánchez-Soto, “Characterization of symmetric, absorbing 50–50 beam splitters,” Appl. Opt. 35, 106–112 (1996). [CrossRef]
  27. A. A. Ungar, “The relativistic velocity composition paradox and the Thomas rotation,” Found. Phys. 19, 1385–1396 (1989). [CrossRef]
  28. A. A. Ungar, “Successive Lorentz transformations of the electromagnetic field,” Found. Phys. 21, 569–589 (1991). [CrossRef]
  29. A. A. Ungar, “Thomas precession and its associated grouplike structure,” Am. J. Phys. 59, 824–834 (1991). [CrossRef]
  30. H. C. Corben, “Factors of 2 in magnetic moments, spin–orbit coupling, and Thomas precession,” Am. J. Phys. 61, 551–553 (1993). [CrossRef]
  31. M. W. P. Strandberg, “Special relativity completed: the source of some 2s in the magnitude of physical phenomena,” Am. J. Phys. 54, 321–331 (1986). [CrossRef]
  32. J. J. Monzón, L. L. Sánchez-Soto, “Fully relativisticlike formulation of multilayer optics,” J. Opt. Soc. Am. A 16, 2013–2018 (1999). [CrossRef]
  33. P. K. Aravind, “The Wigner angle as an anholonomy in rapidity space,” Am. J. Phys. 65, 634–636 (1997). [CrossRef]
  34. K. Creath, “Phase-measurement interferometric techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 351–393.

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.

Figures

Fig. 1 Fig. 2
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited