## Origin of the Thomas rotation that arises in lossless multilayers

JOSA A, Vol. 16, Issue 11, pp. 2786-2792 (1999)

http://dx.doi.org/10.1364/JOSAA.16.002786

Acrobat PDF (304 KB)

### 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

**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: Year | Journal | Reset

### References

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

« Previous Article | Next Article »

OSA is a member of CrossRef.