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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 9 — Sep. 1, 2003
  • pp: 1812–1817

Hyperbolic reflections as fundamental building blocks for multilayer optics

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


JOSA A, Vol. 20, Issue 9, pp. 1812-1817 (2003)
http://dx.doi.org/10.1364/JOSAA.20.001812


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Abstract

We re-elaborate on the basic properties of lossless multilayers by using bilinear transformations. We study some interesting properties of the multilayer transfer function in the unit disk, showing that hyperbolic geometry turns out to be an essential tool for understanding multilayer action. We use a simple trace criterion to separate multilayers into three classes that represent rotations, translations, or parallel displacements. Moreover, we show that these three actions can be decomposed as a product of two reflections in hyperbolic lines. Therefore, we conclude that hyperbolic reflections can be considered as the basic pieces for a deeper understanding of multilayer optics.

© 2003 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: February 13, 2003
Revised Manuscript: April 11, 2003
Manuscript Accepted: April 11, 2003
Published: September 1, 2003

Citation
Alberto G. Barriuso, Juan J. Monzón, Luis L. Sánchez-Soto, and José F. Cariñena, "Hyperbolic reflections as fundamental building blocks for multilayer optics," J. Opt. Soc. Am. A 20, 1812-1817 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-9-1812


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References

  1. B. F. Schutz, Geometrical Methods of Mathematical Physics (Cambridge U. Press, Cambridge, UK, 1997).
  2. J. J. Monzón, L. L. Sánchez-Soto, “Lossless multilayers and Lorentz transformations: more than an analogy,” Opt. Commun. 162, 1–6 (1999). [CrossRef]
  3. J. J. Monzón, L. L. Sánchez-Soto, “Fully relativisticlike formulation of multilayer optics,” J. Opt. Soc. Am. A 16, 2013–2018 (1999). [CrossRef]
  4. H. S. M. Coxeter, Introduction to Geometry (Wiley, New York, 1969).
  5. 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]
  6. 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]
  7. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  8. D. Han, Y. S. Kim, M. E. Noz, “Polarization optics and bilinear representations of the Lorentz group,” Phys. Lett. A 219, 26–32 (1996). [CrossRef]
  9. H. Kogelnik, “Imaging of optical modes–resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965). [CrossRef]
  10. M. Nakazawa, J. H. Kubota, A. Sahara, K. Tamura, “Time-domain ABCD matrix formalism for laser mode-locking and optical pulse transmission,” IEEE J. Quantum Electron. QE34, 1075–1081 (1998). [CrossRef]
  11. R. Melter, A. Rosenfeld, P. Bhattacharya, Vision Geometry (American Mathematical Society, Providence, R.I., 1991).
  12. K. A. Dunn, “Poincaré group as reflections in straight lines,” Am. J. Phys. 49, 52–55 (1981). [CrossRef]
  13. When ambient (0) and substrate (m+1)media are different, the angles θ0and θm+1are conected by Snell’s law n0sin θ0=nm+1sin θm+1,where njdenotes the refractive index of the jth medium.
  14. 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]
  15. 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]
  16. D. Pedoe, A Course of Geometry (Cambridge U. Press, Cambridge, UK, 1970).
  17. A. Mischenko, A. Fomenko, A Course of Differential Geometry and Topology (Mir, Moscow, 1988), Sect. 1.4.
  18. 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]
  19. J. J. Monzón, T. Yonte, L. L. Sánchez-Soto, “Basic factorization for multilayers,” Opt. Lett. 26, 370–372 (2001). [CrossRef]
  20. B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

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