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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. 19, Iss. 5 — May. 1, 2002
  • pp: 985–991

Geometrical setting for the classification of multilayers

Juan J. Monzón, Teresa Yonte, Luis L. Sánchez-Soto, and José F. Cariñena  »View Author Affiliations


JOSA A, Vol. 19, Issue 5, pp. 985-991 (2002)
http://dx.doi.org/10.1364/JOSAA.19.000985


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Abstract

We elaborate on the consequences of the factorization of the transfer matrix of any lossless multilayer in terms of three basic matrices of simple interpretation. By considering the bilinear transformation that this transfer matrix induces in the complex plane, we introduce the concept of multilayer transfer function and study its properties in the unit disk. In this geometrical setting, our factorization translates into three actions that can be viewed as the basic components for understanding the multilayer behavior. Additionally, we introduce a simple trace criterion that allows us to classify multilayers into three types with properties closely related to one (and only one) of these three basic matrices. We apply this approach to analyze some practical examples that are typical of these types of matrices.

© 2002 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: July 30, 2001
Revised Manuscript: October 3, 2001
Manuscript Accepted: October 19, 2001
Published: May 1, 2002

Citation
Juan J. Monzón, Teresa Yonte, Luis L. Sánchez-Soto, and José F. Cariñena, "Geometrical setting for the classification of multilayers," J. Opt. Soc. Am. A 19, 985-991 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-5-985


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References

  1. H. A. Macleod, Thin-film Optical Filters (Adam Hilger, Bristol, UK, 1986).
  2. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  3. J. Lekner, Theory of Reflection (Kluwer Academic, Dordrecht, The Netherlands, 1987).
  4. J. J. Monzón, L. L. Sánchez-Soto, “Lossless multilayers and Lorentz transformations: more than an analogy,” Opt. Commun. 162, 1–6 (1999). [CrossRef]
  5. J. J. Monzón, L. L. Sánchez-Soto, “Fully relativisticlike formulation of multilayer optics,” J. Opt. Soc. Am. A 16, 2013–2018 (1999). [CrossRef]
  6. 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]
  7. 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]
  8. H. S. M. Coxeter, Non-Euclidean Geometry (University of Toronto Press, Toronto, 1968).
  9. 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]
  10. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Sec. 4.6.
  11. 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]
  12. H. Kogelnik, “Imaging of optical modes–resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965). [CrossRef]
  13. M. Nakazawa, J. H. Kubota, A. Sahara, K. Tamura, “Time-domain ABCD matrix formalism for laser mode-locking and optical pulse transmission,” IEEE J. Sel. Top. Quantum Electron. 34, 1075–1081 (1998). [CrossRef]
  14. J. J. Monzón, T. Yonte, L. L. Sánchez-Soto, “Basic factorization for multilayers,” Opt. Lett. 26, 370–372 (2001). [CrossRef]
  15. 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]
  16. When ambient (0) and substrate (m+1) media are different, the angles θ0 and θm+1 are connected by Snell’s law, n0 sin θ0=nm+1 sin θm+1, where nj denotes the refractive index of the jth medium.
  17. I. Ohlı́dal, D. Franta, “Ellipsometry of thin film systems,” in Progress in Optics XLI, E. Wolf, ed. (North-Holland, Amsterdam, 2000), p. 181.
  18. H. H. Arsenault, B. Macukow, “Factorization of thetransfer matrix for symmetrical optical systems,” J. Opt. Soc. Am. 73, 1350–1359 (1983). [CrossRef]
  19. S. Abe, J. T. Sheridan, “Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation,” Opt. Lett. 19, 1801–1803 (1994). [CrossRef] [PubMed]
  20. J. Shamir, N. Cohen, “Root and power transformations in optics,” J. Opt. Soc. Am. A 12, 2415–2423 (1995). [CrossRef]
  21. S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces (Academic, New York, 1978).
  22. V. Degiorgio, “Phase shift between the transmitted and reflected optical fields of a semireflecting lossless mirror is π/2,” Am. J. Phys. 48, 81–82 (1980). [CrossRef]
  23. A. Zeilinger, “General properties of lossless beam splitters in interferometry,” Am. J. Phys. 49, 882–883 (1981). [CrossRef]
  24. Z. Y. Ou, L. Mandel, “Derivation of reciprocity relations for a beam splitter from energy balance,” Am. J. Phys. 57, 66–67 (1989). [CrossRef]
  25. J. Lekner, “Nonreflecting stratifications,” Can. J. Phys. 68, 738–742 (1989). [CrossRef]
  26. J. Lekner, “The phase relation between reflected and transmitted waves, and some consequences,” Am. J. Phys. 58, 317–320 (1990). [CrossRef]
  27. A. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin, 1986).
  28. V. Bargmann, “Irreducible unitary representations of the Lorentz group,” Ann. Math. 48, 568–640 (1947). [CrossRef]
  29. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999) Sect. 1.6.5.
  30. J. Lekner, “Light in periodically stratified media,” J. Opt. Soc. Am. A 11, 2892–2899 (1994). [CrossRef]
  31. J. Lekner, “Omnidirectional reflection by multilayer dielectric mirrors,” J. Opt. A Pure Appl. Opt. 2, 349–352 (2000). [CrossRef]
  32. H. Bacry, M. Cadilhac, “The metaplectic group and Fourier optics,” Phys. Rev. A 23, 2533–2536 (1981). [CrossRef]
  33. M. Nazarathy, J. Shamir, “First order systems–a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982). [CrossRef]
  34. E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985). [CrossRef]
  35. R. Simon, N. Mukunda, E. C. G. Sudarshan, “Partially coherent beams and a generalized abcd-law,” Opt. Commun. 65, 322–328 (1988). [CrossRef]
  36. R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984). [CrossRef]

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