OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: G. I. Stegeman
  • Vol. 23, Iss. 1 — Jan. 1, 2006
  • pp: 114–119

Dispersion theory of the reflectivity of s-polarized and p-polarized light

Kai-Erik Peiponen and Erik M. Vartiainen  »View Author Affiliations

JOSA B, Vol. 23, Issue 1, pp. 114-119 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (100 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The dispersion theory for reflectivity of s- and p-polarized light is considered. The problem of phase retrieval from reflectance of p-polarized light, in the presence of complex zeros of the reflectivity in the upper half of complex frequency plane, is addressed. In such a case the traditional Kramers–Kronig relations are not valid, but the maximum-entropy method will provide the required solution.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(100.5070) Image processing : Phase retrieval
(120.4530) Instrumentation, measurement, and metrology : Optical constants

ToC Category:

Kai-Erik Peiponen and Erik M. Vartiainen, "Dispersion theory of the reflectivity of s-polarized and p-polarized light," J. Opt. Soc. Am. B 23, 114-119 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Kortüm, Reflectance Spectroscopy Principles, Methods, and Applications (Springer, 1969).
  2. J. Räty, K.-E. Peiponen, and T. Asakura, UV-Visible Reflection Spectroscopy of Liquids (Springer, 2004).
  3. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  4. K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, 1999).
  5. D. E. Aspnes, "The accurate determination of optical properties by ellipsometry," in Handbook of Optical Constants of Solids, E.Palik, ed. (Academic, 1995) pp. 69-112.
  6. K.-E. Peiponen and E. M. Vartiainen, "Kramers-Kronig relations in optical data inversion," Phys. Rev. B 44, 8301-8303 (1991). [CrossRef]
  7. M. H. Lee, "Solving certain principal value integrals by reduction to the dilogarithm," Physica A 234, 581-588 (1996). [CrossRef]
  8. M. H. Lee and O. I. Sindoni, "Kramers-Kronig relations with logarithmic cernel and applications to the phase spectrum in the Drude model," Phys. Rev. E 56, 3891-3896 (1997). [CrossRef]
  9. F. W. King, "Efficient numerical approach to the evaluation of Kramers-Kronig transforms," J. Opt. Soc. Am. B 19, 2427-2436 (2002). [CrossRef]
  10. K. F. Palmer, M. Z. Williams, and B. A. Budde, "Multiply subtractive Kramers-Kronig analysis of optical data," Appl. Opt. 37, 2660-2673 (1998). [CrossRef]
  11. V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, "Multiply subtractive Kramers-Krönig relations for arbitrary-order harmonic generation susceptibility," Opt. Commun. 218, 409-414 (2003). [CrossRef]
  12. V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, "Multiply subtractive generalized Kramers-Kronig relations: application on third-harmonic generation susceptibility of polysilane," J. Chem. Phys. 119, 11095-11098 (2003). [CrossRef]
  13. K.-E. Peiponen, V. Lucarini, J. J. Saarinen, and E. M. Vartiainen, "Kramers-Kronig relations and sum rules in nonlinear optics," Appl. Spectrosc. 58, 499-509 (2004). [CrossRef] [PubMed]
  14. P. Grosse and V. Offermann, "Analysis of reflectance data using the Kramers-Kronig relations," Appl. Phys. A 52, 138-144 (1991). [CrossRef]
  15. J. E. Toll, "Causality and the dispersion relations: logical foundations," Phys. Rev. 104, 1760-1770 (1956). [CrossRef]
  16. E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, "Phase retrieval in optical spectroscopy: Resolving optical constants from power spectra," Appl. Spectrosc. 50, 1283-1289 (1996). [CrossRef]
  17. J. J. Saarinen, E. M. Vartiainen, and K.-E. Peiponen, "Retrieval of the complex permittivity of spherical nanoparticles in a liquid host material from a spectral surface plasmon resonance measurement," Appl. Phys. Lett. 83, 893-895 (2003). [CrossRef]
  18. R. M. A. Azzam, "Direct relations between Fresnel's interface reflection coefficients for the parallel and perpenticular polarizations," J. Opt. Soc. Am. 69, 1007-1011 (1979). [CrossRef]
  19. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).
  20. C. E. Shannon, "A mathematical theory of communications," Bell Syst. Tech. J. 27, 379-423 (1948).
  21. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipies (Cambridge U. Press, 1988).
  22. F. Remacle and R. D. Levine, "Time domain information from resonant Raman excitation profiles: a direct inversion by maximim entropy," J. Chem. Phys. 99, 4908-4925 (1993). [CrossRef]
  23. P. K. Yang and J. Y. Huang, "Model-independent maximum-entropy method for the analysis of sum-frequency vibrational spectroscopy," J. Opt. Soc. Am. B 17, 1216-1222 (2000). [CrossRef]
  24. J. P. Burg, "Maximum entropy spectral analysis," presented at 37th Annual Meeting of the Society of Explor. Geophysics, Oklahoma City, Okla., October 31, 1967.
  25. E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, "Maximum entropy model in reflection spectra analysis," Opt. Commun. 89, 37-40 (1992). [CrossRef]
  26. E. M. Vartiainen, T. Asakura, and K.-E. Peiponen, "Generalized noniterative maximum entropy procedure for phase retrieval problems in optical spectroscopy," Opt. Commun. 104, 149-156 (1993). [CrossRef]
  27. E. M. Vartiainen, "Phase retrieval approach for coherent anti-Stokes Raman scattering spectrum analysis," J. Opt. Soc. Am. B 9, 1209-1214 (1992). [CrossRef]
  28. E. M. Vartiainen, K.-E. Peiponen, H. Kishida, and T. Koda, "Phase retrieval in nonlinear optical spectroscopy by the maximum-entropy method: an application to the ∣chi(3)∣ spectra of polysilane," J. Opt. Soc. Am. B 13, 2106-2114 (1996). [CrossRef]

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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited