OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 6 — Jun. 1, 2007
  • pp: 1354–1364

Polynomial fixed-point algorithm applied to the electromagnetic analysis of one-dimensional continuous structures

M. Perez-Molina and Luis Carretero-Lopez  »View Author Affiliations

JOSA B, Vol. 24, Issue 6, pp. 1354-1364 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (688 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We develop a general procedure that allows the determination of the spectral transmittance and reflectance at normal incidence for arbitrary one-dimensional continuous materials as well as the analysis of the time-domain propagation of pulses through them. This procedure consists of a generalization of Fresnel equations, and it is supported by an iterative algorithm also developed here: the polynomial fixed-point algorithm (PFPA). We apply these theoretical results to some concrete examples, such as determining the transmittance and reflectance for an absorptionless photonic crystal, an optical rugate filter, and a photonic crystal with periodic absorption. We also analyze the time-domain propagation of ultrashort Gaussian pulses through different structures.

© 2007 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Physical Optics

Original Manuscript: September 22, 2006
Manuscript Accepted: January 21, 2007
Published: May 17, 2007

M. Perez-Molina and Luis Carretero-Lopez, "Polynomial fixed-point algorithm applied to the electromagnetic analysis of one-dimensional continuous structures," J. Opt. Soc. Am. B 24, 1354-1364 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Ripin, K. Lim, G. Petrich, P. Villeneuve, S. Fan, E. Thoen, J. Joannopoulos, E. Ippen, and L. Kolodziejski, "One-dimensional photonic bandgap microcavities for strong optical confinement in GaAs and GaAs/AlxOy semiconductor waveguides," J. Lightwave Technol. 17, 2152-2160 (1999). [CrossRef]
  2. K. Huang, E. L. E. X. Jiang, J. Joannopoulos, K. Nelson, P. Bienstman, and S. Fan, "Nature of lossy Bloch states in polaritonic photonic crystals," Phys. Rev. B 69, 195111 (2004). [CrossRef]
  3. K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).
  4. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2945 (1969).
  5. M. Moharam and T. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 71, 811-818 (1981). [CrossRef]
  6. M. Moharam and T. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982). [CrossRef]
  7. S. Peng and G. Morris, "Efficient implementation of rigorous efficient-wave analysis for surface-relief gratings," J. Opt. Soc. Am. A 12, 1087-1096 (1995). [CrossRef]
  8. G. Morozov, D. Sprung, and J. Martorell, "Semiclassical coupled-wave theory and its application to TE waves in one-dimensional photonic crystals," Phys. Rev. E 69, 016612 (2004). [CrossRef]
  9. G. Morozov, D. Sprung, and J. Martorell, "Semiclassical coupled-wave theory and its application to TM waves in one-dimensional photonic crystals," Phys. Rev. E 70, 016606 (2004). [CrossRef]
  10. B. G. Bovard, "Derivation of a matrix describing a rugate dielectric film," Appl. Opt. 27, 1988-2005 (1988). [CrossRef]
  11. W. J. Gunning, R. Hall, J. Woodberry, W. H. Southwell, and N. Gluck, "Code-position of continuous composition rugate filters," Appl. Opt. 28, 2945-2948 (1989). [CrossRef] [PubMed]
  12. B. G. Bovard, "Rugate filter design: the modified Fourier transform technique," Appl. Opt. 29, 24-30 (1990). [CrossRef] [PubMed]
  13. R. Letiel, O. Stenzel, S. Wildbrandt, D. Gäbler, V. Janicki, and N. Kaiser, "Optical and non-optical characterization of Nb2O5-SiO2 compositional graded-index layers and rugate structures," Thin Solid Films 497, 135-141 (2004). [CrossRef]
  14. M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1984). [PubMed]
  15. A. Rostami and S. Matloub, "Exactly solvable inhomogeneous Fibonacci-class quasi-periodic structures (optical filtering)," Opt. Commun. 247, 247-256 (2005). [CrossRef]
  16. P. Yeh, Optical Waves in Layered Media (Wiley, 2005).
  17. C. Chen, P. Berini, D. Feng, S. Tanev, and V. Tzolov, "Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media," Opt. Express 7, 260-272 (2000). [CrossRef] [PubMed]
  18. J. Lekner and M. C. Dorf, "Matrix methods for the calculation of reflection amplitudes," J. Opt. Soc. Am. A 4, 2092-2095 (1987). [CrossRef]
  19. G. Burlak, S. Koshevaya, J. Sanchez-Mondragon, and V. Grimalsky, "Electromagnetic oscillations in a multilayer spherical stack," Opt. Commun. 180, 49-58 (2000). [CrossRef]
  20. L. Carretero, M. Pérez-Molina, S. Blaya, R. Madrigal, P. Acebal, and A. Fimia, "Application of the fixed point theorem for the solution of the 1D wave equation: comparison with exact Mathieu solutions," Opt. Express 13, 9078-9084 (2005). [CrossRef] [PubMed]
  21. G. Jameson, Topology and Normed Spaces (Chapman and Hall, 1974).
  22. R. Burden and J. Faires, Numerical Analysis (Brooks Cole, 2000).
  23. L. Carretero, R. Madrigal, A. Fimia, S. Blaya, and A. Belendez, "Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect," Opt. Lett. 26, 786-788 (2001). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited