Advertisement

Transfer Matrix Method and the Graded-Index Waveguide

Chapter
  • 916 Downloads
Part of the Springer Tracts in Modern Physics book series (STMP, volume 266)

Abstract

The transfer matrix method used in thin-film optics is extremely useful when applied to analyze the propagation characteristics of electromagnetic waves in planar multilayer optical waveguides. This chapter aims to extend the transfer matrix method to treat the bound modes of the graded-index waveguide. Beginning with a brief introduction of the transfer matrix, we derived the eigenvalue equations and studied the multilayer optical waveguides. Different from the widely used WKB approximation, the transfer matrix obtained some important but different conclusions when applied to the graded-index waveguide, such as the exact phase shift at the classical turning points.

Keywords

Transfer matrix method Eigenvalue equation WKB approximation Graded-index waveguide 

References

  1. 1.
    M. Born, W. Wolf, Principles of Optics, 6th edn (corrected) (Pergamon Press, Oxford, 1986)Google Scholar
  2. 2.
    A. Yariv, Quantum Electronics, 2nd edn (Wiley, New York 1975)Google Scholar
  3. 3.
    L.I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1955)Google Scholar
  4. 4.
    A. Gedeon, Comparison between rigorous theory and WKB-analysis of modes in graded-index waveguides. Opt. Commun. 12, 329 (1974)Google Scholar
  5. 5.
    H. Friedrich, J. Trost, Working with WKB waves far from the semiclassical limit. Phys. Rep. 397, 359 (2004)Google Scholar
  6. 6.
    M.J. Sun, M.W. Muller, W.S.C. Chang, Thin-film waveguide gyrators: a theoretical analysis. Appl. Opt. 16, 2986 (1977)Google Scholar
  7. 7.
    Z. Cao, Q. Liu, Y. Jiang, Q. Shen, X. Dou, Y. Ozaki, Phase shift at a turning point in a planar optical waveguide. J. Opt. Soc. Am. A 18, 216 (2001)Google Scholar

Copyright information

© Shanghai Jiao Tong University Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.College of Physics and Communication ElectronicsJiangxi Normal UniversityNanchangChina
  2. 2.Hohai UniversityChangzhouChina
  3. 3.Shanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations