OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 11, Iss. 3 — Mar. 1, 1994
  • pp: 984–991

Determination of bound modes of multilayer planar waveguides by integration of an initial-value problem

Lifeng Li  »View Author Affiliations


JOSA A, Vol. 11, Issue 3, pp. 984-991 (1994)
http://dx.doi.org/10.1364/JOSAA.11.000984


View Full Text Article

Enhanced HTML    Acrobat PDF (941 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A numerical method for the determination of the bound modes of multilayer planar dielectric waveguides is presented. It is based on the idea of tracing the evolutions of the eigenvalues (effective indices) of the waveguide as the physical parameters of the waveguide change. The eigenvalues are obtained by numerical integration of an initial-value problem. A mathematical proof is given that shows that the method guarantees that all bound modes of a lossless multilayer waveguide will be found. For a lossy waveguide, a similar mathematical proof is not available; however, numerical evidence shows that the method is still capable of finding all bound modes whose real parts of the effective indices are greater than those of the substrate and cover. The method is conceptually and computationally simple, but it is limited to searching for bound modes only.

© 1994 Optical Society of America

History
Original Manuscript: June 28, 1993
Revised Manuscript: September 7, 1993
Manuscript Accepted: September 10, 1993
Published: March 1, 1994

Citation
Lifeng Li, "Determination of bound modes of multilayer planar waveguides by integration of an initial-value problem," J. Opt. Soc. Am. A 11, 984-991 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-3-984


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. W. Y. Lit, Y-F Li, D. W. Hewak, “Guiding properties of multilayer dielectric planar waveguides,” Can. J. Phys. 66, 914–940 (1988). [CrossRef]
  2. E. Anemogiannis, E. N. Glytsis, “Multilayer waveguides: efficient numerical analysis of general structures,” J. Lightwave Technol. 10, 1344–1351 (1992). [CrossRef]
  3. R. E. Smith, S. N. Houde-Walter, G. W. Forbes, “Numerical determination of planar waveguide modes using the analyticity of the dispersion relation,” Opt. Lett. 16, 1316–1318 (1991). [CrossRef] [PubMed]
  4. R. E. Smith, S. N. Houde-Walter, G. W. Forbes, “Mode determination for planar waveguides using the four-sheeted dispersion relation,” IEEE J. Quantum Electron. 28, 1520–1526 (1992). [CrossRef]
  5. L. M. Delves, J. N. Lyness, “A numerical method for locating the zeros of an analytic function,” Math. Comput. 21, 543–560 (1967). [CrossRef]
  6. E. Marantonio, R. E. Zich, I. Montrosset, “Alternative expression of the dispersion equation in multilayered structures,” Proc. Inst. Electr. Eng. Part J 137, 357–360 (1990).
  7. G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984). [CrossRef]
  8. E. L. Ince, Ordinary Differential Equations (Dover, New York, 1956), Chap. 2, Sec. 13.
  9. L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960), Chap. 1.
  10. J. Chilwell, I. Hodgkinson, “Thin-film field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A 1, 742–753 (1984). [CrossRef]
  11. A. I. Markushevich, Theory of Functions of a Complex Variable, 2nd ed. (Chelsea, New York, 1977), Vol. 2, Pt. 1, Chap. 2, Sec. 15.
  12. The NAG FORTRAN Library–Mark 12(Numerical Algorithm Group, Inc., Downers Grove, Ill., 1987).
  13. R. J. Hawkins, R. J. Deri, O. Wada, “Optical power transfer in vertically integrated impedance-matched waveguide/ photodetectors: physics and implications for diode-length reduction,” Opt. Lett. 16, 470–472 (1991). [CrossRef] [PubMed]

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