OSA's Digital Library

Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 7, Iss. 8 — Oct. 9, 2000
  • pp: 260–272

Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media

Chengkun Chen, Pierre Berini, Dazeng Feng, Stoyan Tanev, and Velko P. Tzolov  »View Author Affiliations

Optics Express, Vol. 7, Issue 8, pp. 260-272 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (164 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



This paper discusses a numerical method for computing the electromagnetic modes supported by multilayer planar optical waveguides constructed from lossy or active media, having in general a diagonal permittivity tensor. The method solves the dispersion equations in the complex plane via the Cauchy integration method. It is applicable to lossless, lossy and active waveguides, and to AntiResonant Reflecting Optical Waveguides (ARROW’s). Analytical derivatives for the dispersion equations are derived and presented for what is believed to be the first time, and a new algorithm that significantly reduces the time required to compute the derivatives is given. This has a double impact: improved accuracy and reduced computation time compared to the standard approach. A different integration contour, which is suitable for leaky modes is also presented. Comparisons are made with results found in the literature; excellent agreement is noted for all comparisons made.

© Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.7390) Optical devices : Waveguides, planar

ToC Category:
Research Papers

Original Manuscript: September 5, 2000
Published: October 9, 2000

Chengkun Chen, Pierre Berini, Dazeng Feng, Stoyan Tanev, and Velko Tzolov, "Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media," Opt. Express 7, 260-272 (2000)

Sort:  Journal  |  Reset  


  1. J. Chilwell and I. Hodgkinson, " Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguide," J. Opt. Soc. Am. A 1, 742-753, (1984) [CrossRef]
  2. L. M. Walpita, " Solutions for planar optical waveguide equations by selecting zero elements in a characteristic matrix," J. Opt. Soc. Am. A 2, 595-602, (1985) [CrossRef]
  3. K. H. Schlereth and M. Tacke, "The complex propagation constant of multilayer waveguides: An algorithm for a personal computer," IEEE J. Quantum Electron., 26, 627-630, (1990) [CrossRef]
  4. L. Sun and E. Marhic, "Numerical study of attenuation in multilayer infrared waveguides by the circle-chain convergence method," J. Opt. Soc. Am. B 8, 478-483, (1991) [CrossRef]
  5. L. M. Delves and J. N. Lyness, "A numerical method for locating the zeros of an analytic function," Math. Comp., 21, 543-560, (1967) [CrossRef]
  6. L. C. Botten and M. S. Craig, "Complex zeros of analytic functions," Comput. Phys. Commun. 29, 245- 259, (1983) [CrossRef]
  7. E. Anemogiannis, and E. N. Glytsis, "Multilayer waveguides: efficient numerical analysis of general structures," J. Lightwave Tech. 10, 1344-1351, (1992) [CrossRef]
  8. R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, " Mode determination for planar waveguides using the four-sheeted dispersion relation," IEEE J. Quantum Electron. 28, 1520-1526, (1992) [CrossRef]
  9. Hermann A. Haus, Waves and Fields in Optoelectronics, (New Jersey, Prentice-Hall Inc., 1984). Ch. 11
  10. J. W. Brown and R. V. Churchill, Complex Variables and Applications, (Sixth Edition, New York: McGraw-Hill, 1996)
  11. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C, (Second Edition, Cambridge, 1994).
  12. J. R. Rice, Numerical Methods, Software, and Analysis, (IMSL Reference Edition. New York: McGraw-Hill, 1983)
  13. A. S. Kronrod, Nodes and Weights of Quadrature Formulas, (NewYork: Consultants Bureau, 1965)
  14. E. Anemogiannis, E. N. Glytsis and T. K. Gaylord, "Efficient solution of eigenvalue equations of optical waveguiding structures," J. Lightwave Tech. 12, 2080-2084, (1994) [CrossRef]
  15. T. Baba and Y. Kokubun, "Dispersion and radiation loss characteristics of antiresonsnt reflecting optical waveguides-Numerical Results and Analytical Expressions," IEEE J. Quantum Electron., 28, 1689-1700, (1992) [CrossRef]
  16. W. Huang, R. M. Shubiar, A. Nathan and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Tech. 10, 1015-1022. (1992) [CrossRef]
  17. J. Deng and Y. Huang,"A novel hybrid coupler based on antiresonant reflecting optical waveguides," J. Lightwave Tech. 16, 1062-1069, (1998) [CrossRef]
  18. B. Ray and G W. Hanson, "Some effects of anisotropy on planar antiresonant reflecting optical waveguides," J. Lightwave Tech. 14, 202-208, (1996) [CrossRef]
  19. E. Anemogiannis, E. N. Glytsis and T. K. Gaylord, "Determination of guided and leaky modes in lossless and lossy planar multiplayer optical waveguides: reflection pole method and wavevector density method," J. Lightwave Tech. 17, 929-941, (1999) [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.

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited