OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 69, Iss. 9 — Sep. 1, 1979
  • pp: 1226–1235

Modes of dielectric waveguides of arbitrary cross sectional shape

L. Eyges, P. Gianino, and P. Wintersteiner  »View Author Affiliations


JOSA, Vol. 69, Issue 9, pp. 1226-1235 (1979)
http://dx.doi.org/10.1364/JOSA.69.001226


View Full Text Article

Acrobat PDF (1170 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A technique is presented for determining the modal propagation properties of a homogeneous cylindrical dielectric waveguide of arbitrary cross sectional shape and index n1, embedded in a medium of index n2. Both the weakly guiding case in which n1n2 and the general case of arbitrary index difference are discussed theoretically. In both cases the approach is to derive integral representations for appropriate components of E and B. These satisfy the appropriate Helmholtz equations inside and outside the guide and also guarantee that the boundary conditions are satisfied. On expansion of the components in certain sets of basis functions, the representations become a set of linear equations. The vanishing of the determinant of this set yields the propagation constants of the various mqdes. Numerical results are given for weakly guiding fibers of various shapes. Among these are rectangles and ellipses, which make comparisons with previous work possible.

© 1979 Optical Society of America

Citation
L. Eyges, P. Gianino, and P. Wintersteiner, "Modes of dielectric waveguides of arbitrary cross sectional shape," J. Opt. Soc. Am. 69, 1226-1235 (1979)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-69-9-1226


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. D. Gloge, "Weakly guiding fibers," Appl. Opt. 10, 2252–2258 (1971).
  2. J. E. Goell, "A circular-harmonic computer analysis of rectangular dielectric waveguides," Bell Sys. Tech. J. 48, 2133–2160 (1969).
  3. E. A. J. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Sys. Tech. J. 48, 2071–2102 (1969).
  4. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  5. N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972).
  6. L. Eyges, "Solution of Schrodinger and related equations for irregular and composite regions," Ann. Phys. 81, 567–590 (1973).
  7. J. D. Love and A. W. Snyder, "Ray analysis of multimode optical fibres," Ann. Telecommun. 32, 109–114 (1977); P. di Vita, "Theory of propagation in optical fibres: Ray Approach," Ann. Telecommun. 32, 115–134 (1977).
  8. L. Eyges and P. D. Gianino, "Polarizabilities of rectangular dielectric cylinders and of a cube," IEEE Trans. Ant. & Prop., July (1979).
  9. A. E. Nelson and L. Eyges, "Electromagnetic scattering from dielectric rods of arbitrary cross section," J. Opt. Soc. Am. 66, 254–259 (1976).
  10. P. C. Waterman, "New formulation of acoustic scattering," J. Acoust. Soc. Am. 45,1417–1429 (1969) and, "Symmetry unitarity, and geometry in electromagnetic scattering," Phys. Rev. D 3, 825–839 (1971).
  11. L. Eyges, "Fiber optic guides of noncircular cross section," Appl. Opt. 17, 1673–1674 (1978).
  12. J. Allard, "Notes on squares and cubes," Math. Mag. 37, 210–214 (1964).
  13. M. Gardner, "Mathematical games," Sci. Am. 213, No. 3, 222–232 (1965).
  14. F. B. Hildebrand, Introduction to Numerical Analysis, (McGraw Hill, New York, 1956) p. 330.
  15. R. W. Hornbeck, Numerical Methods, (Quantum, New York, 1975) p. 65.
  16. C. Yeh, "Modes in weakly guiding elliptical optical fibres," Opt. and Quant. Elect. 8, 43–47 (1976).

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