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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 66, Iss. 3 — Mar. 1, 1976
  • pp: 216–220

Curvature loss formula for optical fibers

Dietrich Marcuse  »View Author Affiliations


JOSA, Vol. 66, Issue 3, pp. 216-220 (1976)
http://dx.doi.org/10.1364/JOSA.66.000216


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Abstract

The loss formula for optical fibers with constant radius of curvature of their axes is derived by expressing the field outside of the fiber in terms of a superposition of cylindrical outgoing waves. The expansion coefficients are determined by matching the superposition field to the field of the fiber along a cylindrical surface that is tangential to the outer perimeter of the curved fiber. This method is a direct extension of my derivation of the curvature-loss formula for slab guides.

© 1976 Optical Society of America

Citation
Dietrich Marcuse, "Curvature loss formula for optical fibers," J. Opt. Soc. Am. 66, 216-220 (1976)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-66-3-216


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References

  1. M. A. Miller and V. I. Talanov, "Electromagnetic Surface Waves Guided by a Boundary with Small Curvature," Zh. Tekh. Fiz. 26, 2755 (1956).
  2. E. A. J. Marcatili, "Bends in Optical Dielectric Guides," Bell Syst. Tech. J. 48, 2103–2132 (1969).
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  4. J. A. Arnaud, "Transverse Coupling in Fiber Optics Part III: Bending Losses," Bell Syst. Tech. J. 53, 1379–1394 (1974).
  5. A. W. Snyder (private communication).
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  8. D. C. Chang and E. F. Kuester, "General Theory of Surface-Wave Propagation on a Curved Optical Waveguide of Arbitrary Cross Section," Scientific Report No. 11, Electromagnetics Laboratory, Dept. Electr. Eng., Univ. of Colo., Boulder, Colo.; also, IEEE J. Quantum Electron. QE-11, 903–907 (1975).
  9. D. Marcuse, Light Transmission Optics (Van Nostrand, Princeton, 1972), 398–406.
  10. D. Gloge, "Weakly Guiding Fibers," Appl. Opt. 10, 2252–2258 (1971).
  11. D. Marcuse, Theory of Dielectric Optical Waveguides, (Academic, New York, 1974).
  12. Reference 11, Eq. (2.2–23), p. 65, and Eq. (2.2–25), p. 66.
  13. Reference 9, Eqs. (8.2–7) through (8.2–10), p. 290.
  14. M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions, Eq. 9. 2.4, p. 364. U. S. Department of Commerce, National Bureau of Standards, Appl. Math. Ser., 55.
  15. Reference 11, Eq. (2.2–38), p. 68.
  16. Reference 11, Eq. (2.2–69), p. 73.
  17. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965).
  18. Reference 17, Eq. 8.468, p. 967.
  19. Reference 14, Eq. 6.1. 18, p. 256.

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