OSA's Digital Library

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)

View Full Text Article

Acrobat PDF (578 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

Dietrich Marcuse, "Curvature loss formula for optical fibers," J. Opt. Soc. Am. 66, 216-220 (1976)

Sort:  Author  |  Year  |  Journal  |  Reset


  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).
  3. L. Lewin, "Radiation from Curved Dielectric Slabs and Fibers," IEEE Trans. Microwave Theory Tech. MTT-22, 718–727 (1974).
  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).
  6. A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from Bent Optical Waveguides," Electron. Lett. 11, 332–333 (1975).
  7. V. V. Shevehenko, "Radiation Losses in Bent Waveguides for Surface Waves," Radiophys. Quantum Electron. 14, 607–614 (1973) (Russian original 1971).
  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.

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