Fiber Optics pp 303-311 | Cite as

Modes of Weakly Guiding Fibers by an Integral Representation Technique

  • Leonard Eyges


We consider a cylindrical homogeneous fiber-optic guide of refractive index n’ and arbitrary cross section, with axis parallel to the z-axis, embedded in a uniform medium of refractive index n. With harmonic time dependence e−iωt split off the field ε(x, y, z) is assumed to have the form ε(x, y, z) = E(x, y)eikgz (and similarly for β(x, y, z), corresponding to field propagation down the guide with wave number kg. If Ф(x, y) is any of the rectangular components of E(x, y) or B(x, y) then Ф satisfies \(\left( {{\nabla ^2} + {{K'}^2}} \right)\Phi = 0\) inside the guide,
$$with{K'^2} = {n'^2}k_0^2 - k_g^2and{k_0} = \omega /c$$
, and \(\left( {{\nabla ^2} + {K^2}} \right)\Phi = 0\) outside the guide,
$$with{K^2} = {n^2}k_0^2 - k_g^2$$


Helmholtz Equation Transverse Electric Arbitrary Cross Section Slab Waveguide Transverse Magnetic Mode 


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  1. 1.
    Gloge, D., Applied Optics 10, 2252–2258 (1971).ADSCrossRefGoogle Scholar
  2. 2.
    Goell, J. E., Bell Syst. Tech. J. 48, 2133–2160 (1969).Google Scholar
  3. 3.
    Eyges, L., and Nelson, A., Ann. Phys. (USA) 100, 37–61 (1976).ADSMATHCrossRefGoogle Scholar
  4. 4.
    Eyges, L., Ann. Phys. (USA) 81, 567–589 (1973).ADSMATHCrossRefGoogle Scholar
  5. 5.
    Waterman, P. C., J. Acoust. Soc. Am. 45, 1417–1429 (1969); Phys. Rev. D3, 825–839 (1971).Google Scholar
  6. 6.
    Ng, F. L., and Bates, R.H.T., IEEE Trans. MIT 20, 658–662 (1972).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Leonard Eyges
    • 1
  1. 1.Rome Air Development CenterDeputy for Electronic TechnologyHanscom AFBUSA

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