Study of spectrum of guided waves of dielectric fibers

A mathematical model characterizing the surface and leaky guided waves on dielectric fibers of arbitrary cross-section is studied. The results of Steinberg (1968), and Vainikko and Karma (1974) are essentially used. The guided waves propagating along the x-axis of the fiber by the law exp[i(βz-ωt)], where the axial propagation coefficient β is an unknown complex parameter, ω is the given frequency of electromagnetic oscillations, are sought. Under the assumption of the nearness of real refractive indices of the fiber (n ₁) and environment (n₂<n₁), this physical problem is reduced to the spectral problem for the Helmholtz equation on the plane, with the Reichardt conditions on infinity