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Mathematical analysis of the guided modes of an optical fiber. (English) Zbl 0729.35090
A mathematical formulation for the guided modes of an optical fiber is derived from Maxwell’s equations: this formulation leads to an eigenvalue problem for a family of selfadjoint noncompact operators. The main spectral properties of these operators are established. Then the Min-Max Principle provides an expression of the nonlinear dispersion relation, which connects the propagation constants of guided modes to the frequency. Various existence results are finally proved and a complete description of the dispersion curves (monotonicity, asymptotic behavior, existence of cut-off values) is carried out.
Reviewer: A.Bamberger

MSC:
35P05 General topics in linear spectral theory for PDEs
78A45 Diffraction, scattering
35Q60 PDEs in connection with optics and electromagnetic theory
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