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High-frequency asymptotics of guided modes in optical fibres. (English) Zbl 0806.35174

Summary: The high-frequency asymptotics of guided modes of dielectric waveguides is studied, firstly under the weak guidance assumptions which lead to a scalar problem, and then for Maxwell’s system. The authors prove that the field tends to vanish everywhere the refractive index is not maximal. Moreover, for the vector model, it is proved that the field tends to become transverse. If the core of the guide is homogeneous, then the limit problem, which is an eigenvalue problem set inside the core, is derived. Various asymptotic estimates on the dispersion curves are established.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
78A50 Antennas, waveguides in optics and electromagnetic theory
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