Mathematical analysis and numerical approximation of optical waveguides (Q2758030)

This paper provides a rigorous mathematical analysis of two practically very important types of optical waveguides, optical fibers and optical integrated waveguides. The authors reduce the study of guided modes to the spectral analysis of a family of selfadjoint unbounded operators in \( \mathbb R^2\) with noncompact resolvent. Both problems are treated as perturbations of problems with simpler reference mediums, which can be analyzed by explicit calculations. Using compact perturbation results, comparison and minimax principles for non-compact self-adjoint operators, the authors analyse the essential and discrete spectrum of the problems and present different results concerning the existence, number, and properties of guided modes, with particular attention given to low- and high-frequency behaviour. For the case of optical fibers they present also a numerical method for the computation of the guided modes and extensions to other waveguides.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00050].