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Mathematical Analysis of the Guided Modes of an Optical Fiber

Alain Bamberger Anne-Sophie Bonnet-Ben Dhia 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : 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 self-adjoint 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 cutoff values) is carried out.
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Alain Bamberger, Anne-Sophie Bonnet-Ben Dhia. Mathematical Analysis of the Guided Modes of an Optical Fiber. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 1990, 21 (6), pp.1487-1510. ⟨10.1137/0521082⟩. ⟨hal-01010733⟩



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