Publications

Les publications des membres de l'UMA sont répertoriées dans la collection HAL de l'unité : Collection HAL de l'UMA

Sont listées ci-dessous, par année, les publications figurant dans l'archive ouverte HAL depuis 2025.

Mathematical Analysis of the Guided Modes of an Optical Fiber
- Bamberger Alain
- Bonnet-Ben Dhia Anne-Sophie
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 1990, 21 (6), pp.1487-1510. 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. (10.1137/0521082)
DOI : 10.1137/0521082