Mathematical Analysis of the Guided Modes of an Optical Fiber

Alain Bamberger and Anne-Sophie Bonnet-BenDhia
Publication type:
Paper in peer-reviewed journals
SIAM Journal on Mathematical Analysis, vol. 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.
    author={Alain Bamberger and Anne-Sophie Bonnet-BenDhia },
    title={Mathematical Analysis of the Guided Modes of an Optical Fiber },
    doi={10.1137/0521082 },
    journal={SIAM Journal on Mathematical Analysis },
    year={1990 },
    volume={21(6) },