Mathematical Analysis of the Guided Modes of an Optical Fiber

作者： A. Bamberger , A. S. Bonnet

关键词: Mathematical analysis 、 Self-adjoint operator 、 Dispersion (optics) 、 Mathematics 、 Eigenvalues and eigenvectors 、 Dispersion relation 、 Optical fiber 、 Expression (computer science) 、 Maxwell's equations 、 Monotonic function 、 Applied mathematics 、 Analysis 、 Computational mathematics

摘要: A mathematical formulation for the guided modes of an optical fiber is derived from Maxwell's equations: this leads to eigenvalue problem a family self-adjoint noncompact operators. The main spectral properties these operators are established. Then min-max principle provides expression nonlinear dispersion relation, which connects propagation constants frequency. Various existence results finally proved and complete description curves (monotonicity, asymptotic behavior, cutoff values) carried out.