Место издания:the Electromagnetics Academy Cambridge, Massachusettes, USA
Первая страница:135
Последняя страница:139
Аннотация:The eigenvalue problems for generalizednatural modes of an inhomogeneous dielectric waveguide without a sharp boundary and a step-index dielectric waveguide with smooth boundaryof cross-section are formulated as problems for the set of time-harmonic Maxwell equations with partial radiation conditions (Sveshnikov radiation conditions) at infinity inthe cross-sectional plane. The original problems by integral equations method are reduced to nonlinear spectral problems with Fredholm integral operations. Theorems on spectrum localization are proved, and then it is proved that the sets of all eigenvalues of the original problems can only be some sets of isolated points on the Reimann surface, and it also proved that each eigenvalue depends continuously on the frequency and dielectric permittivity and can appear and disappear only at the boundary of the Reimann surface. The Galerkin method for numerical calculations of the generalized natural modes are proposed, and the convergence of the method is proved. Some results of numerical experiments are discussed/