%0 Journal Article %T Spectral approximation of a boundary condition for an eigenvalue problem %+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS) %A Bonnet-Ben Dhia, Anne-Sophie %A Gmati, Nabil %< avec comité de lecture %@ 0036-1429 %J SIAM Journal on Numerical Analysis %I Society for Industrial and Applied Mathematics %V 32 %N 4 %P 1263-1279 %8 1995 %D 1995 %R 10.1137/0732058Journal articles %X To compute the guided modes of an optical fiber, the authors use a scalar approximation of Maxwell's equations. This formulation leads to a bidimensional eigenvalue problem set in an unbounded domain. An equivalent formulation set in a bounded domain is derived. The boundary condition involves a Fourier series expansion. For the numerical treatment, only a finite number N of terms of the series is retained. The authors prove that the error on the eigenvalues and the eigenfunctions decreases faster than any power of ${1 / N}$. Copyright © 1995 Society for Industrial and Applied Mathematics %G English %L hal-01010193 %U https://ensta-paris.hal.science/hal-01010193 %~ ENSTA %~ CNRS %~ INRIA %~ INRIA-SACLAY %~ INRIA_TEST %~ TESTALAIN1 %~ UMA_ENSTA %~ INRIA2