Numerical method for the computation of electromagnetic modes in optical fibres

In this article, we propose a new numerical method for the computation of electromagnetic modes in an optical fibre. The main difficulty lies in the fact that we have to solve an eigenvalue problem posed in R². We reduce the problem to a disc with the help of the introduction of non-local boundary operators that can be expressed in terms of Fourier series. Particular attention is drawn to the free divergence condition. Finally, our method is reduced to the resolution of a series of fixed point equations related to the eigenvalues of some self-adjoint operators with compact resolvent.