A local boundary condition coupled to a finite element method to compute guided modes of optical fibres under the weak guidance assumptions

Abstract

An efficient method coupling a local boundary condition to a finite element technique is proposed to compute guided modes of optical fibres under the weak guidance assumptions. This method is designed to provide accurate solutions for optical fibres with no restriction on their shape as well as on their refractive index profile. Several numerical experiments are performed to demonstrate this point. Copyright © 2000 John Wiley & Sons, Ltd.

Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides

“…This distance is considered to be far enough to prevent any reections, as demonstrated in references [74][75].…”

“…This discretization appears to be ne enough to ensure the computation of the guided modes with a high accuracy level [74] [ 75].…”

“…To this end, we employ the direct solver developed in references [74] [75]. This solver requires to rst reformulating EVP 14 in a bounded domain (see Figure 4(a)) as follows:…”

“…To solve numerically the quadratic eigenvalue problem given by (32), we transform it into a generalized eigenvalue problem of the form [74][75]:…”

“…In the rst one, the goal is to determine the refractive index of the core of the ber only, whereas in the second one, we recover both indices. We must point out that the measured guided modes are synthetic data obtained by solving the following dispersion equation (see equation (A9), page 1574, in reference [74]):…”