Projection methods for computation of spectral characteristics of weakly guiding optical waveguides

Abstract

The original problem on surface and leaky eigen modes of a weakly guiding step-index optical waveg uide is considered. The original problem is reduced to a nonlinear spectral problem for the set of weakly singular boundary integral equations. We approximate the integral operator by collocation and Galerkin methods. Their convergence and quality are proved by numerical experiments.

Reconstruction of Dielectric Constants of Core and Cladding of Optical Fibers Using Propagation Constants Measurements

“…Using Tables 2, 3 and Figures 2, 3 we conclude that the optimization algorithm with the proposed first approximations for ε 0 , computed using theory of [7,19], gives stable reconstruction of ε.…”

“…The success in the Tikhonov regularization method largely depends on a good initial approximation to the solution. The matematical analysis of the forward problem has allowed us to find a good first approximation to the refractive index of the waveguide [7,19]. This is confirmed by the numerical experiments of solving the similar inverse problems [8,9].…”

“…The exact values of parameters are chosen as follows: ε i = ε 1 = 2.383936 (quartz) and ε e = 2.21235876 (optical glass). The exact solutions (k 2 i ,β 2 i ) of the forward spectral problem for this waveguide are well known (see, for example, [19]). We constructed the Tikhonov functional using five pairs of eigenvalues corresponding to the fundamental eigenwave, see Table 1.…”

“…It follows from the results of [19] that for the wide range of frequencies the following formula gives a very good approximation from above to the permittivity ε e of the cladding of the waveguide:…”

Methods of analytical regularization in the spectral theory of open waveguides

“…Most of them are also contained in the contributed publications of the authors [1]- [38]. In Section III, we consider more comprehensively generalized eigenwave problems for two types of lossless dielectric waveguides: a "step-index" waveguide with a smooth cross-sectional boundary and an inhomogeneous, in cross-section, waveguide.…”