Determination of Permittivity from Propagation Constant Measurements in Optical Fibers

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

“…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]. Using this initial approximation, in this paper we compute solutions of the investigated problem and demonstrate that the algorithm is accurate and stable.…”

“…In our computations by analogy with [8] we introduced a randomly distributed noise in the propagation constants as…”

“…This method was extended in our previous works to the two-dimensional problem for the waveguide with the piecewise-constant refractive index and an arbitrary cross-sectional boundary [8,9]. The role of the "characteristic equation" is played by the system of two boundary weakly singular integral equations whose kernels depend on the propagation constants and refractive indices of the vaweguide and the environment.…”

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

“…The computed ones are obtained as the roots of well-known characteristic equations. The application of this method has been extended to waveguides with piecewise constant refractive index proles and arbitrary cross-sectional boundaries [48], [50], [52], [53]. The authors propose a strategy that is based on the solution of a nonlinear nonself-adjoint eigenvalue problem corresponding to a system of weakly singular integral equations.…”