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

Abstract

We present new method for the numerical reconstruction of the variable refractive index of multi-layered circular weakly guiding dielectric waveguides using the measurements of the propagation constants of their eigenwaves. Our numerical examples show stable reconstruction of the dielectric permittivity function ε for random noise level using these measurements.

Trigonometric and cylindrical polynomials and their applications in electromagnetics

“…A is a block-diagonal matrix obtained explicitly in [29] which yields the possibility of recursive computation of its determinant and obtaining formulas similar to (15) F M = I (11) (12)…”

An Adaptive Finite Element Method for Solving 3D Electromagnetic Volume Integral Equation with Applications in Microwave Thermometry

“…Different mathematical analytical methods applied for investigation of three-dimensional vector electromagnetic problems related to VIE are presented in [18,19]. Methods applied in computational electromagnetics are widely presented in [20][21][22], and the recently developed numerical methods for solution of inverse problems in electromagnetics are given in [23][24][25]33].…”

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

“…This method seems to suer from the presence of spurious modes. The more recent work presented in [53] proposes a computational procedure to retrieve the refractive index prole of multi-layered circular optical bers from the knowledge of the propagation constants and their corresponding eigenwaves under the weak guidance propagation assumption. This work extends the ideas and techniques developed in [47] and [51] in the case of a one-layered optical ber.…”

“…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.…”