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- Title
A Numerical Solution Technique for Solving an Inverse Eigenvalue Problem of Computing Guided Modes in a Class of Optical Fibers.
- Authors
REZGUI, Hayat; CHOUTRI, Abdelaziz
- Abstract
This paper describes a numerical technique for determining the best approximation of the exact refractive index (of an optical fiber having a circular cross section), allowing a better transmission of a given information. Mathematically, this objective leads to the resolution of an inverse eigenvalue problem that consists in reconstructing the refractive index from a prescribed finite set of eigen data (of the direct problem), knowing only the wavenumber in vacuum (the frequency). The corresponding direct problem (solved by a finite element method) consists of computing guided modes that propagate, under weak guidance assumptions, in a graded-index optical fiber with a circular-shaped section. The numerical resolution of the inverse problem is due to a special Algorithm for solving a convex optimization problem using Lagrange multipliers. Examples and numerical illustrations, related to the inverse problem, show the robustness and the higher efficiency obtained by our suggested method that converges geometrically to the exact refractive index.
- Subjects
INVERSE problems; REFRACTIVE index measurement; EIGENVALUES
- Publication
Palestine Journal of Mathematics, 2018, Vol 7, Issue 1, p167
- ISSN
2219-5688
- Publication type
Article