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Optical and Quantum Electronics

An inverse eigenvalue problem. Application: Graded-index optical fibers

  • 01-10-2017
Published in:
Authors
Hayat Rezgui
Abdelaziz Choutri
Published in
Optical and Quantum Electronics | Issue 10/2017

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Abstract

The main objective of this paper is to solve an inverse eigenvalue problem that consists (for a given frequency) in seeking for a suitable graded-index optical fiber able to carry electromagnetic fields having known propagation constants. This is an ill-posed problem. We present an original iterative method, based on Tikhonov regularization in order to demonstrate the existence of a unique solution (the true refractive index or at least a better approximation of it). Otherwise, we compute the optimal regularization parameter thanks to L-curve method. Numerical results from various test cases show that the regularized (unique reconstructed) solution, which corresponds simultaneously to the corner of the L-curve and minimum of relative error (and even together with the minimum of absolute error at this corner), is in good agreement with the true solution.

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previous article Design and simulation of a flexible and ultra-sensitive biosensor based on frequency selective surface in the microwave range
next article Abundant soliton solutions of the resonant nonlinear Schrödinger equation with time-dependent coefficients by ITEM and He’s semi-inverse method
Title
An inverse eigenvalue problem. Application: Graded-index optical fibers
Authors
Hayat Rezgui
Abdelaziz Choutri
Publication date
01-10-2017
Publisher
Springer US
Published in
Optical and Quantum Electronics / Issue 10/2017
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-017-1154-9
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