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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