Accurate optical fiber refractive index reconstruction from near field

Abstract

An efficient algorithm is proposed for calculating directly and accurately the refractive index profile of cylindrical waveguides from knowledge of the mode near field. This inverse problem is solved using transmission line techniques. For the solution of this problem it is required the mode propagation constant beta in the waveguide. In this work we present the theory for estimating the mode propagation constant beta accurately. The calculation of the propagation constant beta is vital for the refractive index reconstruction and we show that it implies error minimization in the refractive index synthesis from near field. From Maxwellpsilas equations, we derive an equivalent transmission-line circuit for a cylindrical dielectric waveguide. Based on an analytical method, that computes the error in the reconstructed refractive index due to inaccuracy in beta. Subsequently we work out the exact value of the propagation constant beta. The proposed analytical method computes the refractive index error directly without the need for curve fitting or numerical differentiation. We demonstrate this algorithm with example reconstructions for step, triangular and parabolic optical fiber refractive index profiles. This technique is exact, fast and rapidly convergent.