An inverse algorithm to calculate the refractive index profiles of periodically segmented waveguides from the measured near-field intensities

In this paper, the refractive index profiles of the periodically segmented waveguides (PSWs), which are fabricated in soda-lime glasses by the K⁺-Na⁺ ion-exchanged technique, are reconstructed from the measured transmitted near-field (NF) intensity combined with an inverse method. Through the proposed inverse method, the model Δn´=ηΔn, which characterizes the behavior of the PSWs, is also verified. In the numerical process, a finite-difference method is used to discretize the governing equation, and then a linear inverse model is constructed to identify the unknown refractive index profiles. The approach used is to rearrange the matrix form of the governing differential equation and estimate the unknown index profiles of the waveguides. Then, the linear least-squares error method is adopted to find the solutions. The results show that the accuracy of index determination can be accessed even when the measured noise is considered. In contrast to the traditional approach, the advantages of this method are that no prior information is needed on the functional form of the unknown index profiles, no initial guesses are required, no iterations in the calculating process are necessary, no intensity smoothing is required in advance, and the inverse problem can be solved in a linear domain. Furthermore, the existence and uniqueness of the solutions can easily be identified