Phase reconstruction from reflectivity in fiber Bragg gratings

We propose a method for phase, time delay, and impulse response reconstruction from the spectral power reflectance or reflectivity in fiber Bragg gratings (FBGs). This method is based on causality and stability conditions and uses the Hilbert and Wiener-Lee transforms. In order to obtain a complete study of the algorithm, we have applied it to uniform and nonuniform fiber Bragg gratings. Finally, we get a complete characterization of a experimental uniform fiber Bragg grating, from the measured reflectivity, by means of the phase reconstruction algorithm. Results show a good agreement between exact and reconstructed functions.