Real-time Fourier transformer based on fiber gratings.

We use the well-known duality between paraxial diffraction in space and dispersion in time to propose a time-domain analog to spatial Fraunhofer diffraction. This analog permits the design of real-time optical Fourier-transformer systems. These systems are shown to be realizable by use of linearly chirped fiber gratings as dispersive media.

Fiber grating synthesis by use of time-frequency representations.

We propose a method to reconstruct the grating period in fiber grating structures from the field reflection coefficient or the related impulse response. The method is based on the joint time-frequency signal analysis and uses the Wigner-Ville and the spectrogram distributions. Results show good agreement between exact and reconstructed functions.

Phase reconstruction from reflectivity in uniform fiber Bragg gratings.

We propose a method for phase, time-delay, and impulse-response reconstruction from spectral power reflectance or reflectivity and apply it to uniform fiber Bragg gratings. This method is based on causality conditions and uses Hilbert and Wiener-Lee transforms. Results show a good agreement between exact and reconstructed functions.