Continuously Tunable Fractional Hilbert Transformer by Using a Single $\pi$ -Phase Shifted FBG

A continuously tunable fractional Hilbert transformer (FHT) using a π-phase shifted fiber Bragg grating ( π-PSFBG) is proposed and experimentally demonstrated. An FHT has an output that is a weighted sum of the original input signal and its classical Hilbert-transformed signal. The classical Hilbert transform is implemented using a π-PSFBG. The output from the classical HT and the original input signal are controlled to be orthogonally polarized. The combination of the two signals at a polarizer would generate a weighted sum with the weighting coefficients determined by the angle between the principle axis of the polarizer and the polarization direction of the original input signal. A π-PSFBG is fabricated. The performance of the π-PSFBG as a classical HT is evaluated. The incorporation of the π-PSFBG into the proposed system to implement an FHT is studied. A continuously tunable FHT with a tunable fractional order of ρ = 0.7, 0.86, 0.92, 1, 1.06, 1.17, and 1.24 to perform Hilbert transformation of a Gaussian pulse with a temporal width of 80 ps is experimentally demonstrated.