Microwave fractional Hilbert transformer implemented in a dispersion-tailored few-mode fiber

We experimentally demonstrate, for the first time to our knowledge, a microwave fractional Hilbert transformer in a few-mode fiber using a transversal filtering approach. The filter taps are provided by a tunable true-time delay line that is realized by exploiting the spatial dimension of a dispersion-engineered double-clad step-index few-mode fiber. Both the fractional order and operational bandwidth of the fractional Hilbert transformer can be continuously tuned by adjusting the tap coefficients and varying the operational optical wavelength, respectively. The magnitude and phase response for different fractional orders, ranging from 0.17 to 1.00 that correspond to phase shifts of 15° to 90°, are measured. Operational bandwidths of 7.4 to 10.6 GHz are demonstrated for a classical Hilbert transformer. Real-time temporal fractional Hilbert transform of a Gaussian-like pulse is also performed. Our results are in good agreement with theory, validating the viability of our approach for implementation of microwave fractional Hilbert transformers.