Microwave photonic fractional Hilbert transformer with an integrated optical soliton crystal micro-comb

We report a photonic microwave and RF fractional Hilbert transformer based on an integrated Kerr micro-comb source. The micro-comb source has a free spectral range (FSR) of 50GHz, generating a large number of comb lines that serve as a high-performance multi-wavelength source for the transformer. By programming and shaping the comb lines according to calculated tap weights, we achieve both arbitrary fractional orders and a broad operation bandwidth. We experimentally characterize the RF amplitude and phase response for different fractional orders and perform system demonstrations of real-time fractional Hilbert transforms. We achieve a phase ripple of < 0.15 rad within the 3-dB pass-band, with bandwidths ranging from 5 to 9 octaves, depending on the order. The experimental results show good agreement with theory, confirming the effectiveness of our approach as a new way to implement high-performance fractional Hilbert transformers with broad processing bandwidth, high reconfigurability, and greatly reduced size and complexity.