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We propose and experimentally demonstrate a continuously tunable fractional Hilbert transformer (FHT) based on a high-contrast germanium-doped silica-on-silicon (SOS) microring resonator (MRR). The propagation loss of a high-contrast germanium-doped SOS waveguide can be very small (0.02 dB/cm) while the lossless bend radius can be less than 1 mm. These characteristics lead to the fabrication of an MRR with a high Q-factor and a large free-spectral range (FSR), which is needed to implement a Hilbert transformer (HT). The SOS MRR is strongly polarization dependent. By changing the polarization direction of the input signal, the phase shift introduced at the center of the resonance spectrum is changed. The tunable phase shift at the resonance wavelength can be used to implement a tunable FHT. A germanium-doped SOS MRR with a high-index contrast of 3.8% is fabricated. The use of the fabricated MRR for the implementation of a tunable FHT with tunable orders at 1, 0.85, 0.95, 1.05, and 1.13 for a Gaussian pulse with the temporal full width at half-maximum of 80 ps is experimentally demonstrated.

A continuously tunable microwave phase shifter based on slow and fast light effects in a tilted fiber Bragg grating (TFBG) written in an erbium/ytterbium (Er/Yb) co-doped fiber is proposed and experimentally demonstrated. By optically pumping the TFBG, the magnitude and phase responses of the cladding mode resonances are changed, which is used to introduce a tunable phase shift to the optical carrier of a single-sideband modulated signal. The beating between the phase-shifted optical carrier and the sideband will generate a microwave signal with the phase shift from the optical carrier directly translated to the generated microwave signal. A tunable phase shifter with a tunable phase shift of 280° at a microwave frequency tunable from 24 to 36 GHz is experimentally demonstrated.

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