The period-one (P1) nonlinear dynamics of a semiconductor laser subject to both optical injection and optical feedback are investigated for photonic microwave generation. The optical injection first drives the laser into P1 dynamics so that its intensity oscillates at a microwave frequency. A dual-loop optical feedback then stabilizes the fluctuations of the oscillation frequency. Photonic generation at 45.424 GHz is demonstrated with a linewidth below 50 kHz using a laser with a relaxation resonance frequency of only 7 GHz. The dual-loop feedback effectively narrows the linewidth by over an order of magnitude, reduces the phase noise variance by more than 500 times, and suppresses side peaks in the power spectrum.
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