Photonic generation of broadband linearly frequency modulated microwave waveforms based on ultra-short optical feedback in an optically injected semiconductor laser is proposed and numerically demonstrated. The optical injection is employed to induce period-one (P1) oscillation in the semiconductor laser for photonic microwave generation. An ultrashort feedback is introduced to further shift the laser's cavity-resonance frequency, enhancing the generated microwave frequency. By properly modulating the feedback light, the cavity-resonance frequency can be continuously shifted with the variation of the feedback strength, giving rise to a linearly frequency-modulated microwave signal. Because the injection strength remains constant, the proposed approach bypasses the limitations imposed by injection-locking and achieves more than 60 GHz of linearly frequency modulated microwave bandwidth. In addition, the microwave-comb contrast can be further optimized using a weaker long feedback loop whose time delay is equal to the modulation period of the ultrashort feedback. This approach provides a compact and flexible route for high-bandwidth photonic linearly frequency-modulated microwave signal generation.
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