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Under proper optical injection, period-one (P1) dynamics of an optically injected semiconductor laser can be excited by undamping the relaxation resonance of the semiconductor through Hopf bifurcation. The output intensity would oscillate at a microwave frequency, i.e., the P1 frequency. After optical-to-electrical conversion, a microwave signal can be generated with its frequency determined by the detuning frequency and the injection strength. Therefore, it provides a convenient way to dynamically control the instantaneous frequency of the generated microwave signal by manipulating the injection strength. In this work, a flexible frequency-hopping (FH) microwave waveform generator by dynamic control of an optically injected semiconductor laser is proposed and demonstrated. The system has a compact structure, and the key device is a commercial semiconductor laser. The generated FH microwave waveform …