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The modulation waveform, power, and frequency detuning dynamics of a semiconductor optical amplifier fiber-ring laser (SOAFL) harmonic and rational-harmonic mode-locked by using backward injection of a large-signal sinusoidal-wave modulated Fabry-Pe´rot laser diode (FPLD) are studied. The shortest pulsewidth of 53.3 ps at 1 GHz with spectral linewidth of 0.09 nm at modulation power of 17 dBm can be obtained, which corresponds to a time-bandwidth product of 2.8. The threshold modulation power and the maximum frequency detuning range for harmonic mode-locking of the SOAFL are 11.5 dBm and 180 kHz, respectively. The mode-locked SOAFL gradually recovers back to sinusoidal-wave modulation mode at the detuning frequency beyond ±400 kHz. The pulse broadening slopes for the positive- and negative-frequency detuning regions of 0.48 and 0.375 ps/kHz are determined, respectively. By enlarging the modulating power and detuning the modulation frequency of FPLD, the SOAFL can be rational-harmonic mode-locked up to 12 GHz with 33-ps pulsewidth.