I. Introduction
Optical injection technique has an attractive potential as an effective method for modifying the characteristics of a directly modulated semiconductor laser, such as improving the modulation bandwidth, reducing the nonlinear distortion, reducing the partition noise and reducing the chirp [1]–[9]. in a free-running laser, the maximum current modulation bandwidth is determined by the -factor [10]. Studies have revealed that the modulation bandwidth of a properly injection-locked semiconductor laser can be increased beyond the -factor limit and significantly improved relative to the free-running condition [1], [3], [8]. the relaxation oscillation frequency can be increased by 3.7 8.3 times using strong optical injection [5], [8]. in the past two decades, a lot of efforts have been made to ensure the locking conditions, locking range and stability for an injection locked semiconductor laser [11]–[17]. the detuned wavelength range for the locked laser depends on the coupling coefficient, the injection optical power ratio, and the linewidth enhancement factor [7]. It has been shown that both the modulation bandwidth and the damping rate increase with the increasing injection strength [3]. As the wavelength detuning increases from negative to positive, the resonance frequency decreases and flatter frequency response can be obtained [8].