Based on rate equations, we mainly simulate the transient instability characteristics of a 8 µm quantum cascade laser (QCL) subject to optical injection with AC electrical modulation. Simulation results have shown that the 1-periodic oscillation of optical injection-locked QCL is broken
by applying an AC current to the DC bias. Combining external optical injection and induced period current modulation can cause 1-period oscillation dropouts and display chaotic states outside the stable locking region, owing to the cooperative interplay between AC frequency and the periodic oscillation frequency caused by optical injection. To give a clear physical picture of the chaos under different linewidth enhancement factor, we use temporal series, Poincar´e bifurcation diagram, Fourier spectra, phase portraits and first return maps to analyze carefully. These analytical methods are effective for the dynamical behaviors of QCLs with low LEF, which shows that chaos of QCLs strongly rely on external modulation compared with class-B laser systems. This work paves a new way for realizing chaotic signal generation and have an important application in secure communication in mid-infrared and terahertz frequency band.