Basic phase-locking, noise, and modulation properties of optically mutual-injected terahertz quantum cascade lasers.

The phase-locking, noise, and modulation properties of two face-to-face optically mutual-injected terahertz (THz) quantum cascade lasers (QCLs) are analyzed theoretically. In the phase-locking range, the two THz QCLs are in stationary states working at the same frequency. Outside the phase-locking range, the amplitude and the instantaneous frequency of the optical field oscillate with time, and the power spectrum shows a series of discrete peaks. For strong mutual injection, the optical field of the THz QCL array also exhibits oscillatory behavior. Coherent collapse or chaotic behavior is not observed within the range of the parameters used in this simulation. The spontaneous emission noise of phase-locked THz QCLs is higher than that of THz QCLs at free-running operation, and mutual injection may introduce additional modulation peaks in the noise spectrum. The modulation response of the mutual-injected THz QCLs to an individual modulation is investigated. It is found that the modulation bandwidth and the phase difference are significantly dependent on the modulation parameters. These results are helpful for further understanding the nonlinear dynamic behaviors of THz QCLs under optical injection and provide theoretical support for the development of THz QCL phase-locked arrays.