Terahertz quantum cascade lasers (THz-QCLs) are a kind of compact, coherent source in terahertz range. We studied the relative intensity noise and modulation properties of free-running, optical master-slave injection and mutual injection THz-QCLs based on a three-level rate equation approach. For the free-running case, it is found that the spontaneous emission noise in THz-QCLs shows a white noise behavior for low frequency. There is no resonance peak corresponding to the relaxation oscillation in the low frequency region, which is different from the traditional semiconductor lasers. The master-slave injection can effectively reduce the noise of THz-QCLs for more than 20dB which could be an efficient and practical technique to achieve low-noise operation of THz-QCLs. For the mutual injection THz-QCLs, the noise will obviously increase relative to the free-running case even in the phase-locked region. In addition, by applying the injection locking scheme, the modulation bandwidths can be much increased, compared to the direct modulation scheme. Those understandings of noise and modulation behaviors of THz-QCLs are important for their applications in terahertz imaging and spectroscopy.
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