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This work theoretically investigates the frequency noise (FN) characteristics of quantum cascade lasers subject to the optical injection through a set of coupled rate equations with Langevin noise sources. It is shown that the low-frequency FN is completely suppressed by the optical injection, and the suppression bandwidth increases with the increasing injection ratio. The optimal FN peak suppression ratio at an injection ratio of 10 dB reaches 2.9 dB. In addition, it is found that the opticaldoi:10.1364/oe.26.015167 pmid:30114767 fatcat:b2kywawibfcc3c2gdaetli4sgi