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Mode beating via third order nonlinearity in semiconductor ring lasers has been analyzed using a frequency-domain multimode rate equation model. Compared with Fabry-Perot lasers, semiconductor ring lasers are 1.33, 2, and 4 times more efficient in self-gain compression, cross-gain compression, and four-wave mixing processes, respectively, due to its travelling-wave nature. It is shown that, using dual (pump and signal) external optical injections into the ring laser cavity, multiple modes can be locked in phase via the strong four wave mixing phenomenon. This results in modulation of the light wave at the mode beating frequencies which could be used for RF optical carrier generation.