Recent numerical and theoretical studies have demonstrated that the modes at threshold of a random laser are in direct correspondence with the resonances of the same system without gain, a feature which is well known in conventional lasers but not known until recently for random lasers. This paper presents numerical results of the multimode regime that takes place when the pumping rate is progressively increased above threshold. Behavior that is already known in standard lasers, such as mode competition and nonlinear wave mixing, are shown to also take place in random lasers thus reinforcing their recent modal description. However, due to the complexity of the laser modes and to the openness of such lasers, which require large external pumping to compensate for strong loss, one observes that these effects are systematic and can be more pronounced than in a conventional laser.
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