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A multimode rate-equation model, including the effects of carrier diffusion, gain saturation, and mode coupling gain, has been developed. This model has been used to analyze the direct intensity modulation of individual longitudinal modes in a channeled-substrate-planar laser (Hitachi HLP 1400). The carrier diffusion is shown to reduce the intensity modulation of all longitudinal modes by the same fixed factor, while the gain saturation and mode coupling modify the intensity modulation by a factor that is spectrally dependent relative to the main-mode frequency. The gain saturation and mode coupling also modify the frequency dependence of the intensity modulation of each individual mode in relation to the mode power. These features have been experimentally confirmed.