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The dependence of the phase shift of the light output from sinusoidally modulated semiconductor lasers was investigated as a function of the modulation current. This measurement is effective in accurately determining the short damping time constant associated with the relaxation oscillation. The frequency half width of this phase shift was found to be inversely proportional to the damping time constant. For narrow stripe lasers, the phase shift occurs more gradually, which corresponds to the fact that the narrow stripe lasers have shorter damping time constants. To analyze the narrow stripe effect, the recently developed time-dependent self-consistent theory was applied, considering the transverse distribution of both optical field and carrier density and including the carrier diffusion term. This theory can explain the shorter damping time constant for narrow stripe lasers compared with broader stripe lasers.