We consider the optical conductivity $sigma_1(omega)$ in the metallic phase of the one-dimensional Hubbard model. Our results focus on the vicinity of half filling and the frequency regime around the optical gap in the Mott insulating phase. By means of a density-matrix renormalization group implementation of the correction-vector approach, $sigma_1(omega)$ is computed for a range of interaction strengths and dopings. We identify an energy scale $E_{rm opt}$ above which the optical conductivity shows a rapid increase. We then use a mobile impurity model in combination with exact results to determine the behavior of $sigma_1(omega)$ for frequencies just above $E_{rm opt}$ which is in agreement with our numerical data. As a main result, we find that this onset behavior is not described by a power law.
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