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A novel semiconductor laser, with a curved and tapered active region and a split contact, has been experimentally and theoretically mode-locked for the first time. An innovative yet simple traveling-wave rate-equation model has been developed to incorporate the tapered waveguide structure together with external-cavity grating effects and the reverse biased saturable absorber region. Both the experiment and model have demonstrated pulsewidths of around 5.5 ps at a repetition frequency of 2.5 GHz and a tunable emission wavelength around 1550 nm. The model has been used to demonstrate optimized operation of the device with a predicted reduction in pulsewidths down to 1 ps.