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We report the optical characteristics and the linewidth enhancement factor (alpha-factor) of InAs/GaAs quantum dot (QD) laser diodes (LDs) with a 5-mum-wide stripe and 1-mm-long cavity. Continuous wave (CW) operation of the laser yielded a kink-free output power of 160 mW with an external efficiency of 0.35 W/A. The threshold current was 28 mA and the lasing occurred at 1286 nm, solely at the ground state (GS) up to a current of 345 mA, without switching to the excited state (ES). Then, to estimate the alpha-factor of the LDs, we investigated the differential gain and wavelength shift versus the current. The differential gain was 2.37 cm-1/mA at 1286 nm, and the wavelength shift was 0.00046 nm/mA, which resulted in an alpha-factor of 0.057 at 1286 nm. The alpha-factor decreased with increasing wavelength. To the best of our knowledge, this is the lowest value of the alpha-factor that has been reported so far, indicating that our QD-LD has excellent beam quality under high-power operation due to the elimination of the filamentation.