We present a comprehensive study for a new three-branch widely tunable semiconductor laser based on a self-imaging, lossless multi-mode interference (MMI) coupler. We have developed a general theoretical framework that is applicable to all types of interferometric lasers. Our analysis showed that the three-branch laser offers high side-mode suppression ratios (SMSRs) while maintaining a wide tuning range and a low threshold modal gain of the lasing mode. We also present the design rules for tuning over the dense-wavelength division multiplexing grid over the C-band.