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We present an in-depth analysis of the linewidth of a partially slotted semiconductor laser utilized for single mode operation exhibiting integrability with other photonic devices. Theoretically, the reflection coefficients are calculated via the scattering matrix method and implemented within the multimode rate equations for a current-injected quantum well laser while including the effects of noise. The coupling between photon and carrier noise is included for completeness and explicitly derived in this case. The threshold current and linewidth as a function of injection current and cavity length are then calculated for an optimized slot size. Results show state-of-the-art capabilities for this laser to meet industrial requirements for linewidths well under 500 kHz. In addition, experimental data extracted via a heterodyne detection measurement of the electric field spectrum demonstrates similar trends with our theoretical calculations.