Stable dual-wavelength emission from a laser is desirable for microwave signal generation using the optical heterodyning method. As both optical wavelengths are generated from the same cavity, the phase noise of the generated microwave signal is minimized. In this work, we exploit the inherent birefringence in the buried heterostructure semiconductor laser to generate dual polarized modes. We carefully analyze the mode competition between various modes in the cavity and propose the desirable gain modification conditions for stable dual mode oscillations when the laser is operating near the threshold. We show that the required asymmetry in the gain for two stable modes can be obtained from the mode confinement factors and facet losses. We also show the applicability of our results to a homogeneously broadened multimode laser.