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A detailed analysis of the properties of the elliptically polarized state in spin flip model is essential for a full understanding of the experimental results. This paper studies the stationary properties of this state and its stability, considering both birefringence and dichroism. Results show that for small values of the α parameter the transition from the lower frequency mode to the elliptical state may be subcritical. As a consequence, bistability between the linearly and the elliptically polarized modes exists, with jumps from one state to the other when the injected current is varied. In an experiment, the existence of such a bistable domain could lead to noise induced hopping from one state to the other, close to the instability threshold of the lower frequency mode. The authors checked that gain nonlinearities due to spectral hole burning favors subcriticality.