Abstract: The present theoretical work studies optical frequency combs (OFCs) associated with both linear polarizations of a gain switching vertical-cavity surface-emitting laser (VCSEL) subject to optical injection of arbitrary polarization. The overall OFC, formed by the two orthogonally polarized sub-combs, can have an expanded optical span in agreement with experiments reported by Prior et al. We show that the maximum optical span is obtained for a certain angle between the linearly polarized optical injection and the direction of emission of the main mode of the free-running VCSEL. We find that this angle decreases as the injection strength increases. We also characterize the maximum expansion of the optical span of the overall comb. For VCSELs with large birefringence splitting the maximum expansion is the optical span of the free-running OFC, while for small birefringence splitting VCSELs the maximum expansion is the value of the birefringence splitting.

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