Abstract: The transverse mode selection induced by optical injection in a VCSEL emitting in two transverse modes is analyzed from a theoretical point of view. Different pairs of transverse modes with parallel or orthogonal polarizations are considered. In general, we show that transverse mode selection can be achieved when the two modes have parallel or orthogonal polarizations. The selection is not possible only when both modes have parallel polarizations and the mode with the lowest threshold current has a lower injection rate than the other mode. Different forms of the selection region in the injected power-injection current plane appear depending on the polarization of the transverse modes. When both transverse modes are orthogonally polarized the mode with the lowest threshold is selected when the injected power surpasses a value that depends on the injection current. However when both modes have parallel polarizations the selection region has a completely different shape because the selection of the mode is no longer possible if the injected power or the injected current are large enough. We also show that the modal selection is favoured as the frequency of the injected light becomes smaller than the frequency of the mode to be selected.

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