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We present long-wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers (VCSELs) with a buried tunnel junction (BTJ) and a well-defined polarization accomplished by a semiconductor/dielectric subwavelength grating (SWG). The grating is incorporated in the inner VCSEL cavity and exhibits an effective birefringence for polarizations parallel and perpendicular to the grating grooves. Theoretical modeling leads to distinct design rules for VCSELs with grating structure that deviate from the conventional design without grating. Due to the large polarization-mode separation, lasing activity is enabled only for one polarization mode. BTJ-VCSELs with properly chosen SWG parameters show predictable and full polarization stability. In addition, the relevant device parameters such as threshold current are comparable to conventional BTJ-VCSELs.