Vertical-cavity surface-emitting lasers (VCSELs) are inherently multimode with unpredictable polarization due to their relative large transverse dimensions and lack of structural asymmetry. In a number of applications, such as spectroscopy, optical data storage, and demanding fiber-optic communication, a single-frequency light source with low polarization drift is desirable. Several techniques have been developed to achieve single-mode emission in VCSELs, e.g. using an extended cavity [1], anti-resonance reflecting optical waveguide [2], and locally etched surface relief [3], and similar for polarization control, including sub-wavelength gratings in amorphous silicon [4], external feed-back [5], growth on non-(100) substrates [6]. However, only a few methods have been developed for combined mode and polarization selection. These include photonic crystal pattern [7], asymmetric air-post structure [8], and locally etched surface grating. In the latter method, a grating with a period larger than the optical wavelength in the material has been presented [9], and recently we have demonstrated VCSELs with a sub-wavelength grating [10]. A locally etched surface grating allows for the use of a relatively large oxide aperture, which reduces device resistance and thereby self-heating, enabling higher output powers. The advantage of using a sub-wavelength grating compared to a larger grating period is that the diffraction related losses and beam degradation are minimized. The fabrication of a sub-wavelength grating is however challenging since it requires high-resolution definition. In this work we have performed a parametric study to investigate the maximum achievable single-mode and polarization stable output power of 850-nm oxide-confined VCSELs with a locally etched sub-wavelength surface grating, and also how this performance depends on the grating geometry, which gives information on fabrication tolerances.The investigated 850-nm (1-cavity) oxide-confined VCSELs have an epitaxial structure consisting of an active region with three GaAs quantum wells and a top and bottom DBR with 22 and 34 layer pairs of Al 0.9 Ga 0.1 As/Al 0.12 Ga 0.88 As, respectively. Graded interfaces and modulation doping is used in the mirror layers to reduce the differential resistance while maintaining a low free-carrier absorption loss. A 30-nm-thick Al 0.98 Ga 0.02 As layer is positioned just above the active region. This layer is selectively oxidized to form the oxide aperture. For selecting the fundamental mode with a fixed polarization state an "inverted" sub-wavelength surface grating is used: a /4-thick topmost GaAs layer is added to the epitaxial structure to introduce anti-phase reflections, which significantly increases the top mirror loss; a surface grating with a period of 120 nm is etched in a circular region into the top mirror, see Fig. 1, to locally restore the low mirror loss for the fundamental mode with a polarization perpendicular to the grating grooves. The grating etch depth is 60 nm (~ /4). The principle is that the spati...