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In this work we investigate patterned large-active area AlGaAs vertical-cavity surface-emitting lasers (VCSELs) targeting high-power single-transverse-mode emission. As a first step, our in-house 3D electromagnetic vectorial mode solver VELMS is validated against preliminary experimental data. Then, VELMS is applied to implement single-mode operation on VCSELs featuring large-area rectangular oxide apertures. A comparative appraisal of different mode selection strategies based on patterning the outcoupling facet of the device is presented, providing a number of alternatives for a broad audience of technologists.