Single-mode emission is one of the most significant problems in vertical-cavity surface-emitting lasers (VCSELs). To solve it, we propose to embed an antiresonant oxide island inside the VCSEL cavity using a novel planar oxidation technique. This oxide island has a strong impact on the shape of the lateral mode profiles and affects the values of photon lifetimes associated with each mode. In this work, we investigate the physical origin of this impact and determine the dimensions of the oxide island that provide the strongest modal discrimination.