In this study, we propose a two-dimensional (2D) dielectric structure tailored by a systematic design approach on the exit side of a metallic aperture to enhance the off-axis electromagnetic (EM) wave. We adopted a phase field method based topology optimization scheme and designed an arbitrary 2D dielectric structure in order to steer outward beaming through an aperture to a specific direction. Beyond previous one-dimensional structure, we proposed an arbitrary 2D dielectric structure through the introduced design process defining not only x- but also y-directional dielectric structural boundaries simultaneously and experimentally confirmed enhanced EM wave transmission to a desired direction.