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We present a detailed study of oxide-confined, vertical-cavity surface-emitting lasers (VCSELs) where the reflectivity of the top mirror has been patterned by means of a metal grid, which at the same time acts also as an electrode. Owing to their features, these kind of devices are commonly referred to as phase-coupled VCSEL arrays. The analysis is based on a joint experimental and theoretical effort: the former is devoted to a complete characterization of the emission properties, while the latter is based on a comprehensive fully vectorial model for the structure eigenmodes with the details of their complex structure. The detected characteristics make them quite attractive for various applications and the comparison of their modal properties with the model is proved to be essential for a deep understanding of these lasers. In particular, we observed and explain, for the first time, a characteristic behavior of the lasing array, which displays spatially inhomogeneous polarization characteristics with symmetry properties with respect to the array diagonals. The good matching between theory and experiment opens new perspectives for an optimized device, where the typical four lobe far-field emission is converted in a narrow central lobe: two different proposals will be discussed.