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We report high-power single-higher-order transverse mode emission of a large-area oxide-confined rectangular-shaped vertical-cavity surface-emitting laser (VCSEL) with a multispot shallow surface relief. Both a record-high output power of 12 mW and a record-low differential series resistance of 18 Ω are achieved. Stable single-higher-order transverse mode emission with a sidemode suppression ratio (SMSR) exceeding 35 dB is maintained up to thermal rollover. Single-polarization lasing along the major axis is achieved with 27.5-dB spectral orthogonal polarization suppression ratio at thermal rollover. Measurements of near- and far-field intensity profiles of the higher-order mode are also presented.