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A detailed experiment was conducted to characterize the stable fundamental-mode operation of a commercial Laguerre-Gaussian (LG)-mode vertical-cavity surface-emitting laser when single-mode-fiber optical feedback was applied. Two steady-state beam profiles of laser output were established and four radial-intensity profiles obtained through simulation were compared with experimental results. The steady high-order mode can be applied in technology featuring a unitary wavelength and multiple connections. An oscillating competition state of the coupled patterns was analyzed; in this state, the laser output between an LG beam and a Gaussian beam was established after optical feedback.