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The behavior of second-order circular-grating DFB lasers in the above-threshold regime are analyzed. The formulation uses the standing wave method for treating lasers with second-order gratings. The effects of spontaneous emission and the variation of carrier and photon densities in the radial direction are included in a self-consistent fashion in the model. In particular, we examine the output power emitted from the surface of the laser, the near-field, and the far-field pattern of the laser as a function of the injected current.