  We numerically performed wave dynamical simulations based on the
Maxwell-Bloch (MB) model for a quadrupole-deformed microcavity laser with
spatially selective pumping. We demonstrate the appearance of an asymmetric
lasing mode whose spatial pattern violates both the x- and y-axes mirror
symmetries of the cavity. Dynamical simulations revealed that a lasing mode
consisting of a clockwise or counterclockwise rotating-wave component is a
stable stationary solution of the MB model. From the results of a
passive-cavity mode analysis, we interpret these asymmetric rotating-wave
lasing modes by the locking of four nearly degenerate passive-cavity modes. For
comparison, we carried out simulations for a uniform pumping case and found a
different locking rule for the nearly degenerate modes. Our results demonstrate
a nonlinear dynamical mechanism for the formation of a lasing mode that adjusts
its pattern to a pumped area.
