We show that in a laser with a transversally isotropic resonator
operating in a J=1 to J=0 transition the instability of
Circularly Polarized states leads to Linearly Polarized
states with a rotating direction of polarization. This
transition occurs through intermediate states which are
Elliptically Polarized with rotating azimuth. For the range
of pump values for which the intermediate Rotating Elliptically
Polarized states occur, the total output intensity is
constant, and all the energy is pumped into the coherence
between the m_z = 1 m_z= -1 state.
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