We study the steady states of a solid-state laser containing a birefri
ngent frequency-doubling crystal such as a YAG-KTP laser and assess th
eir stability in a systematic way. We show that as the pump power is i
ncreased, different scenarios arise: Hopf bifurcation to antiphased pe
riodic regimes, mode hopping between different cw states, and finally
breakup of the multimode states for a single- or two-mode cw regime in
volving homoclinic points. [S1050-2947(98)07610-0].