We study a homogeneously broadened four-level model for a coherently pumped laser with pump and laser fields having crossed linear polarizations. For a parameter range of the type explored in the experiments by Tang et al. [Phys. Rev. A 44, R35 (1991)]the system exhibits a family of type-III-intermittency transitions to chaos in which the onset of intermittency is preceded by period-2, period-3...
