We have theoretically explored the behavior of a coherently pumped ${J}^{\ensuremath{''}}=\stackrel{\ensuremath{\rightarrow}}{1}J=\stackrel{\ensuremath{\rightarrow}}{0}{J}^{\ensuremath{'}}=1$ isotropic cavity laser and compared it with the behavior of other related laser systems involving atomic or molecular levels with angular quantum numbers
0 and
1. It is shown that at low and moderate pumping strengths it behaves very differently from the ${J}^{\ensuremath{''}}=\stackrel{\ensuremath{\rightarrow}}{0}J=\stackrel{\ensuremath{\rightarrow}}{1}{J}^{\ensuremath{'}}=0$ laser exhibiting no pump-induced gain anisotropy and allowing for linearly polarized (LP) solutions with arbitrary azimuth and circularly polarized (CP) solutions, depending on the values of the molecular relaxation rates. Above the instability threshold, a variety of dynamic regimes involving the polarization degree of freedom can be found, including LP states with rotating azimuth (as in incoherently pumped $J=\stackrel{\ensuremath{\rightarrow}}{0}{J}^{\ensuremath{'}}=1$ or $J=\stackrel{\ensuremath{\rightarrow}}{1}{J}^{\ensuremath{'}}=0$ lasers), antiphase dynamics, and full polarization chaos.
The optical properties of a four-level atomic system via coherent and incoherent pumping fields are investigated. The giant Kerr nonlinearity with reduced linear and nonlinear absorption, which has a major role in decreasing the threshold of optical bistability (OB), can be obtained with subluminal light propagation via adjusting the intensities of coupling fields. An incoherent pumping field is noticed to be an extra parameter to reduce the threshold of OB and multistability, and it can be used as an effective parameter in producing lasing with or without population inversion. In this model, optical multistability is achieved simply by tuning the intensity of coupling laser fields. Furthermore, it is shown that the subluminal and the superluminal light propagation can be obtained by appropriate values of the incoherent pumping rate.