Abstract
We theoretically investigate the behaviour of optical bistability (OB) and optical multistability (OM) in a generic double two-level atomic system driven by two orthogonally polarized fields (a π-polarized control field and a σ-polarized probe field). It is found that the behaviour of OB can be controlled by adjusting the intensity or the frequency detuning of the control field. Interestingly enough, our numerical results also show that it is easy to realize the transition from OB to OM or vice versa by adjusting the relative phase between the control and probe fields. This investigation can be used for the development of new types of devices for realizing an all-optic switching process.