Optical Multistability in a Four-Level System Interacting with Two Fields

We have studied the case of optical multistability in a four-level system interacting with two coherent fields. The system, shown in fig. 1, consists of two pairs of energy levels, 1, 2, and 3, 4, absorption occurs between levels 1- 4 and emission takes place from 3-2. The 'intra-band' transitions, 4-3 and 2- 1 are assumed non-radiative and extremely fast. The system is irradiated by two beams, one tuned to the absorption spectrum, the other to the emission spectrum, in a Fabry-Perot cavity. Solution of the optical Bloch equations following [1] enables us to write the input-output equations, la and lb, in the form where Yi, Xi, are the appropriately scaled input and output fields, Ci the 'bistability' parameter, and Δi, ϕi, the atomic and cavity detuning respectively, of field i.