Controlling the optical bistability beyond the multi-photon resonance condition in a three-level closed-loop atomic system

► We investigate optical bistability of a three-level closed-loop atomic system, beyond the multi-photon resonance condition. ► By applying Floquet decomposition to the equation of motion, the different scattering processes contributing to the medium response are determined. ► It is shown that the phase dependence of optical bistability arises from the scattering of the driving and coupling fields into the probe field frequency.