Fig. 4

The transmission efficiency \(|t_{p_{1}}|^2\) (blue solid curve) and \(|t_{p_{2}}|^2\) (red dashed curve) are plotted as functions of the \(\Omega /\omega _m\) under different powers \(\mathrm {P_c}\) and coupling strengths \(\lambda\) (including \(\lambda _{1}\) and \(\lambda _{2}\)) in panels (a), (b) and (c) with \(\kappa _2=0.5\kappa _1\). In panel (d), the isolation ratio \(\textrm{I}\) of the probe field nonreciprocal transmission is plotted as a function of the \(\kappa _1/\kappa _2\). The other parameters are the same as in Fig. 3.