Direction-dependent optical bistability and non-reciprocity in asymmetric ring cavity. We take α₀l = 3.75, and R₁ = 0.8, R₂ = 0.9 to present the asymmetry of the cavity. Panel (a) shows the I_t versus I_in, where the black solid line refers to the forward input case and red dashed line to the backward input case. The two vertical green dotted lines indicate the optimal input intensity window. Panel (b) shows T versus I_in in the optimal window, where the black line denotes the forward transmittivity T_f and the red curve represents the backward transmittivity T_b.