Gain-loss deformation of equilibrium families in a(Formula presented) PT[jls-end-space/]-symmetric saturable optical dimer

We study a saturable (Formula presented) PT -symmetric optical dimer and show how balanced gain–loss deforms the families of in-phase and out-of-phase equilibrium states that originate in the conservative limit. In the low-power regime, where the saturable nonlinearity reduces to the Kerr case, the system reproduces the standard (Formula presented) PT -symmetry transition from the unbroken to the broken phase, with an exceptional point delimiting the existence of bounded stationary dynamics. At finite power, the saturable dimer supports a richer stationary and multistable structure than the Kerr model, opening a broader nonlinear (Formula presented) PT phase space through additional branch rearrangements. Within the unbroken region, the gain–loss deformation continuously reshapes the equilibrium branches and their stability. The out-of-phase family remains a center throughout, while the in-phase family is unstable below a gain–loss-controlled threshold and develops an intermediate instability window associated with homoclinic excursions and large phase-space deformations. At high power, the saturable correction becomes negligible and the system approaches a quasi-linear regime, thereby recovering the same qualitative behavior as in the low-power limit. These features show that saturation enriches the nonlinear (Formula presented) PT landscape and suggest potential utility for switching and routing in saturable photonic platforms.