We introduce a new type of synthetic saturable absorber based on quantum-inspired Jx photonic arrays. We demonstrate that the interplay between optical Kerr nonlinearity, interference effects and non-Hermiticity through radiation loss leads to a nonlinear optical filtering response with two distinct regimes of small and large optical transmissions. More interestingly, we show that the boundary between these two regimes can be very sharp. The threshold optical intensity that marks this abrupt "phase transition" and its steepness can be engineered by varying the number of the guiding elements. The practical feasibility of these structures as well as their potential applications in laser systems and optical signal processing are also discussed.