Controlling the sing and magnitude of Kerr nonlinearity in four-level N-type EIT medium

Third-order nonlinear susceptibility in a four-level system with N-type configuration is studied by applying the electromagnetically induced transparency (EIT). The system is irradiated with a weak probe and two strong coupling fields. Behaviour of real (Kerr nonlinearity) and imaginary parts of third-order susceptibility and linear absorption spectrum of probe field is investigated with coupling field intensity and its frequency detuning. Results are shown that, the sign of both imaginary and real parts of third-order nonlinear susceptibility in one of Kerr peaks, changes from positive to negative with increasing the coupling field intensity. The EIT windows are not sensitive for intensity but extend for negative and shortened for positive detuning's. Furthermore, the magnitude of Kerr and nonlinear absorption (or gain) peaks efficiently modify with increasing the intensity. This can be important in practical applications such as lasing without inversion, subluminal and superluminal propagation and optical limiting effect based on self-focusing or self-defocusing process.