Tuning 2nd and 3rd order exceptional points with Kerr nonlinearity

To achieve Exceptional Point (EP) in a gain/loss coupled pair resonators, both the real and imaginary parts of two eigenfrequencies should coincide. Therefore, it usually imposes difficulties in these systems since during the fabrication process, perturbations may change the resonant frequencies lifting the degeneracy. In this work we reveal that Kerr non-linearity can compensate the initial difference in resonant frequencies, therefore, the EP can occur in a coupled resonators with unequal resonant frequencies, and this unequality is correlated to the contrast between the nonlinear coefficients incorporated in the resonators.