Spectral singularities with directional sensitivity

We propose a class of spectral singularities that are sensitive to the direction excitation and arise in nonlinear systems with broken parity symmetry. These incident beam result diverging transmission reflection for left (right) incident, while right (left) side system remain finite. For pedagogical reason, first we review scattering formalism using an abstract $\ensuremath{\delta}$-function model. Then, symmetry consisting two $\ensuremath{\delta}$ functions, one linear other nonlinear, prove existence our proposed singularities. Finally, use experimentally feasible realistic model based on coupled disk resonators demonstrate singularity directional sensitivity (SSDS). Our SSDS might have applications design sensors provide solution hole-burning problem pumped laser ring resonators.