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