  A stationary inflection point (SIP) is a spectral singularity of the Bloch
dispersion relation $\omega(k)$ of a periodic structure where the first and the
second derivatives of $\omega$ with respect to $k$ vanish. An SIP is associated
with a third order exceptional point degeneracy in the spectrum of the
unit-cell transfer matrix, where there is a collapse of one propagating and two
evanescent Bloch modes. At the SIP frequency, the incident wave can be
efficiently converted into the frozen mode with greatly enhanced amplitude and
vanishing group velocity. This can be very attractive for applications,
including light amplification. Due to its non-resonant nature, the frozen mode
regime (FMR) has fundamental advantages over common cavity resonances. Here, we
propose a novel scheme for FMR-based unidirectional amplifiers by leveraging a
tailored amplification/attenuation mechanism and a single nonlinear defect. The
defect breaks the directional symmetry of the periodic structure and enables
nonlinearity-related unidirectional amplification/ attenuation in the vicinity
of the SIP frequency. We demonstrate the robustness of the amplification
mechanism to local impurities and parasitic nonlinearity.
