  Full wavefront control by photonic components requires that the spatial phase
modulation on an incoming optical beam ranges from 0 to 2{\pi}. Because of
their radiative coupling to the environment, all optical components are
intrinsically non-Hermitian systems, often described by reflection and
transmission matrices with complex eigenfrequencies. Here, we show that
Parity-Time symmetry breaking -- either explicit or spontaneous -- moves the
position of Zero singularities of the reflection or transmission matrices from
the real axis to the upper part of the complex frequency plane. A universal 0
to 2{\pi}-phase gradient of an output channel as a function of the real
frequency excitation is thus realized whenever the discontinuity branch
bridging a Zero and a Pole, i.e a pair of singularities, is crossing the real
axis. This basic understanding is applied to engineer electromagnetic fields at
interfaces, including, but not limited to, metasurfaces. Non-Hermitian
topological features associated with exceptional degeneracies or branch cut
crossing are shown to play a surprisingly pivotal role in the design of
resonant photonic systems.
