  In time-reversal invariant electronic systems the scattering matrix is
anti-symmetric. This property enables an effect, designated here as "scattering
anomaly", such that the electron transport does not suffer from back
reflections, independent of the specific geometry of the propagation path or
the presence of time-reversal invariant defects. In contrast, for a generic
time-reversal invariant photonic system the scattering matrix is symmetric and
there is no similar anomaly. Here, it is theoretically proven that despite
these fundamental differences there is a wide class of photonic platforms - in
some cases formed only by time-reversal invariant media - in which a scattering
anomaly can occur. It is shown that an optical system invariant under the
action of the composition of the parity, time-reversal, and duality operators
(PTD) is characterized by an anti-symmetric scattering matrix. Specific
examples of photonic platforms wherein the scattering anomaly occurs are given,
and it is demonstrated with full wave numerical simulations that the proposed
systems enable bidirectional waveguiding immune to arbitrary deformations of
the propagation path. Importantly, our theory unveils a new class of fully
three dimensional structures wherein the transport of light is fully protected
against reflections and uncovers unsuspected links between the electrodynamics
of reciprocal and nonreciprocal materials.
