PTD Symmetry Protected Scattering Anomaly in Optics

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.