Parity Time-reversal Duality Symmetric Structures

Topological Edge modes (TPEMs) are the electromagnetic (EM) equivalent of the edge states in the integer quantum Hall effect that occurs due to topological phase transitions of matter, the discovery at the origin of the Nobel Prize awarded to Thouless, Haldane and Kosterlitz in 2016. The EM extension of TPEMs, originally found at atomic level, was then moved to plasmonics and microwaves areas, open ing new and unexpected opportunities for innovation. The novel aspect of TPEMs is that they can be "protected against backscattering" thus, enabling a wave-guiding not affected by reflections due to disorder, imperfections, obstacles or deformations of the propagation path. TPEMs protection normally requires non-reciprocal ele ments. However, recent researches have shown that it can be also generated by reciprocal materials and this aspect is the main subject of this thesis. A class of structures supporting modes protected against backscattering is the one of PTD-symmetric systems, i.e, systems invariant under the combination of the parity (P), time reversal (T) and duality (D) operators. This condition can be also fulfilled by passive and lossless reciprocal structures, provided that the electro magnetic properties become dual in Babinet sense upon mirroring with respect to a certain plane. If this condition is verified, the system is capable of supporting prop agation without backscattering, i.e. the guiding structures, even if not rigorously unidirectional in topological sense, are intrinsically matched even in the presence of discontinuities if also these latter are PTD-symmetry complaint. The work in this thesis starts from the following considerations. Practical realization of dual volumetric materials can be cumbersome. However, for a homogeneously filled guiding structure, PTD-symmetry condition reduces to the duality of the boundary conditions (BCs), which can be implement through metasurfaces (MTSs). For in stance, a possible PTD-symmetric structure consists of the combination of two dual parallel plate waveguides with one perfect electric conductor (PEC) and one perfect magnetic conductor (PMC) wall.