Polarization Inversion with $\mathcal{P}\cdot\mathcal{T}\cdot\mathcal{D}$ Symmetric Scatterers

We demonstrate, both theoretically and experimentally, that arbitrary scatterers preserving parity-time-duality ($\mathcal{P}\cdot\mathcal{T}\cdot\mathcal{D}$) symmetry inherently produce a backscattered wave whose electric field is the mirror-symmetric counterpart of the incident electric field, up to an amplitude factor, with respect to the system's characteristic mirror plane. Specifically, we establish that a general elliptically polarized wave, when reflected from such structures, exhibits a polarization state related to the polarization ellipse of the incident wave by a parity transformation. Notably, a circularly polarized wave reflects with spin angular momentum opposite to that of the incident field, in stark contrast to reflection from conventional conducting screens. These findings enable several applications such as reflective polarizers.