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.

Self-dual media (SDM) coatings provide a powerful means to enhance wave transmission through subwavelength apertures in conducting screens. When applied around an aperture, SDM suppresses reflections and directs incident electromagnetic energy exclusively through the opening. Experimental and numerical studies show that a finite, double-sided SDM coating with dimensions of about [Formula: see text] increases transmitted power by roughly 10 dB compared to an uncoated reference. This effect is non-resonant, enabling broadband operation constrained only by the material design. Unlike earlier methods that mainly improved radiation directivity without altering the transmitted power, this approach significantly boosts power density within the aperture itself. These findings highlight SDM coatings as a versatile strategy for efficient energy transmission through sub-wavelength structures, with potential applications in waveguiding, sensing, phased arrays and energy harvesting technologies.

We demonstrate, both theoretically and experimentally, that arbitrary scatterers preserving parity-time-reversal-duality (P·T·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 objects. These findings enable several applications such as reflective polarizers and spin-selective devices.

We demonstrate, both theoretically and experimentally, that arbitrary scatterers preserving parity-time-duality (𝒫·𝒯·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.

Coats of self-dual media (SDM), that cover the surfaces adjacent to small apertures in conducting screens, are capable of collecting electromagnetic energy from around the aperture and force it to funnel through it. This effect is due to the non-reflecting nature of the SDM, that allows no outlet for the energy except through the hole. Compared with a reference bare structure, an enhancement of several tens of dBs are seen in simulations, and close to 10 dB in initial experiment. Coating can reside on either side of the screen or on both sides, with further enhancement in the latter case. This structure is non-resonant, allowing for potentially wide band realizations depending on the bandwidth of the synthesized materials involved.

$\mathcal{P}\cdot\mathcal{T}\cdot\mathcal{D}$ and rotational symmetries of electromagnetic and photonic systems have recently been shown, separately, to characterize different non-reflecting structures. In this work, we provide a general framework for both types of symmetries, casting the rotational symmetry in terms of a new $\mathcal{R}\cdot\mathcal{T}\cdot\mathcal{D}$ - type symmetry. Out of this analysis, a third option emerges; namely, a combined $\mathcal{P}\cdot\mathcal{T}\cdot\mathcal{D}/\mathcal{R}\cdot\mathcal{T}\cdot\mathcal{D}$ symmetry condition. With this option, the door opens for synthesis of many new non-reflecting media, as shown in the examples below.

Definitions of incident and reflected modes in the P . T . D formulation result in co-polarized non-reflection for 45 degrees and 135 degrees polarizations with respect to the mirror plane. For other incident polarizations, the non-reflection angle is rotated and reflections are inverted. A number of applications is envisioned, including a reflective polarizer described below.

The Riemann-Silberstein time domain vectors are shown to be solutions to each of the two first order factors that constitute the decomposed vector wave equation. The entire electromagnetic problem is then re-formulated in a simpler, compact form, at the cost of using complex time domain entities. Advantage is seen, e.g., in finite difference implementations that require fewer operations.

Self-dual media (SDM) have been shown to enable the design of inherently reflection-less radiating elements for phased array applications with extreme scanning demands. As a natural continuation to this work, we lay here the foundations for a complete SDM-based feeding and beamforming network system in the form of SDM-based power splitters. The scope of this work includes simulations and optimization of the splitters in several forms, as well as a transition from a conventional microstrip to SDM.

A pair of field consistuents, denoted herein as $\mathbf{E}^{\mathrm{R}}$ and $\mathbf{E}^{\mathrm{L}}$ , are suggested as an altenarive to the conventional pair E, H. These fields obey lower order equations, i.e., the first order Maxwell's curl equations are replaced by a zero order (algebraic) relationship, while the wave equation is now traded for a first order equation. As a result, the conventional use of the $6\times 6$ scalar, real time domain set is now consolidated a $3\times 3$ complex equations. This consolidated solution tracks exactly the one obtained with the original finite difference scheme.

We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-travelling in a (generally lossy) Lorentzian-like medium scatters from the temporal "half-space interface" that results from an abrupt temporal change in its plasma frequency (while keeping its resonance frequency constant). In order to achieve momentum preservation across the temporal discontinuity, we show how, unlike in the well-known problem of a nondispersive discontinuity, the second-order nature of the dielectric function now gives rise to two shifted frequencies. As a consequence, whereas in the nondispersive scenario the continuity of the electric displacement D and the magnetic induction B suffice to find the amplitude of the new forward and backward wave, we now need two extra temporal boundary conditions. That is, two forward and two backward plane waves are now instantaneously generated in response to a forward-only plane wave. We also include a transmission-line equivalent with lumped circuit elements that describes the dispersive time-discontinuous scenario under consideration.

Structural and material symmetries can be engineered to create unique electromagnetic effects including backscattering-immune propagation. In this work we investigate the scattering properties of a class of structures with combined rotational and dual symmetries, i.e., self-dual structures. We demonstrate how self-duality will be manifested through different forms of zero backscattering in periodic and non-periodic structures.

The six scalar components of the Maxwell's real time domain equations are reduced in this work into two decoupled sets of 3 × 3 complex equations. Each set consolidated the entire information into three new complex field constituents. Contrary to the conventional staggered grid, all field samples reside on a single finite difference grid. The total number of unknowns is thus reduced, and interpolations are eliminated.

Confining and controlling electromagnetic energy typically involves a highly resonant phenomenon, especially when subwavelength confinement is desired. Here, we present a class of nonresonant, self-dual planar metastructures capable of protected energy transmission from one side to the other, through arbitrarily narrow apertures. It is shown that the transmission is in the form of matched propagating modes and is independent of the thickness and specific composition of the surface. We analytically prove that the self-dual condition is sufficient to guarantee 100% transmission that is robust to the presence of discontinuities along the propagation path. The results are confirmed numerically through study of various scenarios. The operation is broadband and subject only to the bandwidth of the constituent materials. The polarization of the internal field can also be independently controlled with respect to the incident one. Our structures are promising for applications in sensing, particle trapping, near-field imaging, and wide scan antenna arrays.

Duality between electric and magnetic fields and parameters has long been recognized as a useful shortcut for inferring solutions to certain problems from their known duals. In this article, we suggest the use of "half-way dual" fields for extending the range of problems that can be addressed in this way. To this end, a workable expression for the fractional curl operator of order one-half is derived. While general expressions for fractional derivatives are purely formal and hard to implement, the special case of electromagnetic fields enables substantial simplification that leads to this closed form expression. It is then used to formulate a four-field set of Maxwell-type equations that include two half-way dual fields in addition to the original E and H. As an example, the solution to a reactive surface is inferred from its perfect electric conductor (PEC) half-way dual.

We introduce a generalized class of arbitrarily sized/shaped particles that satisfy the Kerker zero backscattering condition for normal incidence for all incident polarizations. We prove that self-duality is a sufficient condition to achieve zero backscattering.

Duality between electric and magnetic fields and parameters has long been recognized as a useful shortcut for inferring solutions to certain problems from their known duals. In this work, we suggest the use of "half-way dual" fields for extending the range of problems that can be addressed in this way. To this end, a workable expression for the fractional curl operator of order one-half is derived. While general expressions for fractional derivatives are purely formal and hard to implement, the special case of electromagnetic fields enables substantial simplification that leads to this closed form expression. It is then used to formulate a four-field set of Maxwell-type equations, that include two half-way dual fields in addition to the original E and H. As an example, the solution to a reactive surface is inferred from its PEC half-way dual.

Self-dual structures, whose electric and magnetic parameters can be interchanged without causing any change to the structure, are shown to be inherently matched to free space. With proper design, in such structures, the normally incident energy is funneled through arbitrarily thin air gaps that support TEM or quasi-TEM modes. A finite-length self-dual waveguide, as suggested herein, is inherently matched at both input and output interfaces, even though the field within the waveguide may be substantially complex and have its own characteristic polarization. This structure looks promising for several applications, as detailed below.