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Being a powerful tool for linear time-invariant (LTI) systems, system response analysis can also be applied to the so-called linear space-invariant (LSI) but time-varying systems, which is a dual of the conventional LTI problems. In this paper, we propose a system response analysis method for LSI problems by conducting Fourier transform of the field distribution on the space instead of time coordinate. Specifically, input and output signals can be expressed in the wavenumber (spatial frequency) domain. In this way, the system function in wavenumber domain can also be obtained for LSI systems. Given an arbitrary input and temporal profile of the medium, the output can be easily predicted using the system function. Moreover, for a complex temporal system, the proposed method allows for decomposing it into multiple simpler subsystems that appear in sequence in time. The system function of the whole system can be efficiently calculated by multiplying those of the individual subsystems., Comment: This article has been withdrawn due to an unresolvable internal author dispute

Chiral structures have reported radiation of circular polarized electromagnetic waves (CPs) in a specific direction. Here we report a class of torus knot radiators that is not only chiral but also three-dimensional (3-D) rotational symmetric along X, Y and Z axes. Because of this exotic chirality and symmetry, the knot radiator presented is able to demonstrate omnidirectional circular polarized radiation, which has never been reported in any known structures., Comment: This article has been withdrawn due to an unresolvable internal author dispute

Inspired by the epidemic contact tracing technique, we propose a method to efficiently solve electromagnetics by tracing the energy distribution. The computational domain is adaptively decomposed, and the available computational resources are focused on those energy-active (infections) and their adjacent (exposed) domains, while avoiding the unnecessary computation of energy-null (unexposed) domains. As an example, we employ this method to solve several optics problems. The proposed method shows high efficiency while maintaining a good accuracy. The energy tracing method is based on the causality principle, and therefore is potentially transformative into other computational physics and associated algorithms., Comment: This article has been withdrawn due to an unresolvable internal author dispute

Time-varying materials bring an extra degree of design freedom compared to their conventional time-invariant counterparts. However, few discussions have focused on the underlying physical difference between spatial and temporal boundaries. In this letter, we thoroughly investigate those differences from the perspective of conservation laws. By doing so, the building blocks of optics and electromagnetics such as the reflection law, Snell's law, and Fresnel's equations can be analogously derived in a temporal context, but with completely different interpretations. Furthermore, we study the unique features of temporal boundaries, such as their nonconformance to energy conservation and causality., Comment: This article has been withdrawn due to an unresolvable internal author dispute

One of the core concepts from the non-Hermitian skin effect is the extended complex wavevectors (CW) in the generalized Brillouin zone (GBZ), while the origin of CW remains elusive, and further experimental demonstration of GBZ is still lacking. We show that the bulk states of an open quantum system dynamically governed by the Lindblad master equation exhibit non-Bloch evolution which results in CW. Experimentally, we present temporal topolectrical circuits to serve as simulators for the dynamics of an open system. By reconstructing the correspondence between the bulk states of an open system and circuit voltage modes through gauge scale potentials in the circuit, the non-Bloch evolution is demonstrated. Facilitated by the simulators and proper approach to characterize the non-Bloch band proposed here, the GBZ is confirmed. Our work may advance the investigation of the dissipative topological modes and provide a versatile platform for exploring the unique evolution and topology for both closed and open systems., Comment: 5 figures

Optical activity is the ability of chiral materials to rotate linearly-polarized (LP) electromagnetic waves. Because of their intrinsic asymmetry, traditional chiral molecules usually lack isotropic performance, or at best only possess a weak form of chirality. Here we introduce a knotted chiral meta-molecule that exhibits optical activity corresponding to a 90{\deg} polarization rotation of the incident waves. More importantly, arising from the continuous multi-fold rotational symmetry of the chiral torus knot structure, the observed polarization rotation behavior is found to be independent of how the incident wave is polarized. In other words, the proposed chiral knot structure possesses two-dimensional (2-D) isotropic optical activity as illustrated in Fig. 1, which has been experimentally validated in the microwave spectrum. The proposed chiral torus knot represents the most optically active meta-molecule reported to date that is intrinsically isotropic to the incident polarization.

Knots have been put forward to explain various physical phenomena because of their topological stability. Nevertheless, few works have reported on the exotic symmetry properties that certain knots possess. Here we reveal an exceptional form of symmetry for a family of knots that are both chiral and three-dimensional (3-D) rotationally symmetric about every axis of a standard Cartesian coordinate system. We call these unique knotted structures chiral balls. To demonstrate the unprecedented physical characteristics exhibited by these unique structures, we study the electromagnetic scattering properties of a representative conductive chiral ball. In particular, a characteristic mode analysis is performed to investigate the intrinsic scattering properties of this chiral ball. With both chirality and 3-D rotational symmetry, the chiral ball is shown to exhibit an extraordinary isotropic circularly polarized scattering property, which has not been previously reported for any known electromagnetic structures. Because of their unique properties, chiral balls are expected to not only have a profound impact on the fields of electromagnetics and optics but also far beyond.