It is shown that a new type of metamaterial, a 3D-array of toroidal solenoids, displays a significant toroidal response that can be readily measured. This is in sharp contrast to materials that exist in nature, where the toroidal component is weak and hardly measurable. The existence of an optimal configuration, maximizing the interaction with an external electromagnetic field, is demonstrated. In addition, it is found that a characteristic feature of the magnetic toroidal response is its strong dependence on the background dielectric permittivity of the host material, which suggests possible applications. Negative refraction and backward waves exist in a composite toroidal metamaterial, consisting of an array of wires and an array of toroidal solenoids.
An expression for the electromagnetic field energy density in a dispersive lossy left-handed metamaterial, consisting of an array of split-ring resonators and an array of wires, is derived. An electromagnetic field with general time dependence is considered. The outcome is compared with previously published results. In the absence of losses, agreement with the general result for the energy density in a dispersive material is obtained. The formulae are verified using the finite-difference time-domain numerical method. The applicability of two commonly used permeability models to the problem of calculating the energy stored in an array of split-ring resonators is discussed.
In this letter, we present the first experimental study of a new chiral metamaterial consisting of toroidal wire windings. We show that the metamaterial exhibits three bands of circular dichroism in the GHz range. We discuss the response of the structure in terms of multipole moments, including the (magnetic) toroidal dipole moment.Toroidal, doughnut-shaped structures are ubiquitous in nature, appearing on scales which range from the subatomic [1, 2] to the astronomical [3]. On the molecular level, the torus shape is preferred by numerous biological and chemical macromolecules, such as DNA condensates [4], proteins [5] and oligosaccharides [6], to name just a few. Toroidal symmetries are also encountered frequently in solid-state systems including carbon nanotubes [7] and ferroelectrics [8,9]. Although the behavior of such systems has been studied extensively, their interaction with electromagnetic radiation is not well understood. Indeed, within the framework of classical electrodynamics, unusual phenomena associated with violation of Lorentz reciprocity [10] and non-radiating configurations [11] have been predicted for toroidal structures and their interactions. Nevertheless, such phenomena are usually weak [12,13] and, therefore, experimental investigations are rare. In this letter, we study a new artificial chiral medium, originally suggested in [14], consisting of an array of toroidal wire windings in a metamaterial' configuration. We show that such a metamaterial exhibits strong gyrotropic response which is attributed to different terms of its multipole expansion.In contrast to artificial gyrotropic media, where handedness is usually associated with the direction of a "twist vector" following a cork-screw law along the helicity axis, the situation is more complicated when the structure possesses toroidal symmetry. Here, the twist vector rotates along the torus, and therefore a corresponding direction can not be defined. However, although no helicity axis exists, the structure has two well-defined enantiomeric forms, corresponding to different directions of the winding (see Fig. 1a). Based on this concept, we manufactured a chiral toroidal metamaterial with a unit cell consisting of four connected square loops that were formed by horizontal and vertical copper wire segments (see Fig. 1b). The resulting windings were embedded in dielectric bars with permittivity = 4.5 − 0.081i. The size of the unit cell was 15x15 mm rendering the metamaterial non-diffracting up to 20 GHz. Transmission experiments were performed at normal incidence, from 2 to 14 GHz, in an anechoic chamber using two broadband horn antennas (Schwarzbeck M. E. model BBHA 9120D). The transmission spectra were recorded with a vector network analyzer. The intensity and phase of the structure's response to right and left circularly polarized light are presented in Figs. 2a and 2b, respectively. As it can be seen in Fig. 2a, experimental results (solid line) are in good agreement with finite element numerical simulations (solid circles). Two resonan...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.