Gyrotropy of a Metamolecule: Wire on a Torus

Abstract

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...

Electromagnetic toroidal excitations in matter and free space

“…Early works on toroidal metamaterials predicted the presence of backward waves and negative refraction in such material systems 53 . Experimental signatures of a toroidal dipole response were first seen in the microwave dichroism spectra of chiral toroidal solenoid arrays in 2009 54 , obscured however by the presence of dipole and higher order electric and magnetic multipoles. First observation of an isolated toroidal dipole absorption resonance was reported in 2010 55 in a metamaterial whose metamolecules were formed by a ring-shaped arrangement of microwave resonators (see Fig.…”

“…In the past optical activity was linked to the presence of the electric and magnetic dipole (or electric quadrupole) moments in the medium 1 . Following early work that indicated the toroidal moment contribution to optical activity 54 , a recent experimental demonstration showed a dominant role for the toroidal moment in the polarization properties of a purposely designed microwave metamaterial 78 .…”

Metamaterials at the University of Southampton and beyond

“…In 2004 I won a very rare and highly sought-after EPSRC adventure grant entitled 'Supertoroids challenge established laws of physics,' GR/S48165/01, run with my co-investigators Professor Allan Boardman in Salford University and Professor Tony Bland in Cambridge. Initially, evidence of toroidal response was seen in a chiral metamaterial-an array of wire helix bent into a torus [117]-but the announcement had to wait until 2010, when we clearly saw a toroidal dipole response by detecting a resonant toroidal electromagnetic response in an artificially engineered metamaterial [118]. Observations of toroidal response in terahertz [119], optical plasmonic [120][121][122] and dielectric metamaterials [123] followed soon together with the developing theory [124].…”

“…Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion and optical activity. We were interested in toroidal excitation in matter from the very first days of our metamaterial research [116,117], and in 2004 we hosted the first international workshop on toroidal electrodynamics at Southampton, attended by many earlier researchers on the subject including G N Afanasiev, E V Tkalya, A Ceulemans, M A Martsenyuk, H Schmid and A Dereux. In 2004 I won a very rare and highly sought-after EPSRC adventure grant entitled 'Supertoroids challenge established laws of physics,' GR/S48165/01, run with my co-investigators Professor Allan Boardman in Salford University and Professor Tony Bland in Cambridge.…”

Exciting dynamic anapoles with electromagnetic doughnut pulses

“…FD pulses can be seen as propagating counterparts of the localized toroidal dipole excitations in matter [11]. The toroidal dipole is distinct from the conventional electric and magnetic dipoles [12,13] and have attracted significant interest in recent years as important contributors to the electromagnetic properties of media with non-local response or elements of toroidal symmetry [11,[14][15][16][17][18][19][20][21]. Superposition of dynamic electric and toroidal dipoles leads to anapoles which, through destructive interference, exhibit vanishing radiated fields outside the source [20,22].…”