Experimental Observation of Toroidal Dipole Modes in All‐Dielectric Metasurfaces

Abstract

helix (a solenoid) bent in a ring (a toroid). The current flowing through the helix cre ates a magnetic field trapped inside the toroid. The resulting moment of such a system is oriented along the axis of revo lution of the toroid, and it is defined as a toroidal moment. If the toroid is rigid, then no magnetic field produced by external sources can act on the toroid as a whole. In the nonideal case, an electro magnetic coupling with such a toroidal moment is possible, although one can expect that this effect should be very weak and hardly measurable. Despite this, the toroidal moment was found to exist in different problems of condensed matter physics, and it was studied in many papers. [2][3][4][5] Similar to the standard multipole expansion [6] related to the electromag netic potentials and sources, the toroidal multipoles originated from the decompo sition of the moment tensor have a dual nature. [7] It means that there appears a distinction between magnetic and electric toroidal multipoles manifested in different flow paths of their polarization cur rents. In particular, a magnetic (polar) toroidal dipole is created by the polarization currents flowing on a surface of a toroid along its meridian (the poloidal direction), whereas an electric (axial) toroidal dipole appears from a ring of polarization cur rents flowing along the toroid (the toroidal direction).The study of toroidal dipole modes has attracted a growing attention due to the specific properties of the toroidal electromagnetic response which differs from more familiar electric and magnetic dipole modes. Herein, toroidal dipole modes generated by metasurfaces composed of trimer clusters of high-index dielectric particles are observed. Both far-field transmission measurements and direct near-field mapping of the electromagnetic fields are performed in microwave experiments, and two distinct types of the toroidal dipole modes are observed in a single geometry of the metasurface design, where the toroidal modes are generated either inside of the three- particle clusters (the so-called intra-cluster toroidal modes) or between the neighboring particles in the clusters (inter-cluster toroidal modes). A transient response of the toroidal dipole modes excited by a pulse is studied in detail.Since the metasurface is composed of simple dielectric disks without the use of any metallic components, the proposed design can be feasibly scalable to both micro-and nanometer-size dielectric structures, and it can be employed in the flat-optics platform for realizing the beams shaping and efficient light-matter interaction for multiple hotspot energy localization, nonlinear frequency conversion, and highly efficient trapping of light. Toroidal Dipole ModesAppearance of a toroidal moment is an intriguing phenomenon in the physics of light-matter interaction, first predicted theo retically in the middle of the last century. It was introduced in the particle physics in the study of the interaction with parity violation for elementary particles and weak electromagnetic f...

Nonradiating photonics with resonant dielectric nanostructures

“…It was shown theoretically and experimentally in Ref. [137] that the dielectric metasurface consisting of trimer clusters of high-index dielectric particles demonstrate strong toroidal response in GHz frequency range in the near-and far-field region. This design can be scaled for measurements in the visible range.…”

Metasurface Engineering through Bound States in the Continuum

“…1(c)]. The existence of the TD mode in the metasurface whose lattice is formed by trimers arranged in square unit cells was examined in [31]. Here we introduce some modifications to the structure of unit cell studied earlier to provide further degree of freedom for resonance manipulation in both near-and far-fields.…”

“…The corresponding quality factors of leaky resonances depend on the degree of the introduced structural asymmetry [20]. The concept of manipulating the transition between the symmetry-protected BICs and leaky resonances was first proposed for plasmonic metasurfaces composed of metallic split-ring resonators [21], and then it was developed for all-dielectric metasurfaces [22][23][24][25][26][27][28][29][30][31]. The recent development in topological photonics has demonstrated a wide class of topologically protected states [32].…”

Toroidal Dipole Resonances in All‐Dielectric Oligomer Metasurfaces

“…To corroborate the existence of toroidal dipolar responses, we employ multipole expansion including the toroidal dipole term to quantify the contribution of each multipole to the far-field scattering in one of the meta-molecules [43] (see Supporting Information for details). [31] This trimer scenario also serves as a cornerstone for further discussion on other types of dielectric oligomers. It is evident that in the selected wavelength range, the scattering cross section of the toroidal dipole (TD) dominates all other multipoles, as shown by the green line in Figure 2d.…”