Coupled Toroidal Dipole Modes in Silicon Nanodisk Metasurface: Polarization Independent Narrow Band Absorption and Directional Emission

Abstract

refractive index dielectric (e.g., silicon (Si), germanium and gallium phosphide, etc.) nanostructures have emerged. [1-4] The low loss feature [5-8] together with the unique optical responses associated with the electric and magnetic multipole resonances provides an additional degree of freedom for light manipulation. [1-3,9-11] Recently, in addition to the electric and magnetic multipole moments, toroidal multipole moments, which are derived by multipolar decomposition of induced currents in dielectric resonators, have been attracting significant attention. [12] The lowest order toroidal multipole, i.e., the toroidal dipole (TD), is a current loop along a meridian of a torus in a dielectric resonator. The TD mode has the far-field radiation pattern identical to that of the electric dipole (ED) mode, and thus the destructive interference of the two modes produces a non-radiating state. [12,13] The state is called "anapole." The radiation-less anapole state can be realized in a simple dielectric nanodisk (ND) structure when the diameter-to-height ratio is higher than ≈5. [12] At the anapole state, electromagnetic fields are confined inside a ND, [14] which are utilized for the enhancement of the nonlinear optical responses, [15-19] the emission rate by the Purcell effect, [20] the Raman scattering, [21] and the photocatalytic activity. [22] TD moments exist not only in an isolated dielectric nanostructure, but also in coupled dielectric nanostructures like oligomers [23,24] and two dimensional arrays. [25-28] Basharin et al. suggested the existence of TD resonances in cluster arrays of subwavelength high-index dielectric cylinders in the terahertz frequency region. [25] Liu et al. theoretically demonstrated a high Q-factor response and resultant strong field confinement by TD resonances in square arrays of silicon split nanodisks. [26] Luo et al. proposed a metasurface consisting of two silicon split-ring resonators and theoretically demonstrated a high-Q TD resonance in the near-IR region. [27] These researches indicate that compared to TD resonances of isolated nanostructure, those of coupled nanostructures have higher degree of freedom in designing TD mode-related optical responses. However, experimental studies on TD responses of coupled dielectric nanostructures are still limited [29,30] and the application for the control of light-matter interactions has never been reported. In this work, we propose a two-dimensional hexagonal array of very thin (20-50 nm in thicknesses) circular Si NDs as the metasurface supporting coupled TD modes. We first calculate

Angle‐, Polarization‐, and Wavelength‐Resolved Light Scattering of Single Mie Resonators Using Fourier‐Plane Spectroscopy

“…A sub-wavelength optical resonator enables efficient manipulation of electromagnetic fields at the nanoscale and can be a building block of functional metamaterials and metasurfaces. [1][2][3][4][5][6][7][8][9] Recently, dielectric resonators made of highrefractive-index semiconductors are energetically studied due to the possession of high scattering efficiency and low-loss Mie resonances. [10] In planar metasurface devices made from all-dielectric Mie resonators, the transmission efficiency reaches the value equivalent to that of a glass plate (>90%).…”

All‐Dielectric Toroidal Metasurfaces for Angular‐Dependent Resonant Polarization Beam Splitting

“…[25][26][27][28] As a result, the growing research efforts put in the study of toroidal MS have led to numerous demonstrations of their practical potential, for example, for polarization conversion, [29] beam steering, [30] high-quality factor filtering, [23,[31][32][33][34][35] and narrowband absorption and directional emission. [36] Although several of the thus far investigated toroidal MS employ metallic meta-atoms, [31,[37][38][39] in certain cases these have an intricate shape and they anyhow suffer from ohmic losses, which can dampen their EM response and hinder their up-scaling to higher frequencies. That being the case, all-dielectric MS are gaining ground also in the context of toroidal MS as a simpler technological solution with lower intrinsic losses thanks to the availability of numerous low-loss dielectric materials.…”

“…[43] At infrared and optical frequencies, toroidal MS can be fabricated by lithographic definition of high-index materials, such as silicon or titanium dioxide. [35,36] In this work, we theoretically and experimentally demonstrate a not yet explored functionality of toroidal MS, namely, angular-dependent resonant polarization beam splitting (PBS) in the microwave K-band. The metasurface is composed of a square periodic array of high-permittivity, low-loss ceramic resonators, embedded in a 3D-printed polylactic acid (PLA) substrate.…”

“…[ 25–28 ] As a result, the growing research efforts put in the study of toroidal MS have led to numerous demonstrations of their practical potential, for example, for polarization conversion, [ 29 ] beam steering, [ 30 ] high‐quality factor filtering, [ 23,31–35 ] and narrowband absorption and directional emission. [ 36 ]…”

“…[ 43 ] At infrared and optical frequencies, toroidal MS can be fabricated by lithographic definition of high‐index materials, such as silicon or titanium dioxide. [ 35,36 ]…”