Mie Voids as broadband directional light sources

TL;DR

The paper addresses the narrowband limitation of Kerker-directional scattering in conventional nanostructures by introducing Mie voids—air cavities in a high-index host—as broadband directional sources. By leveraging a Lorenz–Mie multipolar framework, it shows that spectrally overlapping multipoles in Mie voids produce a broadband generalized Kerker effect, yielding forward scattering under plane-wave illumination and distinct dipole-excitation regimes. Spherical voids demonstrate robust forward directionality across the visible range, while non-spherical (conical) voids in substrates retain forward-leaning scattering, including practical substrate-coupled geometries. When coupled to emitters, voids exhibit a directional Purcell effect: inside the void, Purcell enhancement up to $F \approx 5$ occurs, and outside the void, backward-directed emission emerges due to destructive interference. These results establish Mie voids as versatile broadband nanoscale directional sources with potential for antenna design and energy harvesting on high-index platforms.

Abstract

The Kerker effect arises from the interference between electric and magnetic multipoles, enabling directional light scattering in nanophotonics. However, conventional dielectric and plasmonic nanoparticles can only act as Kerker sources in narrow spectral regions, limiting their applicability. Here, we show that the recently discovered Mie voids overcome this limitation by supporting a broadband generalized Kerker effect spanning the whole visible range. We investigate the optical response of Mie voids under both plane-wave and dipolar excitation. For plane waves, the voids preferentially scatter light in the forward direction. Under dipolar excitation, the resulting radiation emission towards the void and beyond is suppressed due to destructive interference between the dipole field with the directional scattered field of the void. These findings identify Mie voids as versatile broadband directional sources, opening pathways for antenna design and energy harvesting at the nanoscale.

Figures (7)

• Figure 1: Illustration of the scattering and radiation behavior of spherical Mie voids under different kinds of illumination: (a) plane wave excitation. (b) Directional Purcell enhancement effect in the case of a dipole excitation. We denote the emitted radiation towards the dipole and beyond as 'foward radiation'. The emitted forward radiation, which is the linear superposition of the scattered and dipole fields, is suppressed, whereas the radiation to the opposite or backward direction remains. (c) Generalized forward Kerker effect of spherical Mie voids in the case of plane waves. The far-field emission is predominantly in the forward direction.
• Figure 2: (a) and (b): The first six multipole contributions to the scattering efficiency $Q_{\text{sca}}$ for a Mie void with $100nm$ radius as a function of the vacuum wavelength $\lambda$. The scattering angle $\vartheta$ is defined in the upper right corner of each panel. (c) and (d): The asymmetry parameter $g$ as a function of $R$ and $\lambda$. Panels (a) and (c), respectively, display $Q_{\text{sca}}$ and $g$ for a 'conventional' Mie resonator case $n_{\text{sphere}} >n_{\text{host}}$, whereas the results in panels (b) and (d) have been derived for Mie voids with $n_{\text{sphere}} <n_{\text{host}}$ .
• Figure 3: (a) Numerically calculated intensity distribution $I_{\text{sca}}$ of the scattered electric field around an isolated conical void for an incident plane wave coming from the top at a wavelength of $\lambda=600n m$. The local field intensity is normalized to $I_{\text{inc}}$ as the intensity of the incident field. The Mie void with upper radius $r=200n m$, lower radius $r=150n m$, and height $h=410n m$ is embedded n a substrate with $n_{\text{host}} = 4$. (b) Penetrated relative intensity $I_{\text{sca}}/I_{\text{inc}}$ along the symmetry axis in the center of the void compared to the penetrated relative intensity in the absence of the void. (c) Asymmetry parameter for the same void as a function of $\lambda$.
• Figure 4: (a) Illustration of the directional Purcell effect in the case of a local dipole illumination. The scattered field of the Mie void destructively interferes with the dipole field, leading to backward radiation. (b) Spatial distribution of the decomposition of the radiated electric field intensities $|\vb{E}_i|^2$ for a $100nm$ void in the presence of a dipole with wavelength $\lambda = 600nm$, which is placed $160nm$ away from the void center. The index $i$ indicates the dipolar, the scattered, or the radiated field. If the scattered electric field has a different phase than the dipolar field, this leads to destructive interference. As a result, the radiated field intensity has a minimum in the forward direction.
• Figure 5: The asymmetry parameter $g$ for spherical particles excited by plane waves. $g$ is plotted as a function of the size parameter $kR = 2\pi n_{\text{host}}R/\lambda$ and the relative refractive index $n_{\text{sphere}}/n_{\text{host}}$.The boundary between Mie-void and Mie resonator regimes is displayed by the dashed black line