Transverse Scattering and Generalized Kerker Effects in All-Dielectric Mie-Resonant Metaoptics

All-dielectric resonant nanophotonics lies at the heart of modern optics and nanotechnology due to the unique possibilities to control scattering of light from high-index dielectric nanoparticles and metasurfaces. One of the important concepts of dielectric Mie-resonant nanophotonics is associated with the Kerker effect that drives the unidirectional scattering of light from nanoantennas and Huygens metasurfaces. Here we suggest and demonstrate experimentally a novel effect manifested in the nearly complete simultaneous suppression of both forward and backward scattered fields. This effect is governed by the Fano resonance of an electric dipole and off-resonant quadrupoles, providing necessary phases and amplitudes of the scattered fields to achieve the transverse scattering. We extend this concept to dielectric metasurfaces that demonstrate zero reflection with transverse scattering and strong field enhancement for resonant light filtering, nonlinear effects, and sensing.

Figure 1

(a) Transverse scattering pattern for a cubic nanoparticle. Small forward scattering corresponds to a contribution of higher-order multipoles in accordance with the optical theorem. (b) Concept of the formation of an ideal transverse scattering pattern. Electric dipole (ED) is in phase with a magnetic dipole (MD), and an electric quadrupole (EQ) is in phase with a magnetic quadrupole (MQ), whereas the dipoles are out of phase with the quadrupoles.

Figure 2

(a) Normalized differential scattering cross sections calculated with the Mie theory for a silicon sphere of 120-nm radius in free space as functions of the size parameter $=k\times \text{radius}$. The solid lines are calculations for the dipole-quadrupolar sphere [$d\sigma /d\mathrm{\Omega }$, Eq. (3)] while the dashed lines describe the total set of multipoles [$d{\sigma }^T/d\mathrm{\Omega }$, Eq. (7)]. In the legend, $\theta =0°$ refers the forward direction, and $\theta =180°$ to the backward direction. (b) Transverse scattering patterns at 609-nm wavelength with permittivity $15.44+0.196i$ (1.23 size parameter) [30]: the green (blue) line corresponds to the plane of the incident electric (magnetic) field polarization.

Figure 3

(a) Comparison of the extinction cross section calculated with the Mie theory and measured experimentally. (b) Scattering patterns at the frequency $f=7.85\mathrm{GHz}$ (1.23 size parameter), where the green (blue) curve corresponds to the plane of the incident electric (magnetic) field polarization. Results are obtained for the ceramic sphere with permittivity $ϵ=16+0.0179i$ and radius 7.5 mm.

Figure 4

(a) Amplitudes and phases of the multipole ratios from Eq. (8) for a cubic Si nanoparticle with the edge of 250 nm. The arrows show the wavelength corresponding to the transverse scattering $\lambda =788\mathrm{nm}$. (b),(c) Two- and three-dimensional scattering patterns at $\lambda =788\mathrm{nm}$. (e),(f) Calculated electric field inside the nanoparticle with the transverse scattering pattern $\lambda =788\mathrm{nm}$ in the $xy$ and $xz$ planes, respectively. All calculations were conducted by comsol multiphysic [23] and the silicon permittivity from Ref. [30].

Figure 5

(a) Schematics of a metasurface being a lattice of cubic nanoparticles with strong transverse scattering. The substrate and the Gaussian beam are shown for better visibility; numerically we consider the metasurface in free space irradiated with a plane wave. (b) Amplitudes (blue) and phases (red) of the multipole ratios defined by Eq. (8) for Si cube with the edge of 250 nm and the lattice spacing 400 nm, and the corresponding reflection ($R$) and transmission ($T$) coefficients. Note that the reflection and transmission coefficients are plotted in accordance with the left $y$ axis.