Structured light excitation of toroidal dipoles in dielectric nanodisks

Conventional electromagnetic multipoles can be completed by complementary sources of toroidal moments, opening the door to the engineering of nanophotonic devices. The main contribution of this study is comparing different light sources for enhancing the toroidal dipole response in a given system. We theoretically study the toroidal dipole excitation in an individual dielectric nanodisk by structured light illumination, including the tightly focused radially polarized beam and the focused doughnut pulse. The toroidal dipole and anapole can be excited by the interplay of the radial and longitudinal components of the incident light. As opposed to the plane wave illumination, the tightly focused radially polarized light can excite a near-ideal toroidal dipole while the contributions of the Cartesian electric dipole and other modes are significantly suppressed. We also show that the focused doughnut pulse is a promising tool for exciting a resonant toroidal response in nanophotonic systems. Furthermore, it is demonstrated that toroidal-driven field confinement leads to an enhancement of energy concentration inside the nanodisk that can potentially increase light harvesting and boost both linear and nonlinear light-matter interactions.

Figure 1

(a) Poloidal currents and (b) their corresponding magnetic field distribution that is associated with the excitation of the toroidal moment.

Figure 2

(a) Configuration of the toroidal dipole excitation where an electromagnetic plane wave illuminates a dielectric nanodisk. (b) Contributions of multipoles up to quadrupole order in the spherical representation. (c) Cartesian electric and toroidal dipoles. The red arrow indicates the toroidal dipole excitation when $P_{\mathrm{car}}=0$ and $P_{\mathrm{sph}}\ne 0$. (d) Electric energy within the nanodisk as a function of radius. The toroidal dipole led to a concentration of electric energy inside the nanodisk of 300 nm.

Figure 3

(a) Configuration of toroidal mode excitation by the tightly focused radially polarized beam. The radial and longitudinal components of the electric field (red arrows) are built by a focusing lens. (b,c) Multipoles in the spherical and the Cartesian representations. Three points corresponding to the electric dipole excitation, the toroidal dipole excitation, and the anapole state are marked by red, green, and blue circles, respectively. (d–f) Far-field radiation patterns of three marked spots. (g) Electric field energy within the nanodisk as a function of radius. The maximum energy concentration within the nanodisk happens at toroidal excitation. (h–j) Near-field distribution at three different excitations of the electric dipole, the toroidal dipole, and the anapole.

Figure 4

(a) Configuration of toroidal mode excitation by a focused doughnut pulse. A transverse magnetic (TM) focused doughnut pulse illuminates a nanodisk at its focus point. Blue and gray arrows represent the $E$ and $H$ fields, respectively. (b) Multipolar decomposition in the spherical representation. A dip around 310 nm in the total scattering spectrum is observed that is attributed to an anapole state. (c) Multipolar decomposition in the Cartesian representation. Weak resonance around 360 nm corresponds to toroidal dipole excitation. Black line points to the nonideal anapole. (d) Electric energy within the nanodisk as a function of its radius.