Enhanced Third Harmonic Generation in Single Germanium Nanodisks Excited at the Anapole Mode

TLDR

A thin germanium nanodisk displays a pronounced valley in its scattering cross section at the dark anapole mode, with electric field energy maximized inside the disk due to strong confinement. The study presents an all‑dielectric germanium nanosystem designed to achieve a strong third‑order nonlinear response and efficient third‑harmonic generation in the optical regime. The authors examine how third‑harmonic output varies with disk size and pump wavelength to elucidate the anapole mode’s role, using an all‑dielectric germanium nanodisk system. The nanodisks exhibit an effective third‑order susceptibility of 4.3 × 10⁻⁹ esu and a third‑harmonic conversion efficiency of 0.0001 % at 1650 nm, four orders of magnitude higher than unstructured germanium and outperforming dipolar resonances by an order of magnitude, demonstrating the potential for nanoscale upconversion optimization.

Abstract

We present an all-dielectric germanium nanosystem exhibiting a strong third order nonlinear response and efficient third harmonic generation in the optical regime. A thin germanium nanodisk shows a pronounced valley in its scattering cross section at the dark anapole mode, while the electric field energy inside the disk is maximized due to high confinement within the dielectric. We investigate the dependence of the third harmonic signal on disk size and pump wavelength to reveal the nature of the anapole mode. Each germanium nanodisk generates a high effective third order susceptibility of χ(3) = 4.3 × 10–9 esu, corresponding to an associated third harmonic conversion efficiency of 0.0001% at an excitation wavelength of 1650 nm, which is 4 orders of magnitude greater than the case of an unstructured germanium reference film. Furthermore, the nonlinear conversion via the anapole mode outperforms that via the radiative dipolar resonances by about 1 order of magnitude, which is consistent with our numerical simulations. These findings open new possibilities for the optimization of upconversion processes on the nanoscale through the appropriate engineering of suitable dielectric materials.