Toroidal dipole plasmon resonance modes in upright split ring resonators
Authors: Bicket Isobel , Bellido Edson , Elsharabasy Ahmed , Bakr Mohamed , Botton Gianluigi 
Published: December 2016

Nanoscale split ring resonators (SRRs) have been a popular topic of study due to their surface plasmon resonance (SPR) modes and their many interesting interactions with light. They can be used as components in metamaterials exhibiting, among other properties, a negative refractive index. The surface plasmon properties of these structures are strongly dependent on their size and spatial arrangement. Most studies so far have focussed on the horizontal SRR due to the ease of fabrication. However, there are some advantages to be gained in the design of materials using upright SRRs. We are studying a structure composed of four upright SRRs as shown in Figure 1. The coupling of these four upright SRRs produces a magnetic dipole moment and a toroidal dipole moment.

The toroidal dipole moment, when compared to electric and magnetic dipole moments, shows a higher quality factor and lower gain threshold for a nanoscale laser analogue, the spaser (surface plasmon amplification by stimulated emission of radiation) [1]. The presence of a strong toroidal dipole moment isolated from magnetic and electric dipole moments makes the structure under study a promising candidate for a spaser for use in on‐chip telecommunications.

A similar structure was first realized experimentally in the microwave regime of the electromagnetic spectrum [2]. Scaling the geometry down to nanoscale dimensions has been shown by simulation to shift the toroidal dipole energies into the near infra‐red regime [1]. In this work we demonstrate the experimental fabrication (Figure 2) and characterization of this structure using electron energy loss spectroscopy (EELS), with confirmation of the modes provided by finite element method (FEM) simulations.

We have fabricated this structure using a double patterning process in electron beam lithography, with precise alignment of the second lithography layer to the first. The structures are made from gold deposited on a 50 nm thick silicon nitride membrane. We probe the plasmon modes using EELS on a monochromated scanning transmission electron microscope, collecting spectrum images with nanometer spatial resolution and 60 meV energy resolution. We extract site‐specific spectra (Figure 3a) and energy‐resolved maps of the SPR modes (Figure 3b, c). We apply the Richardson‐Lucy algorithm to further increase the effective energy resolution and identify the magnetic and toroidal dipole modes at energies of 0.52 eV and 0.72 eV, with SPR maps as shown in Figure 3b and 3c, respectively.

We are able to correlate our EELS results with COMSOL Multiphysics FEM simulations. The simulated SPR response is given in Figure 3a, d, and e, showing close agreement in the peaks with our experimental data. Simulations confirm the low energy magnetic dipole mode (0.56 eV) and reveal two closely spaced toroidal dipole modes (0.61 eV, 0.66 eV) which are not perfectly resolved in the EELS data. We are able to tune the energy and strength of the toroidal dipole moment through tuning of the fabrication parameters; with careful design this structure is a promising spaser design for a range of applications near telecommunications frequencies.