[Paper Review] Controlling the toroidal excitations in metamaterials for high-Q response

Yuancheng Fan, Fuli Zhang+3 more|arXiv (Cornell University)|Sep 19, 2016

Plasmonic and Surface Plasmon Research1 references3 citations

TL;DR

This paper demonstrates that tuning the asymmetric factor of asymmetric split ring resonators (ASRRs) in a planar metamaterial significantly enhances toroidal dipole excitation and simultaneously increases the Q-factor by over an order of magnitude. By optimizing geometric asymmetry, the study achieves a Q-factor of 15,849—demonstrating a direct link between enhanced toroidal excitation and high-quality resonant response for subwavelength light-matter interactions.

ABSTRACT

The excitation of toroidal multipoles in metamaterials was investigated for high-Q response at a subwavelength scale. In this study, we explored the optimization of toroidal excitations in a planar metamaterial comprised of asymmetric split ring resonators (ASRRs). It was found that the scattering power of toroidal dipole can be remarkably strengthened by adjusting the characteristic parameter of ASRRs: asymmetric factor. Interestingly, the improvement in toroidal excitation accompanies increment on the Q-factor of the toroidal metamaterial; it is shown that both the scattering power of toroidal dipole and the Q-factor were increased more than one order by changing the asymmetric factor of ASRRs. The optimization in excitation of toroidal multipole provide opportunity to further increase the Q-factor of metamaterial and boost light-matter interactions at the subwavelength scale for potential applications in low-power nonlinear processing, and sensitive photonic applications.

Motivation & Objective

• To investigate the control of toroidal multipoles in planar metamaterials for enhanced electromagnetic response.
• To explore how geometric asymmetry in split ring resonators affects toroidal dipole excitation and Q-factor.
• To establish a correlation between enhanced toroidal excitation and increased Q-factor in subwavelength metamaterials.
• To enable high-Q responses for applications in low-power nonlinear optics and sensitive photonic devices.

Proposed method

• The study employs a planar metamaterial composed of asymmetric split ring resonators (ASRRs) with tunable asymmetric factors.
• The asymmetric factor δ is varied from -0.4 mm to +0.4 mm to control the structural asymmetry and its impact on excitation.
• Finite-element simulations are used to calculate scattering cross-sections and extract toroidal dipole moments.
• The Q-factor is computed using a Fano resonance model, with central frequency and full width at half maximum derived from dip and peak frequencies (fd and fp).
• A modified Q-factor formula Q = (fd + fp)/(fd - fp) is applied to Fano-shaped resonances, validated against Fano fitting.
• Numerical validation is performed on realistic materials (metal and commercial microwave substrate) to confirm robustness.

Experimental results

Research questions

• RQ1 How does the asymmetric factor of ASRRs influence the excitation strength of toroidal dipole moments?
• RQ2 Can enhanced toroidal excitation lead to a significant increase in the Q-factor of metamaterials?
• RQ3 What is the relationship between geometric asymmetry and the binding strength of trapped modes in ASRRs?
• RQ4 Does the Q-factor enhancement via toroidal excitation hold in realistic material systems?

Key findings

• The scattering power of the toroidal dipole increases significantly with decreasing asymmetric factor, peaking when the gap is near the center of the meta-molecule.
• The Q-factor increases from 432 (at δ = -0.4 mm) to 15,849 (at δ = 0.1 mm), representing a more than 36-fold improvement.
• The Q-factor calculated via the Fano resonance formula (Q = (fd + fp)/(fd - fp)) matches closely with values obtained from Fano fitting, validating the method.
• The enhancement in toroidal excitation and Q-factor is confirmed in simulations using realistic metal and commercial microwave substrates.
• The variation trends of Q-factor and toroidal dipole scattering power are identical, confirming a direct correlation between enhanced excitation and high-Q response.
• The study demonstrates that geometric optimization of ASRRs enables high-Q toroidal modes suitable for subwavelength light-matter interaction.