Resonant Electric-Magnetic Toroidal Duality in Height-Modulated Hexagonal Metasurfaces

TL;DR

This paper demonstrates electric-magnetic toroidal duality in a hexagonal metasurface, revealing high-Q resonances and polarization control through finite element simulations, with implications for advanced optical device design.

Contribution

It establishes electric-magnetic toroidal duality in a metasurface, analyzing modes and resonances with a novel design framework for high-Q optical applications.

Findings

Identification of electric and magnetic toroidal modes with complementary topologies

Discovery of high-Q quasi-BICs at mode intersections

Polarization responses can be selectively reversed between mode families

Abstract

Toroidal modes enable high-Q resonances, but electric toroidal excitations remain unexplored compared to magnetic ones. This work establishes electric-magnetic toroidal duality in a hexagonal metasurface. Using finite element simulations, we analyze electric and magnetic toroidal modes in a hexagonal silicon nanorod supercell under mirror-symmetry breaking via height modulation. Eigenfrequencies, Q-factors, power flow, and polarization responses are computed. We identify electric TO and ATO modes with complementary near-field topologies to magnetic analogues. Direct frequency intersections (magnetic and electric TO/ATO) yield high-Q quasi-BICs. Polarization selectivity reverses between families: 0{\deg} excites magnetic TO/electric ATO; 90{\deg} excites magnetic ATO/electric TO. A loss hierarchy (magnetic TO > magnetic ATO > electric ATO > electric TO) and protective layers compatibility are demonstrated. Electric and magnetic toroidal responses are dual manifestations of the same symmetry, providing a unified design framework for high Q metasurfaces in sensing, nonlinear optics, and loss-tolerant devices.