Toroidal Dipolar Response Of Metasurfaces

Toroidal multipole is a special electromagnetic excitation,which exhibits different response properties from conventional electric and magnetic multipoles.As the fundamental mode of toroidal moment,toroidal dipole is more complex than electric dipole and magnetic dipole.In natural materials,toroidal dipole resonance is often relatively weaker as compared with other multipole resonances and thus it has not revived much attention.In recent years,the emergence of electromagnetic metamaterials has opened a new pathway for studying toroidal dipole resonance.Among metamaterials,split-ring resonators(SSRs)are the typical structure for realizing toroidal dipole response.To further explore the excitation and resonant properties of toroidal dipole,we designed and fabricated metasurface made of SSRs in the mid-infrared region.Our theoretical and experimental results indicate that near-field coupling of SSRs lead to multiple toroidal dipole resonances,whose excitations strongly depend on polarization of incident light.Our main research results are as follows:(1)On the basis of resonance properties of classical SRR,a metasurface made of double SSRs was designed and its resonant properties were simulated.The designed metasurface consisted of metallic SRRs on top of a ZnSe substrate.A FDTD simulation model was constructed to simulate transmission spectra of the metasurface under different polarizations.The calculated results show that there are three resonant modes,excited at5.2μm,7.9μm and 13.7μm.The response intensities at these resonance frequencies change with the polarization state of the incident light.Our simulated,surface currents and magnetic fields suggest these three resonances are toroidal dipole modes.In addition,our multipole expansion analysis also reveal that radiations at these three resonant frequencies are dominated by the toroidal dipole moment,which further verifies their nature of toroidal dipole response.(2)The metasurface with double SSRs structure was fabricated and its resonant properties were characterized.We fabricated the metsurface sample by using electronbeam lithography.SEM images show that structural geometries of sample are close to theoretical design.There are only minor discrepancies due to imperfection in fabrication.The metasurface sample was characterized with a FTIR spectrometer at different polarization conditions.The measured transmission spectral reveal three resonance peaks at 5μm,7.6μm and 12μm.The evolutions of these resonances with polarization are similar to those simulated results with only small deviations,which likely originate from the difference of optical and structural parameters between the simulation model and the experimental sample,and possible surface light scattering.Our research results indicate that coupling of SRRs could result in excitation of multiple toroidal dipole modes within a metasurface structure.The response of each toroidal dipole mode strongly depends on incident polarization.These findings are helpful for further understanding the fundamental properties of toroidal dipole resonance in metamaterials.