Toroidal topology appears in many types of metamaterials, which makes it impossible to describe the electrodynamic properties of such objects correctly without toroidal dipole. Dynamic toroidal dipole is excited by a closed loop of magnetic dipoles, which are caused by electric currents flowing along the meridians of the torus (poloidal currents). One of the most promising cases of toroidal excitation is toroidal excitation in planar metamaterials, which we discuss in this work. We show the peculiar properties of such metamaterials, like extremely high Q-factor and strong electric and magnetic field localization and tunable toroidal metamaterials. Especially we discuss the role of losses in toroidal metamaterials: radiating and non-radiating nature and show that the playing with them can be crucial for effects of high Q-factor applications. We demonstrate experimental characteristics that are in good agreement with modeling results. To prove the toroidal nature of our metamaterial we show the results of multipole expansion that considers toroidal dipole response.
The static toroidal dipole was predicted by Zeldovich, which appears due to the static currents in atomic nuclei and explain disturbance of parity in the weak interaction. Physically, toroidal dipole is separated element of multipole expansion that corresponds to electrical currents circulating on a surface of gedanken torus along its meridians. Recently, the demonstration of dynamic toroidal dipolar response became possible in metamaterials composed of metamolecules of toroidal topology. Metamaterials with toroidal dipolar response allow to demonstrate a number of special properties such as novel type of EIT, optical activity, extremely strongly localized fields and anapole. We are interested in another property of toroidal metamaterials – magnetic Fano-type response caused by toroidal and magnetic moments in a particular metamolecule. In this paper we demonstrate theoretically and experimentally in microwave at the first time Fano-excitation in toroidal metamaterials. We suggested metamaterials based on a special structure of two types of planar metamolecules separated by dielectric layer.
One of them “Electric” type metamolecule is a planar conductive structure consisting of two symmetric split loops. The incident plane wave excites circular currents along the loops leading to a circulating magnetic moment and, as a result, to a toroidal moment. Moreover, due to the central gap electric moment can be excited in metamolecule. At the same time, destructive/constructive interference between toroidal and electric dipolar moments gives us unique effect as very strong E- field localization inside the central gap and anapole mode.
“Magnetic” type metamolecule is the inverted and rotated variant of the first structure. In contrast to the first case, here we expect very strong localization of magnetic field instead electric field. The magnetic field lines are whirling around the central junction of the metamolecule due to interference between toroidal and magnetic quadrupole moment. Importantly, this configuration allows us to reduce electric moment. Hence, we observe very strong magnetic field localization. Combined together, they support coupled Fano- response with separated strongly concentrated electric and magnetic fields. We discuss this effect and show diamagnetic response due to toroidal Fano-excitation. These metamaterials are promising for magnetic photonics and as Huygens elements.
We present metamaterials based on dielectric slab with perforated identical cylindrical clusters with perforated holes, which allow to support the toroidal dipolar response due to Mie-resonances in each hole. Note that proposed metamaterial is technologically simple for fabrication in optical frequency range.
Metamaterial can be fabricated by several methods. For instance, we may apply the molecular beam epitaxy method for deposition of Si or GaAs layers, which have permittivity close to 16. Next step, nanometer/micrometer holes are perforated by focused ion beam method or laser cutting method. Fundamental difference of proposed metamaterial is technological fabrication process. Classically all- dielectric optical metamaterials consist of nano-spheres or nano-discs, which are complicated for fabrication, while our idea and suggested metamaterials are promising prototype of various optical/THz all-dielectic devices as sensor, nano-antennas elements for nanophotonics.
The main research efforts in the metamaterials science are focused on achieving negative permittivity and permeability, as well as on effects such as superresolution, subwavelength guiding, enhancement of field localization, nanoantennas etc. At the same time, there is a wide range of interesting problems, beyond the issues of negative refraction. One of them is the problem associated with the excitation of toroidal response in metamaterials and the unusual phenomena associated with such response.
In this paper, we demonstrate that, owing to the unique topology of the toroidal dipolar mode, its electric/magnetic field can be spatially confined within sub-wavelength, externally accessible regions of the metamolecules, which makes the toroidal metamaterials a viable platform for sensing, enhancement of light absorption and optical nonlinearities, and, especially, ingredient for qubits and quantum metamaterials.
The metamolecules employed in the present study are planar conductive structures consisting of two symmetric split loops. The excited circular currents along the loops lead to a circulating magnetic moment and, as a result, to a toroidal moment. We note that the electric field is strongly localized in the splits of the loops and allows achieving the extremely high Q-factor of such types of resonators.