Toroidal Dipolar Metamaterials And Their Characteristics

In Classical Electrodynamics, an electric (or charge) dipole results from a separation of positive and negative charges, whereas a magnetic dipole is produced by the closed circulation of an electric current. Mathematically, they appear in the series expansion (known as the multipole expansion) of an electromagnetic potential generated by a distribution of charges and currents. The toroidal dipole, an elusive counterpart of the charge and magnetic dipoles, is another special phenomenon of electromagnetic excitation. Whereas the importance of toroidal moments in particle physics was established some time ago, there is no known observation of toroidal response in the classical electromagnetism. This is because the effects associated with toroidal response in materials that exist in nature are weak. Toroidal moments are intensively discussed in the literature with only a few experiments claiming to having detected them. It has been suggested that the complete multipole expansion requires the inclusion of toroidal moments along with the electric and magnetic ones. In fact, toroidal moments have already been acknowledged in nuclear and particle physics. First-principles calculations have revealed the existence of toroidal dipoles for certain molecular structures and ferroelectric systems. As the most fundermental member of the toroidal moments, toroidal dipole has very special electromagnetic properties. In recent years, because of the randomicity of electromagnetic Metamaterials (MMs), it enables enhancement the toroidal dipole resonance, so as to make its measurement possible. Therefore, by reasonable MMs, the achievement of toroidal dipolar response has become possible. Studies the related characteristics and application are also very important.Results in this thesis can be summarized as follows on the base of MMs with toroidal dipolar response.1. The theory about toroidal dipolar response. We derived the scattering energy calculation method of multipole moments, including electric multipole moments, magnetic multipole moments, and toroidal multipole moments. This method makes a link between MMs’ resonance and multipole’s scattering energy. We also derived the relationship between MMs’internal microscopic multipole excitation and transmission characteristics. Then we showed the fundamental principles of dipole-dipole interactions in MMs. We believed that an understanding of the fundamental coupling mechanisms would provide significant insight into the design and optimization of metamaterial structures with desirable properties as well as resonant behavior.2. The achievement and properties of electric toroidal dipolar MMs. We put forward the most classic model to achieve electric toroidal dipolar response, i.e. the splitted current ring located in the equatorial plane. It is concluded that the electric toroidal dipolar resonance strength is associated with the number N of the slits. For the first time we present an electric toroidal dipole model based on metamaterials experimently, which is composed of split-ring resonators. It shows that an electric toroidal dipolar response located at the frequency of 11.2 GHz. Calculated scattered powers of various multipole moments derived from the current density proved that it is an elusive electric toroidal dipole response. Another electric toroidal dipolar metamaterial has been achieved based on spoke-like aperture element at 14.16GHz. This proposed metamaterial exhibits resonant transparency of 93.2% under linearly polarized incidence caused by destructive interference between magnetic dipole and electric toroidal dipole. Notably, it also provides circular cross-polarization conversions between left-handed circularly polarized wave and right-handed circularly polarized wave at the same frequency. These properties associated with elusive electric toroidal dipolar moment offer an avenue for various potential applications in microwave devices.3. The achievement and properties of magnetic toroidal dipolar MMs. We put forward the most classic model to achieve magnetic toroidal dipole response, i.e. the toroidal solenoids. And then we deduced the expression of magnetic dipole, magnetic quadrupole and magnetic toroidal dipole moment. We also provided two ways to compensate the z-component of the magnetic dipole moment and enhance magnetic toroidal dipole response. Then, we designed a simplified form of toroidal metamaterials, and study the mechanism and optical activities of magnetic toroidal dipolar MMs. Another magnetic toroidal dipolar response has been achieved by metamaterial at 6.14GHz. This proposed metamaterial exhibits resonant transparency of 98.8% by destructive interference between electric dipole and magnetic toroidal dipole. After that, we proposed and theoretically studied all-dielectric MMs that represent a simple electromagnetic system supporting toroidal dipolar excitations at 411.5THz.4. Planar toroidal dipolar MMs. In view of the complicated structure, large thickness, complex interference in MMs with lateral incidence, we designed two planar toroidal dipolar MMs. Model 1 is an electric-induced magnetic toroidal dipole MMs. It has a thickness of 0.813mm(0.024λ0). We studied the influence of split resonant ring on the magnetic toroidal dipolar response. Mode 2 can not only achieve an electric toroidal dipolar response, but also a magnetic toroidal dipolar response. It has a thickness of 2mm(0.019λr,0.078λG). In view of the design feasibility of planar metamaterial, these resonance-enhanced toroidal dipolar responses could provide an avenue for various interesting phenomena associated with the elusive toroidal moments.This thesis employs a variety of methods, such as transmission characteristics, scattered powers of multipole moments, surface current distribution and the electromagnetic field distribution, to prove the existence of electric/magnetic toroidal dipolar responses in proposed MMs. We also explored toroidal MMs’ other important characteristics, i.e. circular polarization manipulation characteristics, circular dichroism and resonant transparency and so forth. In a word, these models proposed in this thesis can be used for the research on elusive toroidal response and their applications.