Research On The Design Methods And Applications Of Metamaterial Devices Based On Coordinate Transformation

Based on the form invariance of the equation, coordinate transformation theory achieves the arbitrary control of field distribution by changing the equivalent physical parameter distribution of materials in the physical space, and provides a powerful and convenient way for the flexible design of metamaterial devices. Following this theory, all kinds of metamaterial electromagnetic devices with broad application prospects and novel functions have sprung up like mushrooms. Furthermore, application scope of the theory has been gradually extended from electromagnetics to other engineering fields, such as acoustics, plasmonics, elastodynamics, thermodynamics and electronics. However, as an emerging field, there are still many issues in coordinate transformation based metamaterial devices that need to be resolved. In this paper, research on the methods of parameter simplification, parameter inversion and equivalent circuit realization of typical metamaterial electromagnetic devices and the design methods of novel metamaterial devices are systematically and comprehensively carried out according to coordinate transformation theory. The performances of the devices are analyzed in depth using COMSOL and ADS software. This study enriches the coordinate transformation theory and technologies, and has great reference value and guidance meaning to the similar devices. To sum up, the main work includes the following five aspects:1. Two design methods of parameter simplification for electromagnetic shrinking device are proposed. First, electromagnetic shrinking device with material parameters of constant radial and azimuthal components and radius varying axial component is designed through choosing the specific transformation function. The effects of excitation source, material loss and parameter perturbation on the performance of the device are also investigated. Second, two-dimensional and three-dimensional electromagnetic shrinking devices with homogeneous anisotropic material parameters are designed based on the linear transformation along orthogonal directions. In addition, two-dimensional case is taken as an example to discuss its isotropic layered realization method based on effective medium theory, and the illusion effect of layered shrinking device under different incident angle are analyzed.2. The inverse method of material parameters for the electromagnetic transparent device, electromagnetic shrinking device and electromagnetic concentrator is presented without any knowledge of the corresponding transformation function beforehand. Boundary conditions satisfied by the coordinate transformation process of the device and an introduced generating function replace the transformation function. Material parameters are directly represented in the form of the generating function, and its derivation process is independent of the transformation function. Moreover, to eliminate the inhomogeneity and anisotropy of material parameters, the effective medium theory-based layered realization method of the device is further examined.3. Equivalence between the material parameters of metamaterial electromagnetic device and the lumped element parameters of transmission line equivalent circuit is established using field-circuit idea. Equivalent circuit realization methods of the left-handed material-based open resonator, the near zero material-based multibeam antenna, and the inhomogeneous anisotropic material-based electromagnetic transparent device and electromagnetic concentrator are presented. The effectiveness of the method and electromagnetic characteristics of the device are validated and analyzed based on ADS software.4. Design methods for two novel metamaterial electromagnetic devices are put forward. First, in order to achieve a unidirectional and bidirectional control on the field distribution, an arbitrary control device of field distribution without any energy loss in the process of controlling is designed. Potential applications of this device in the waveguide connector, high-gain directional antenna, signal restorer and perspective device are explored. Second, a metamaterial electromagnetic device is capable of achieving three functions is proposed. The presented device can act as a transparent device, a closed invisible cloak having the capability of information exchange, and an external cloak allowing the hidden object to move freely. 5. Application of coordinate transformation theory in the acoustics and thermodynamics is expanded. Design methods of acoustic external cloak with simplified parameters and thermal concentrator with arbitrary shapes are proposed. The corresponding material parameter expressions are derived, and numerical simulations using COMSOL software are performed to verify the invisible property of the cloak and the thermal-focusing effect of the concentrator.