Configuration Design Optimization And Transmission Performance Analysis For Patch-typed Left-handed Metamaterials

The left-handed metamaterial origin, classifications, novel features and their applications are reviewed in the framework of classical physics. Left-handed metamaterials have developed by leaps and bounds along with the ever-changing material preparation technology, especially for the patch-typed left-handed metamaterials based on resonance mechanism. Negative refractive index is the core character of left-handed metamaterials and decides the left-handed transmission performance, which is the basic premise of various electromagnetic device applications. Wide application requirements of left-handed metamaterials are to control left-handed transmission attenuation and broaden its bandwidth. And broadband transmission with low attenuation is particularly important and practical for electromagnetic devices of rapid development in the radio frequency band. Focusing on the left-handed transmission performance, structural size, shape and topology optimization design of patch-typed left-handed metamaterials are realized in this dissertation through theoretical analysis and numerical simulation. The main contents and conclusions of this dissertation are as follows:Transmission performance for existing configurations of patch-typed left-handed metamaterials is analyzed. Firstly, a complete analytical expression of the refractive index is theoretically derived, and three different cases in magnetic media are introduced to generate a negative refractive index. Then left-handed transmission performance indicators for representing configurations of patch-typed left-handed metamaterials are numerically analyzed respectively. It is found that stronger magnetic resonance is internal mechanism for broader bandwidth and high attenuation of split-ring resonator-like structure configurations. Dual-axis distribution graphs of transmission performance indicators from the representing configurations are plotted, and the goal of left-handed metamaterial design is pointed out: broadband transmission with low attenuation performance.Corrected theoretical models are presented for structural electromagnetic performance analysis of patch-typed left-handed metamaterials with thin circle metal rods and metal split-ring resonators. Size designs for the transmission performance are also proposed for the classic patch-typed configuration.(1) The prediction models about periodic array of thin circle metal rod and the split-ring resonators are theoretically derived. The electric plasma frequency expression and the damping factor expression of Drude model are corrected. The magnetic resonance frequency expression of Pendry model is also improved. The numerical examples show that these modified theoretical prediction models have higher accuracy.(2) The left-handed bandwidth with different structural size parameters of the square split-ring resonators configuration is numerically analyzed respectively, and their results show that the outer ring radius has an overwhelmingly greater effect than other parameters. The left-handed transmission performance with different material parameters of the square split-ring resonators configuration is also numerically analyzed respectively. It is found that to achieve the goal of low attenuation has been greatly restricted.(3) Based on the above sensitivity studies, a shape-size cooperative design is proposed to maximize relative bandwidth of regular polygon split-ring resonators through an automatic parametric modeling technology and the sensitivities from the finite difference method. Sequential quadratic programming method and induction by simple enumeration are applied to solve the optimization problem in two steps. The reasonability of the optimal results, that is, square split-ring resonator with a bigger radial distance is qualitatively discussed by the improved magnetic resonance theoretical model.New analysis methods for structural electromagnetic performance of the metamaterials are presented.(1) Mesh-dependency in simulation results of metamaterial electromagnetic performance is analyzed based on finite element analysis. It is found that the retrieval metamaterial equivalent electromagnetic parameters have a strong dependence on the calculation accuracy of scattering parameters, especially in the resonant frequency-domain where the phase error of transmission parameters may be cause a qualitative error of the electromagnetic parameters. An improved electromagnetic simulation analysis two-step method is presented and used to obtain accurate S-parameters by determining a proper solution frequency. The numerical results show that the new method can effectively improve the accuracy of the simulation analysis through a reasonable cost.(2) The scattering performance with different periodic cells structure is numerically analyzed respectively, and their results show that a key of the electromagnetic coupling impact between those cells is the uniformity of metamaterial microstructure. So a five-layer model is established to quickly and accurately predict scattering parameters of any finite periodic cells structure by decoupling bits of numerical results of sample structure, and the electromagnetic coupling impact between structural cells is taken into consideration. The numerical examples show that the five-layer model is very cost-effective.A topology optimization design method for improving the transmission performance of patch-typed microstructure configurations is presented. A topology optimization model of microstructure configuration design of patch-typed left-handed metamaterials is established, with the objective function defined by the ratio of the mean attenuation to the absolute left-handed bandwidth and the design variables defined by the presence or absence of discrete magnetic resonance patch lattices. Based on genetic algorithm, a flow chart for the optimization problem is also given. Three new patch-typed configurations are given according to the optimization results, and their excellent transmission performance indicators are analyzed by numerical simulation. Further analysis demonstrates that a U-shaped-like structure with half unit cell height is the core configuration of broadband transmission with low attenuation. Comparing their surface current density distributions, it is found that the distribution of conduction currents of magnetic resonance patch, that is, a reasonable arrangement of magnetic resonance patch lattices is the key to the broadband transmission with low attenuation. A new topology optimization design with the perimeter constraint is proposed to solve the problem in the manufacturing process for checkerboard-typed lattices from those configurations. The new optimum configuration of robot head-shaped-like structure shows that the new strategy is very effective.