Simulation of Simultaneously Negative Medium Metamaterials
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Metamaterials are artificial materials and named by those who work in the microwave material area. According to existing documentation, the metamaterials have relative permittivity and/or relative permeability of values less than 1, including negative values. If the material has negative permittivity and permeability at the same time, the material is also referred to as simultaneously negative medium (DNG medium). Such medium has several features that any natural medium is not equipped with: negative refraction, backward phase, and evanescent wave amplification . Though the medium does not exist in nature, it seems that it can be artificially made through synthesizing metallic insertions inside the natural dielectrics . Due to its unique feature of negative refraction and this feature is not equipped with any reported natural medium, the concept of making perfect lenses with metamaterials has attracted attentions in recent years. However a number of questions need to be answered: How can we quantize the refractive index of the metamaterial given that the permittivity and permeability are known or vice versa; can the metamaterial be made isotropic medium under effects of different incident angles? The answer to the first question will help us to define the dimension of the lenses more efficiently; and the answer to the latter question will help determine if such medium is capable of being used to make lenses. Previous publications from others demonstrated the negative refraction phenomenon of metamaterials though this phenomenon is restricted to a very narrow band  . The derivation of the negative refractive index through full-wave simulation and comparison with its value through calculating the simulated negative permittivity and permeability obtained from the simulated scattering matrix have not been reported. The work carried in this thesis fully explored the ways to address this and answer those questions mentioned in previous paragraph. To fully understand the negative refraction effect of metamaterial, the author built a mathematical geometric model to calculate refractive index for rectangular metamaterial slab. With this approach, the refractive index can be obtained provided that incident and peak-receive angle are known. In order to achieve a metamaterial with isotropy property, the author also presented three different types of metamaterial slabs: parallel-arranged, vertical-arranged and cross-arranged slab of capacitive-loaded-loops (CLL) in front of standing probes or posts, which are also called CLL-P slabs. The three arrangements are differentiated by the way unit cell is oriented. With the geometric model, the author obtained refractive indexes for three metamaterial slabs at different incident angles through numerical simulation. The refractive indexes have negative values at all circumstance, which shows the negative refraction phenomena unique to the metamaterial. Unlike the other two CLL-P slabs, the cross-arranged CLL-P slab has near constant refractive index and constant received amplitude regardless of incident angles. This result can be attributed to the symmetrical topology of unit cell in x-y plane. To better explain refractive effects occurred for those three CLL-P slabs, the author also employed a way to calculate the effective permittivity and permeability using scattering matrix. Based on effective permittivity and permeability obtained, the analytical values of refractive indexes have been calculated at resonance point. To check the refractive indexes calculated from two different methods: using Snellâ s Law based geometric approach and using permittivity/permeability obtained from scattering matrix, two results are compared against each other and agree well. Knowing effective permittivity and permeability is very useful for calculating other parameters of the CLL-P slab such as wave impedance and mismatch loss etc. With all the simulation for parallel-arranged, vertical-arranged, and cross-arranged CLL-P slabs, from simulation results, it is found that the cross-arranged slab has the property of isotropy at different incident angles since the coupling between incident magnetic field and CLL loop will maintain constant. As a validation process, the CLL-P simulation result in parallel waveguide is compared with prior simulation (HFSS) and measurements of refractive focusing of the same structure, and both simulation results agree with measurements. The full-wave simulation tools FEKO that employs the Method of Moments (MoM) is used in the two ways of estimating the negative refractive index of the medium.
- Masters Theses