Study Of Equivalent Circuit Theory And Experimentation For Left-Handed Materials

The most general representation of constitutive relations in universe is bianisotropic in form. In the EH representation,Under time harmonic excitations, the constitutive matrices and are usually complex and frequency-dependent. In general, there are altogether 72 real parameters. For isotropic media, the constitutive relation becomes:For many common materials, the real parts of the ￡ and μ are positive, but there are exceptions. For example, in plasmas the combination of ordinary displacement current density with electron-convection current density can yield a net negative real part of the permittivity for sufficiently low frequencies. When one (but not both) of the real part of ￡ and μ is negative, plane waves decay exponentially. However, when both the real part of ￡ and μ are negative, waves can still propagate in such a medium. In 1968, Veselago theoretically investigated materials with simultaneously negative permittivity and permeability, and pointed out some of their electrodynamic properties, such as the reversal of Snell's law, the Doppler effect, and Cerenkov radiation. Veselago named such material to be left-handed material (LHM). But his idea was forgotten because of the unavailability of LHMs at that time. Until recently, based on Pendry's theoretical work on the array of split-ring resonator (SRR) and rods, Smith et al. realized the first left-handed material, which brought Veselago's result into limelight. Now this field has become a hot topic of scientific research and was regarded as one of the most ten significant progresses in science community in 2003.In the area of left-handed material, experimental works are very important. However, the growth of experimental activity has been rather slow compared with the theoretical studies. The main reason could be the lack of the experimentalsamples with a good performance. So the experimental measurements are very difficult to perform. Thus left-handed materials with good performance are very important both in the experiments and in the applications.So the goal in the proposed thesis is to develop high-performance metamaterials that can be used in a wide variety of applications. Through designing and optimizing the geometry of the rings, various configurations of metamaterials with special properties are experimental realized, such as the S-shaped resonators, which has a reliable performance compared with original SRR/Rod structure, the brick-wall shaped left-handed material, which has an ultra wide frequency band, the dual-band extended S-shaped resonator, etc. Based on the experimental work, an efficient equivalent circuit model is presented to analyze the electromagnetic properties of these different metamaterial structures. The dissertation also studied some experimentations to verify the reversal electromagnetic properties of the metamaterials. The T-junction waveguide experiment to characterized left-handed properties of the metamaterials is proposed. The original works and valuable results are detailed as follows:1. The left-handed material composed of S-shaped resonator is proposed. Theoretical analysis, simulations and experimental results indicate the superiority of S-shaped metamterials. Compared with the metamaterial composed of the SRR/rod structures, the metamterials composed of S-shaped resonators has some advantages: (1) The negative permittivity frequency band is subtly lowered down to the level of the negative permeability frequency band, allowing the overlapping to occur, therefore, the structure works as a stand alone and does not require the use of an additional rod. The fabrication of the structure is much easier. (2) The inner scatterings are reduced due to the simple geometry, so the loss is reduced. (3) Because the effective capacitances between the S-shaped metallic pattern and the top & bottom parallel waveguide plates are increased, the sensitive problem that exists in the SRR/rod structure are removed, the performance is much stable.2. The brick wall shaped metamaterial with ultra wide bandwidth is proposed for the first time. Both the simulation results and the experimental data show that a bandwidth ratio of 37.5% is achieved, which is the widest bandwidth that was reported up to date.3. The multiple bands left-handed metamaterial is firstly proposed andrealized. Because the effective capacitances and inductances of the structure can be tuned to introduce many resonant frequencies, the metamatereial will exhibit negative electromagnetic parameters over multiple frequency bands. Three methods are also proposed to design multiple bands left-handed metamaterials. The first one is to introduce more magnetic resonant frequencies within the frequency range of negative permittivity by changing the values of the inductances and capacitances of the split-rings, while keeping the overall number of split-rings constant. The second method is the dual of the first method and consists in introducing multiple electric resonances within the frequency range of negative permeability. Finally, the third method is based on the property that the upper limit of the number of left-handed passbands is twice of the number of the stacked S-rings, if this limit is not already reached, additional rings can be introduced in the structure.4. Based on the experimental studies on these left-handed material composed of different metallic patterns, a general equivalent circuit model to calculate the effective permeability of these structures is proposed. The interaction between the individual SRRs is integrated into the model by introducing a mutual inductance M. By comparing with numerical simulations, it is shown that the effective permeability predicted by the equivalent circuit model with the introduction of M is more accurate than that predicted by the circuit model where M is not accounted for. The equivalent circuit model is applicable to analyze nearly all the reported SRR structures, including the structures contains multiple loops such as the S-shaped resonator, fl-shaped patterns and extended S-shaped resonators. It is also applicable to multi-dimensional resonators, such as 2-D cross embedded split-ring, Q-shaped and S-shaped resonators. The equivalent circuit model is therefore a general method to extract the effective parameters of these metamaterials. Inversely, using the equivalent circuit model as a designing tool, the geometry of the metamaterial structures can be realized and optimized to achieve certain desired properties.5. The T-junction waveguide experiment is proposed to verify the left-handed properties of SRR/Rod based metamaterial. The results show that when the T junction is empty, most of the power is received at the output port directly facing the input port, whereas when it is loaded with the sample ofmetamaterial, most of the power is received at the output port perpendicular to the input axis. This indicates that the energy is bent by the oblique edge of the sample by an angle of -45° with respect to the normal, which suggests a negative index of refraction. The beam detected in the two outputs ports of the T waveguide undergoes uniform loss. Therefore, the results are more reliable, which indicates the effectiveness of the experimentation to characterize the left-handed properties of metamaterial.