| In recent years, the left-handed metamaterial (LHM) has attracted more and more attentions in the fields of solid physics, material science, optics and electromagnetism. However, the detail research on the LHM is just at its beginning stage, and it is still incomplete in many research aspects such as the electromagnetics (EM) analysis of the LHM, the design of the high performance LHM and the applications of the LHM to microwave, radio-frequency and optical devices for the improvement of the performance. In this paper, we make a comprehensive research on the LHM in order to develop the different research directions in a complementary way.Firstly, the essential principle for the left-handed properties of the LHM is deeply investigated. The analytical models for the constitutive parameters of the LHM consisting of SRR and wires are derived based on the constitutive relations and equivalent transmission line theory. The accuracy of these analytical models is verified through different methods. Compared with previously published results, the theoretical derivation process of our analytical models is simpler and clearer, and the corresponding physical concept is easier to understand.Secondly, a particle-type LHM with miniaturized unit cell and broad bandwidth is designed. Its unit cell length is only 0.11 wavelength at the lowest working frequency, and the frequency range, where the LHM is available, is from 9.2 GHz to 11.8 GHz. Compared with other reported LHMs, the unit cell length has been reduced by 41%. The left-handed properties of the designed LHM are demonstrated through detailed discussions of double-negative, backward wave and negative refraction characteristics. Results show that the negative refraction and backward wave phenomena for the LHM are clearly observed in 9.2 ~ 11.8 GHz where the effective permittivity and permeability are simultaneously negative. Moreover, a miniaturized LHM patch antenna dependent on backward wave characteristics of the LHM is proposed, and the length of the patch antenna has been reduced to 0.17 from original conventional 0.5 working wavelength by embedding real particle-type LHM units instead of a theoretical model. Results show that both near field distribution and radiation pattern of the miniaturized patch antenna are in good agreement with the theoretical analysis.Thirdly, a novel resonance structure dependent on above designed LHM is presented and used to design and fabricate an improved miniaturized cavity resonator (IMCR), whose length and width are less than half of a conventional cavity resonator. Compared with the reported miniaturized LHM cavity resonator based on Engheta's miniaturized resonance structure, both the length and the width reduction for the IMCR have been obtained simultaneously, instead of the miniaturization realized only in the length. The numerical simulations and experimental measurements are used to confirm the performance of the IMCR, and results show that both the simulation results and measurement results are in good agreements. Moreover, two types of cavity filters based on the MCR are designed, fabricated and tested, and the performance is verified by the simulation results and measurement results, which coincide very well with each other.Finally, a miniaturized rectangular horn antenna with the high gain is designed based on an improved zero refraction metamaterial (ZRM). The results show that the gain is enhanced with over 2 dB in the bandwidth of 1.1 GHz compared with a conventional horn antenna, and the longitudinal length shortens to only 56% of that of the optimized horn antenna for the same antenna performance.The analysis, design and application for the LHM are developed in this research. It is summarized as that a LHM with good performance is designed and applied to improve some microwave devices after EM characteristics of the LHM is analyzed. These important research results will be useful for the applications of the LHM to microwave and millimeter wave circuits and devices.
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