The Theoretical Study On Left-handed Materials

Left-handed materials with simultaneously negative permittivity and permeability, have attracted a lot of interest within scientific community in recent years. Up to now, a lot of novel phenomena concerning LHM have been revealed, such as negative refraction, backward waves, and amplification of evanescent waves. Based on the EM theory, some theoretical problems concerning LHM have been studied in this thesis:1. Characteristics of surface modes at the interface between an isotropic medium and an indefinite medium that has a dispersion relation of hyperbolic form are studied. Four cases for the isotropic medium, including normal, left-handed, magnetic (with negative permeability), and metallic media, are considered. The conditions for the existence of surface modes in each case are analyzed in detail, and the results are expressed explicitly, indicating that the existence of surface modes is determined by the nature of the indefinite medium as well as the orientation of the boundary surface of this anisotropic medium. The energy flows associated with the surface modes are also discussed.2. The coupling between a negative and positive index medium waveguides is investigated theoretically in the present paper. A coupled mode theory is developed for such a waveguide system and its validity is verified. Interesting phenomenon in the coupled waveguides, which occur in the case when the negative index medium waveguide in isolation guides wave backward, are demonstrated. A new type of coupled mode solution, which varies exponentially with the coupling length, is found in the case when the propagation constants of two individual waveguides are nearly the same. A coupler operating in this case is insensitive to the coupling length, and its coupling efficiency can reach 100% as long as the coupling length is long enough. However, when the propagation constants of two individual waveguides differ apparently, the coupled mode solution is still a periodic function of the coupling length, but the coupled power is output backward. In addition, the modes in thecomposite waveguide system are also studied using the coupled mode theory, and some fundamental properties of guidance are revealed.3. A new type of open cavity is proposed. The cavity is formed by a pair of parallel waveguides and a uniaxial slab for the purpose of phase shift. The waveguides are a left-handed materials (LHM) waveguide and a conventional dielectric waveguide, which guide waves with opposite power flow directions. From the coupled mode theory, it is investigated that the power flow loop is established in the structure to make waves localized. The amplitude of the field attenuates exponentially from the center of the structure, where the energy concentrates. We employ the finite difference time-domain (FDTD) method to verify the theoretical propositionwith excellent results. The quality factor of the cavity is also calculated, which can achieve a high value if the length of the waveguide is long enough.