Theory Of Homogenization And Electromagnetic Properties Of Metamaterials

Metamaterials carry the concept of artificial medium into one step further: the constituent material is structured into sub-units, and on a length scale of incident wave length much greater than of the sub-units (usually it means lattice constant), properties of homogenous medium are determined by an effective permeability and permittivity valid on a length scale greater than the size of the constituent unites. The flexibility in design enables metamaterials to have special properties which are not encountered both in nature and constituent medium. Studies on metamaterials focus on specific electromagnetic properties, homogenization and designs of metamaterials. In this thesis, we investigated the special properties in negative refractive index medium. Then we further investigated the homogenization theory and homogenized the given metamaterials. Finally, we concerned on description and characterization the binary nanospheres system which is candidate for negative refractive index medium.In this thesis, we studied on electromagnetic properties in the special metamaterials. Fist, the electromagnetic properties on the interface between a left-handed material and a conventional nonlinear material are investigated theoretically and numerically. For self-defocusing nonlinear systems, we studied the effect of incident angle, incident intensity and mode of electromagnetic field and permeability ratio of materials to the properties of field on the interface with the analytic reflection and transmission coefficients. Secondly, with the macroscopic Maxwell equations, a generalized method is presented for analyzing TE modes of nonlinear planar waveguides with linear film bounded both sides by nonlinear materials. General dispersion relations, modal field functions and power functions are derived. Then, we studied on the dispersion relations in the uniaxial and biaxial mediums. In some frequencies, phase velocities in uniaxial and biaxial mediums with negative or zero permittivities became very slow for some angles between the wave vector and the principal optical axis of the crystal. Last, we reported the coexistence of TE and TM surface modes in the same certain frequency domain at the interface between one isotropic regular medium and another biaxially anisotropic left-handed medium. The constraints for the existence of TE and TM polarized surface waves in biaxially anisotropic left-handed materials are identified, respectively. The Poynting vector and the density of energy associated with surface modes are calculated. Depending on the system parameters, either TE or TM surface modes have the time averaged Poynting vector directed opposite or same to the mode phase velocity. It is seen that the characteristics of surface waves in biaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.Goos-H?nchen shifts of reflected and transmitted beams from the interface between air and weakly absorbing positive/negative refractive index medium were theoretically studied by stationary phase approach. We showed the effect of permittivity and permeability of the medium on the Goos-H?nchen shifts. Then, the Goos-H?nchen shift on the interface of uniaxially anisotropic left-handed materials is investigated detailedly, and the analytical expression of Goos-H?nchen shift is presented for the case of the optical axis is perpendicular and parallel to the interface, respectively. Moreover, the constraints for the existence and the sign of Goos-H?nchen shift in uniaxially anisotropic left-handed materials are identified. With Fresnel approximation, the expression of Goos-H?nchen shift around the critical angle is obtained, and the result shows that the shift around the critical angle is a function of the beam waist and incident angles.Considering the frequency dispersion and spatial dispersion, we established the micro-dipole homogenization theoretical model with the dipole approximation and the average field method. We calculated material parameters of special structures of metamaterial by homogenization model and compared the results to that of retrieved by S parameter retrieval method. In the region of resonance, they are matched. From the Maxwell equations in the form of Landau, Lifshitz form, we descried the relationship between the Landau, Lifshitz form and the general form of the constitutive equation and made the foundation for the homogenization in the form of Landau, Lifshitz form constitutive equation.We presented a new set of binary nanospheres artificial structures which can exhibit a negative refractive index band in the terahertz region. The structures are composites of two different kinds of spheres, one made from inherently non-magnetic polaritonic and the other from a Drude-like material, dispersed in liquid crystal host. Using extended Maxwell-Garnett theory, we calculated the effective parameters of the structure for different permittivity of the host.