Study On Propagation Properties Of Light Beams In Anisotropic Metamaterials

Metamaterial is a new type of aritificial electromagnetic material or sturcture,and has electromagnetic properties that are not found in nature and can be artificially tuned at will. Thus, metamaterials lead to many extensive applications in electronics and communications. In this thesis, we pay our attention on the properties in the propagation of wave in anisotropic metamaterials and the focusing characteristics of vectorial fields by a slab of anisotropic metamaterials, the obtained results are listed below:Firstly, we investigate the reflection and refraction of an electromagnetic wave between vacuum and semi-infinite anisotropic metamaterials. It is found that determined by anisotropic parameters and polarization state, the refraction behaviors of both phase and energy flow are significantly different. In the meatmaterials with a single-sheeted hyperboloid dispersion relation, waves can exhibit different refraction characteristics in different propagation planes.Secondly, consider the situation that the principal axis of metamaterial parallels the propagating direction of beams, we study the focusing properties of an anisotropic metamaterial slab lens by means of angular spectrum representation. The analytical expressions of vectorial fields in all the regions are obtained. Quantitative relationship between focusing characteristics and anisotropic parameters of anisotropic metamaterial slab lens is employed. It is demonstrated that the polarization state of focusing beam is changed due to the effects of anisotropy. As an application of vectorial theory, we analyze the focusing property of beams by an anisotropic metamaterial slab for which the permeability along longitudinal axis is -1. This slab lens can redirect beam, which is initially polarized along a transverse axis, to a partial focus. We also show that a clear polarization rotation occurs.Thirdly, assume that the principal axis of metamaterial is perpendicular to the propagating direction of beams, we analyze the transmission properties of a paraxial beam through a slab of metamaterial with different dispersion relations, respectively. We find that a paraxial beam undergoes focusing in both x and y axes for the slab with a ellipsoid dispersion relation, and undergoes focusing or dispersion in different axes for the slab exhibiting a dispersion surface of single-sheeted hyperboloid; while the beam cannot transmit in the slab with a double-sheeted hyperboloid dispersion relation. The inherent physics underlying this phenomena is that the effective refractive indices of the metamaterials with different kinds of dispersion relations have different sign combinations. Moreover, the paraxial scheme is generalized to describe the propagation of slightly nonparaxial beams in the metamaterial slabs and the nonparaxial correction to the paraxial solution is derived. It is demonstrated that the contribution of nonparaxial correction to the longitudinal component is greater than the corresponding contribution to the transverse component. Importantly, we find that, due to the coupling effect of vectorial field components in the metamaterial, the beam suffers a slight change of polarization state.