| Left-handed materials (LHM) have attracted much attention during the last few years because they possess peculiar electromagnetic properties. This dissertation presents the theoretical study on Goos-H?nchen shift on the surface of anisotropic LHM and the dispersion properties in multilayered film structures containing negative index metamaterials extensively.Firstly, the Goos-H?nchen shift on the surface of uniaxially anisotropic LHM is discussed for the configuration where the optical axis of the LHM is perpendicular and parallel to the interface of two media, respectively. The result shows that the Goos-H?nchen shift on the surface of the anisotropic LHM is significantly different from that of isotropic LHM. And under certain conditions, anomalous Goos-H?nchen shift shall occur, i.e., the Goos-H?nchen shift is negative on the surface of the anisotropic LHM. Meanwhile, the expression of Goos-H?nchen shift on the surface of biaxial anisotropic LHM is also presented.Secondly, with Fresnel approximation, the expression of the 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 the incident angle. Moreover, the brief approximative expression of the lateral shift with incident angle equal to the critical angle is also presented. Thus, the general expression of Goos-H?nchen shift for any incident angles is obtained.Finally, the dispersion properties in multilayered metamaterials are investigated theoretically. The electromagnetic translation matrix in periodic media composed of alternating layers of positive and negative index material is derived, and the dispersion relation between the Bloch wave vector and incident wave vector is obtained, which is different from that in the stacks composed of alternating layers of two different positive materials. Using the dispersion relation, the spatial dispersion for the reflection configuration is obtained, which...
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