The Goos-Hänchen shift on the surface of uniaxially anisotropic left-handed materials

In this paper, the Goos-Hänchen shift on the interface of uniaxially anisotropic left-handed materials is investigated exhaustively, and the analytical expressions of Goos-Hänchen shift is presented for the cases of the optical axis being perpendicular and parallel to the interface, respectively. Moreover, the conditions for the existence and the sign of Goos-Hänchen shift are determined. Under Fresnel approximation, the expression of Goos-Hänchen 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 angle. A simple approximate expression of the lateral shift with incident angle equals the critical angle is also presented. Thus, the general expression of Goos-Hänchen shift for any incident angles is obtained.