Goos–Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface

The Goos–Hänchen shift at the surface of a uniaxially anisotropic left-handed material film is investigated, for the situation of that there is an arbitrary angle between the optical axis and the interface of the material. The analytical expressions of the Goos–Hänchen shifts are derived, for both cases of that the total reflection occurs and does not occur at the first interface. The sign of the Goos–Hänchen shifts in the two situations is analysed. The results show that the Goos–Hänchen shift of the reflected wave is the same as that of the transmitted one for the case that the total reflection does not occur at the first interface; the Goos–Hänchen shift of the transmitted wave oscillates as the thickness of the film is increased, and its overall tendency is increased; the Goos–Hänchen shift of the transmitted wave realizes its absolute maximum when the transmitted wave resonances, the absolute maximum is almost several 10 times of the wavelength of the incident wave; the Goos–Hänchen shift of the transmitted wave is significantly influenced by the incident angle and the angle between the optical axis and the interface.