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Goos-Hänchen shift in anisotropic left-handed materials

In this paper, the Goos-Hänchen shift on the interface between one regular isotropic medium and another anistotropic LHM is analyzed extensively. The analytical expression of Goos-Hänchen shift on the uniaxially anisotropic LHM is derived for the configuration where the optical axis of the LHM is perpendicular and parallel to the interface of two media, respectively. Meanwhile, the expression of Goos-Hänchen shift on the surface of biaxially anisotropic LHM is also presented. The result shows that the Goos-Hänchen shift on the surface of the anisotropic LHM is significantly different from that of isotropic LHM. And under certain conditions, anomalous Goos-Hänchen shift shall occur, i.e., the Goos-Hänchen shift is negative on the surface of the anisotropic LHM. The constraints for the existence of anomalous Goos-Hänchen shift in anisotropic LHMs are identified, respectively.