Negative and positive Goos–Hänchen shifts of a light beam transmitted from an indefinite medium slab

We study the lateral shift of a light beam transmitted from an indefinite medium slab. The analytic expressions for the transmission coefficient and the lateral shift are obtained by using the stationary-phase method, and different conditions for the occurrence of a negative lateral shift are deduced. It is shown that the thickness of the indefinite medium strongly affects the properties of the lateral shift. For a larger thickness, the sign of the lateral shift depends only on the signs of the permittivity and permeability, while, for a smaller thickness, the sign of the lateral shift is determined by the combined effect of the incident angle of the light, the signs of the permittivity and permeability, and the thickness of the indefinite medium slab. In addition, the lateral shift at the transmitted resonance points is found to be enhanced greatly, and the sign of the lateral shift around the transmitted resonance points is strongly dependent on the permittivity and permeability of the indefinite medium. Some examples are given to validate the obtained theoretical results. PACS 41.20.Jb; 42.25.Gy; 42.25.Bs; 78.20.Ci; 78.68.+m