The reversibility of the Goos-H\"anchen shift near the band-crossing structure of one-dimemsional photonic crystals containing left-handed metamaterials

We perform a theoretical investigation on the Goos-H\"achen (GH) shift in one-dimensional photonic crystals (1DPCs) containing left-handed metamaterials (LHMs). We find an unusal effect of the GH shift near the photonic band-crossing structure, which is located at the condition, $% -k_{z}^{(A)}d_{A}=k_{z}^{(B)}d_{B}=m\pi $ $(m=1,2,3...)$, under the inclined incident angle, here A denotes the LHM layer and B denotes the dielectric layer. Above the frequency of the band-crossing point (BCP), the GH shift changes from negative to positive as the incident angle increases, while the GH shift changes reversely below the BCP frequency. This effect is explained in terms of the phase property of the band-crossing structure.