The properties of photon tunneling through the asymmetry structure with left-handed materials

Based on the transfer matrix method, the transmission and reflection coefficients for photon tunneling through the asymmetry structure containing negative index materials are obtained. Through using the stationary-phase approximation, properties of the lateral shift and tunneling time are disclosed. It is shown that the lateral shifts of reflection and transmission are not equal. The lateral shift and tunneling time are always negative, and tend to be negative constants as the thickness of left-handed materials increases, demonstrating a negative Hartman effect. These properties are opposite to the case when the negative refraction material is substituted by the positive index material. The negative tunneling time indicates that superluminal propagation can be observed when photons tunnel through the left-handed materials.