▎ 摘　　要

In this work, we demonstrate that photonic crystals made with alternating layers of graphene and nanometer-scale split-ring-resonator metamaterials can be treated as single negative-index materials with broad zero- e f f gaps in the mid-IR frequency range. These provide a versatile platform for the fabrication of anti-interference multichannel filters whose tunability can be realized flexibly by adjusting the conductivity of the graphene layer. Specifically, by inserting dielectric defects into the periodic system, one can obtain tunable tunneling modes inside the zero- e f f gap, which are highly robust against scaling and structural disorder. Moreover, without altering the structure of the system, the number of defect modes multiplies as the graphene chemical potential is decreased appropriately. In addition, the tunneling modes are nearly invariant with the incident angle in the range of 0 degrees- 5 degrees. Also, the bandwidths of the tunneling modes are compressed by decreasing the chemical potential, which could be utilized to improve the Q values of the filters. Furthermore, THz amplification could also be accomplished when taking into account the damping constant of the permittivity of graphene. As a result, these characteristics may facilitate the design of optical devices in the mid-IR range, especially leading to more practical applications of these filters.