Time-domain investigation of the tunneling modes in photonic heterostructure containing single-negative materials

We present a theoretical investigation into the energy transport and transient wave propagation in metamaterial tunneling structures consisting of e-negative (ENG) and μ-negative (MNG) materials. It is proved that a conjugated matched ENG/MNG bilayer and a (zero-index-material doped) photonic crystal heterostructure can work as a sub-wavelength resonator at tunneling frequency. The tunneling modes need a certain time to achieve the steady state and the charge up characteristic time increases (nearly) exponentially with the thickness of the structures. Under the steady state, the wave in the single-negative-material structures is not evanescent, but a hybrid of a traveling wave and a reactive standing wave. The phase difference between the electric field and the magnetic field varies with the position and time. The investigation of transient wave propagation in the metamaterial tunneling structures will help us to understand the interaction process between wave and metamaterial and to design special functional apparatus.