Dynamics of the wave packet in a tunnel-coupled structure consisting of amplifying right-handed and absorbing left-handed media

The dynamics of forward and backward waves in the tunnel-coupled waveguide structure that consists of materials with different signs of real and imaginary parts of refractive indices is analyzed. The expressions for the amplitudes of propagating waves and reflection and transmission coefficients are derived. It is demonstrated that such a structure can be used as a slow-wave structure whose parameters can be controlled using an external magnetic field. The absence of the spontaneous generation of the radiation that propagates in the structure is also demonstrated for the given effective gain, phase mismatch of the interacting modes, and waveguide length.