Terahertz amplification and lasing by using transverse electric modes in a two-layer-graphene-dielectric waveguide...

We study for the first time the interaction between the waveguide modes of graphene structure and freely propagating terahertz (THz) electromagnetic waves (this interaction takes place within the light cone). We revealed a new and rather unexpected physical phenomenon by showing that freely incident THz electromagnetic waves can resonate with the surface transverse electric (TE) modes of the graphene waveguide in virtue of these modes having their dispersions in the vicinity of the light cone. The dispersion and amplification of surface TE modes in a dielectric waveguide covered with two graphene layers biased by direct current (DC), as well the amplification and lasing of incident THz wave by excitation of TE mode resonances, are investigated. The DC flows perpendicular to the direction of the surface wave propagation and creates the capacitive complex conductivity of graphene at THz frequencies, which is necessary for the existence of surface TE modes in graphene. The real part of graphene conductivity can be negative at THz frequencies due to DC in graphene which leads to amplification and lasing of THz radiation. Such structure can be of great practical importance because an external THz wave can be amplified or generated in lasing process without using special coupling elements commonly needed for ensuring the interaction between external THz wave and surface waveguide modes. The use of a two-layer graphene structure makes it possible to reduce the charge-carrier drift velocity required for reaching the lasing threshold at those resonances, as compared to a structure with a single graphene layer.