Resonant amplification of slow surface plasmon polaritons in a DC current pumped semiconductor/graphene waveguide with a groove defect

We propose the principle of a planar surface plasmon polariton amplifier composed of a complex waveguide structure based on a semiconductor thin film separated from a dielectric substrate by a graphene monolayer. The amplification of surface plasmon polaritons in that waveguide in the terahertz regime is driven by a direct current in the graphene layer under a synchronism condition that allows an efficient energy exchange from the collective flux of charge carriers in graphene and the surface electromagnetic wave in the semiconductor film. Positive feedback required for resonant amplification is achieved through surface plasmon polariton reflections at the edges of the active waveguide, one of which is formed by a local thickness defect (a groove) at the upper surface of the semiconductor film that also provides an exit channel for the energy of the amplified surface wave to be transferred to an adjacent passive thin film semiconductor waveguide. We determine the conditions required for the resonant amplification of surface plasmon polaritons in that complex structure, which are essentially governed by the geometry of the groove as well as by the characteristic parameters of the active and passive waveguides.