  In this paper, we design and simulate a terahertz (THz) controllable active
plasmonic waveguide structure based on a single graphene layer that is placed
on a random silicon grating substrate. Optical gain in the proposed THz active
plasmonic waveguide structure is provided by the stimulated emission process in
the photoexcited graphene monolayer that leads to the amplification of surface
plasmon polariton (SPP) waves. We use a random grating substrate to introduce
Anderson localization of the SPP waves propagating through the graphene
monolayer to enhance their optical amplification at resonant frequencies. It is
shown that the enhancement factor of the resonant peaks corresponding to the
graphene SPPs can be as high as 175. We also analyze their corresponding field
intensity distributions along the graphene monolayer and find out that their
intensities and localization positions are different from each other. By
investigating the pump dependent and temperature dependent variations of the
transmittance of the structure, it is shown that the resonant peak frequencies
are blue-shifted by increasing the temperature and the external pump intensity.
Also, we show that increasing the ambient temperature by 60 K can dramatically
reduce the output amplified intensity by a factor of 70. This property of the
proposed graphene-based THz plasmonic waveguide structure makes it useful in
temperature sensing applications and on/off switchable laser devices.
