In this article, we review numerical and analytical methods of electronic-electromagnetic multiphysics modeling for terahertz plasmonic applications. Approaches within semiclassical regime of electronic transport are considered, as these are appropriate for examining plasma-wave phenomenology in 2-D electron gas systems, commonly found in high-electron-mobility transistors (HEMTs) and graphene sheets. In modeling of such electronic-plasmonic devices, coupling of incident electromagnetic wave to the device or emission from the device needs to be modeled. Therefore, electronic-electromagnetic coupled multiphysics multiscale models are required. In such modeling problems, the domain consists of large regions where electrodynamic equations are to be solved. Therefore, overall time efficiency relies on the speed of solution of electrodynamic equations. Nevertheless, the electrodynamic solution's speed is limited by the smallest grid sizes, which are a function of electronic transport equations. To address these issues, unconditionally stable finite-difference time-domain (FDTD) and iterative alternating directional implicit (ADI)-FDTD methods, coupled with hydrodynamic equations, are reviewed. Advantages and compromises between FDTD, ADI-FDTD, and iterative ADI-FDTD-based global modeling are discussed and conclusions are summarized.
