FDTD Simulation of Three-Wave Scattering Process in Time-Varying Cold Plasma Sheath

In this paper, a three-dimensional finite-difference time-domain (FDTD) method is developed to simulate the three-wave scattering process as a numerical experiment of the nonlinear interaction between two monochromatic plane waves in a plasma slab. This electromagnetic (EM)-plasma coupled system is governed by Maxwell's equations and the momentum equations of electron-only cold plasma. To model the system using the FDTD method, a simple and efficient periodic boundary condition is proposed and analyzed using the Floquet mode theory. The simulation result for the plasma slab with a linearly increasing electron density profile demonstrates that it is feasible to use the proposed formulations for the three-wave scattering process. Then, additional simulations are performed for the plasma slab with different electron density profiles and different incident angles of a signal wave as case studies to show the capability of the developed method for various environments.