Explicit matrix formulation for the analysis of synthetic linearly and non linearly loaded materials in fdtd – abstract

We present a new matrix differential equation formulation for the analysis of the response of linearly and non linearly loaded molecules to an incoming electromagnetic wave. The molecule is defined as an electrically small dipole or loop antenna connected to an electronic circuit called the load. Because we have a Maxwell FDTD code, we use a finite difference scheme to solve the differential equations, which greatly simplifies the problem. If the load is linear, a simple linear system of update equations can easily be derived from the system of differential equations describing the behavior of the load circuit. This approach leads to a natural choice for the intermediate unknowns in the use of the Auxiliary Differential Equation method, and gives a fully explicit matricial update equation. If the load contains one or more non linear devices, this method can be generalized and leads to the resolution of a system of non linear update equations with a simple Newton Raphson or Runge Kutta algorithm. Several numerical examples are shown, for dielectric molecules.