DGF-FDTD method as ABC and its 2D application for waveguide structures

A new discrete Green´s function (DGF) formulation of the finite difference-time domain (FDTD) method is presented. The implementation of the DGF method does not require an absorbing boundary condition (ABC) because it can determine the field at any point, at any time step, directly from the current without computing the free space nodes in between. This makes it an ideal choice for application as an ABC for the FDTD grid. The DGF-FDTD method and Yee algorithm (see Yee, K.S., IEEE Trans. Antenna and Propag., vol.14, p.302, 1966) follow the same discrete scheme; they are two different exact solutions for the same problem and can be combined without any interfacing problems or numerical errors. The performance of the application of the DGF-FDTD method applied as an ABC is investigated, firstly using a simple point source located at the centre of the FDTD grid and secondly by its application to the modelling of a 2D waveguide. Evidence is given that the DGF-FDTD performance is comparable in accuracy to that obtained using PML, but has the advantage of being faster and less memory intensive.