On the synthesis of exact free space absorbing boundary conditions for the finite-difference time-domain method

An exact and nonlocal analytical absorbing boundary condition (ABC) for use in the finite-difference-time-domain (FDTD) method is proposed. The ABC requires no assumptions regarding a minimum spacing between scatterers and the artificial termination planes, and is not a function of the angle of an incident wave component with respect to the ABC truncation plane. Hence the size of the volumetric computational domain may be kept to a minimum. The derivation of the ABC makes use of the surface equivalent theorem and the vector potentials after an analytical frequency to time domain transformation. The new ABC contains derivatives with respect to both time and space, and may be approximated in the FDTD method via appropriate finite difference approximations