Perfect plane wave injection for Crank-Nicholson time-domain method

The authors derive a 1D multipoint auxiliary source propagator for perfect plane wave injection (PWI) with the Crank-Nicholson time-domain scheme for the first time. By projecting the 2D dispersion equation onto the 1D case, the identical dispersion relation can be realised between the 1D case and the 2D case, which leads to a perfect PWI at any angle forming an integer grid cell ratio. Several numerical experiments are conducted, which show leakage errors on the order of finite precision (-300-dB for double precision) when -t is around the Courant-Friedrichs-Levy (CFL) limit. Beyond the CFL limit, the leakage error is still kept low even though it deteriorates with increasing time-step increments. Good agreement is observed between the proposed method and analytic solution for scattering of a 2D perfect electric conductor circular scatterer.