A Perfectly-Matched Layer Formulation Capable of Absorbing Multi-Modal Waves in Cylindrical FDTD

The perfectly-matched-layer (PML) absorbing boundary condition as applied to the finite-difference time-domain method in cylindrical coordinates is investigated. A critical error in implementing coordinate stretching which is present in various published works is identified and shown to diminish wave absorption efficiency for all wave modes except rotationally invariant ones. A correction to the underlying coordinate stretching formulation is proposed and confirmed to improve wave absorption by approximately two orders of magnitude for higher cylindrical wave modes even when the PML absorber is placed within the near-field region to the axis of rotation.