Impedance-matched absorbers for finite-difference parabolic equation algorithms

In this paper, a perfectly matched layer (PML) absorber, recently introduced into the electromagnetic propagation literature by Berenger [J. Comput. Phys. 114, 185-200 (1994)], is adapted for use with both paraxial and wide-angle acoustic parabolic equations (PEs). Our procedure incorporates an imaginary component into the transverse coordinate that mimics the introduction of a fictitious absorber on the edge of the computational grid. Use of such an impedance-matched layer can significantly reduce spurious reflections compared to physical absorbing layer methods and thus allows a smaller number of boundary points to be employed in PE calculations. Numerical results obtained with several higher-order propagator approximations confirm that such impedance-matched absorbers efficiently eliminate reflections.