Complex Padé approximants for wide-angle acoustic propagators

Procedures for constructing wide-angle propagators that attenuate evanescent modes in parabolic equation (PE) models of underwater sound propagation are examined. In this context, two new split-step Padé approximations to exponentiated square-root operators are proposed. The first method involves a propagator derived from a Padé approximant of a square-root operator that has been rotated in the complex plane while the propagator of the second method is obtained from a complex coefficient rational approximation of the square-root operator. Numerical evidence confirms that these proposed methods yield improved behavior compared to previously suggested techniques in selected areas of the spectral domain.