Complex Padé approximant operators for wide-angle beam propagation

Abstract The conventional rational Hadley( m ,  n ) approximant of wide-angle beam propagator based on real Pade approximant operators incorrectly propagates the evanescent modes. In order to overcome this problem, two complex Pade approximants of wide-angle beam propagator are presented in this paper. The complex propagators of the first approach are obtained by using the same recurrence formula from the scalar Helmholtz equation of the conventional approximant method with a different initial value while those of the second method derived from Hadley( m ,  n ) approximant of a square-root operator that has been rotated in the complex plane. These resulting approaches allow more accurate approximations to the Helmholtz equation than the well-known real Pade approximant. Furthermore, our proposed complex Pade approximant operators give the evanescent modes the desired damping.