Mode functions for the wide-angle approximation to the parabolic equation

The parabolic approximation to the wave equation is examined within the context of normal mode theory. In a layered waveguide, the horizontal propagation constants and modal amplitudes of the field Ψ satisfying the standard parabolic equation (SPE) approximation can be mapped exactly into the amplitudes and wave numbers of the normal modes for the field p satisfying the Helmholtz wave equation. However, this is not the case for certain other parabolic approximations, such as the wide-angle parabolic equation (WAPE) approximation. Approximate mode functions for the WAPE approximation are developed. These mode functions are then used to decompose range-independent sound-pressure fields computed using the WAPE approximation. The resulting modal coefficients and eigenfunctions obtained using the WAPE mode functions are compared with those obtained using standard normal mode theory.