A New Parabolic Approximation to the Helmholtz Equation

Parabolic or forward scattering approximations are often used to investigate acoustic or electromagnetic wave propagation in inhomogeneous media. Recently there has been an intensified interest in these approximations traceable in large measure to the work of Tappert1 and Claerbout2. Tappert’s work, reviewed in context in 1 applies the Leontovich-Fock (LF) approximation with considerable success to the study of underwater acoustics. Claerbeut has applied these approximations in a geophysical context. The LF parabolic approximation is very well suited to the study of sound propagation in model oceans that have range independent sound speeds. It has also been used to study propagation in fiber optics material,3 as well as in the study of laser propagation in the atmosphere.</p