Optimal absorber potentials in PE modeling

Abstract

The parabolic equation (PE) approximation—essential in solving range‐dependent propagation problem—relies on iterated fast Fourier transforms (FFTs). Preventing significant errors due to the periodicity of the finite FFT (“ringing”) requires inserting an absorber potential to confine the wave energy to the range of interest. Such potentials, or sponges, have, to date, been strictly ad hoc. The problem of creating an optimal sponge by using an optical model analogy of the reflectionless potential U = U0* [sech(a*x)]2 of 1‐D quantum mechanics is studied. This approach permits the development of closed‐form expressions for both transmission and reflection coefficients in terms of elementary transcendental and gamma functions of complex argument. Using these coefficients and an efficient technique for evaluating such gamma functions yields a quantitative study of the problem of the optimal sponge. These results demonstrate that, for relevant parameter domains, there may be several “branches” of minimal paths ...