Electromagnetic edge diffraction problems involving parallel half-planes are traditionally attacked by the Wiener–Hopf technique, or asymptotically for a large wavenumber (k→∞) by ray-optic techniques. This paper reports a novel method in which the electromagnetic wave equation is first converted to a heat equation via the Laplace transform. The heat equation together with the original boundary condition is next solved approximately in terms of a path integral over the Wiener measure. For several examples involving two parallel half-planes, the path integral is evaluated explicitly to yield an asymptotic solution of order k0 for the field on the incident shadow boundary. Those solutions agree with the ones derived by traditional techniques, but are obtained here in a much simpler manner. In other examples involving multiple half-planes, the use of a path integral leads to new solutions. We have not succeeded, however, in generating higher-order terms beyond k0 in the asymptotic solution by path integrals.
Based on three formulations of the Huygen's principle, explicit expressions is given for the far field contribution from a small ray tube. This expression is useful in shooting and bouncing rays for solving complex scattering problems.
This paper studies sound propagation in a layered atmosphere bounded by a ground, whose impedance is described by the Delany–Bazley–Chessell’s empirical model. The problem is formulated in terms of a Green’s function integral in the spectral domain, and is numerically evaluated by a Fast Field Program (FFP). Numerical results are included to show that (i) in simple test cases, the FFP solution is in excellent agreement with existing asymptotic solutions; (ii) numerical overflow arises when the number of layers is large and/or the frequency is high, and a method to circumvent this difficulty is described; and (iii) the FFP is a most powerful tool in solving propagation problems in layered media bounded by complex impedances.
In an earlier paper, the present authors’ work in adapting the fast field program (FFP) formulation to atmospheric propagation above a complex impedance boundary was described. It was found that numerical overflow problems for high frequencies and multiple layers limited the utility of the FFP in solving atmospheric problems. In this paper is a description of a new formulation which eliminates the overflow problems inherent in the earlier formulation. The results of these two formulations are compared for a test case and the superiority of the new formulation is demonstrated. Results of the FFP2 for a simple atmospheric profile are compared with field measurements and the applicability discussed.
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