Mode theory of wave propagation in a bilinear medium: The WKB approximation

Abstract

Normal-mode calculations are made of wave propagation in a bilinear medium with a free surface (the surface duct). The WKB approximation is used. In the usual way, the integral expression for the field is transformed into an infinite series of the residues (normal modes) of the integrand at its poles (eigenvalues). Approximations for the eigenvalues of the trapped normal modes are obtained from WKB formulas. The eigenvalues of the untrapped modes are obtained by quadratic extrapolation of the eigenvalues of the trapped modes. The accuracy of the real part of the eigenvalues of all modes is improved by taking into account the imaginary part when solving the characteristic equation. On comparing a number of WKB calculations of transmission loss with exact calculations, it is found that when there is little fine structure in the transmission loss curve, the WKB result is a good representation of the exact result. When there is significant fine structure, however, the WKB results are often in error by several decibels, and occasionally by up to 20 dB. Subject Classification: [43]30.20; [43]20.15; [43]30.50.