V.V. Akhiyarov

In this work the scalar diffraction problems solution using parabolic equation (PE) is considered. The reduction of initial Helmholtz equation to standard PE, valid in paraxial approach, is stated. All necessary PE for forward and backward propagation in free space and medium with refraction are shown. The algorithm of PE numerical solution based on Fourier split-step transform is presented. Various truncation methods are discussed: the absorbing and perfectly matched layers, and recommendations for their use are given. It is shown, that perfectly atched layer can be viewed as a lossy medium and so it is equal to Hanning window usage as for the absorbing layer. Half-plane diffraction for the directional radiation and forward and backward propagation is presented. That allows modeling not only the diffraction field, but also reflections from the half-plane. It is shown, that PE method corresponds with Young and Fresnel ideas about the diffraction effect. The diffraction problem solution for the radio wave propagation above the earth surface with the Dirichlet boundary condition is considered. Comparison with calculations using V.A. Fock diffraction formula for the surface with real electri-cal parameters is produced. This calculation shows that the Dirichlet boundary condition is quite suitable for path loss prediction in VHF range.