V.V. Akhiyarov

IRE of RAS; JSC «SPC «SRI of Long-Distance Radio Communications» (Moscow, Russia)

The diffraction on the wedge plays a key role in the investigation of scattering fields for the real objects. For a perfectly conductive wedge, this problem has been fully investigated: the rigorous analytical solutions obtained by the separation of variables method and based on the Sommerfeld integral, as well as the approximation of the physical optics, the geometrical theory of diffraction and the physical theory of diffraction are well known. The reflection method allows us to give a clear physical interpretation of the diffraction phenomenon and to solve some diffraction problems.

In the case of an impedance wedge, the number of analytical solutions is significantly smaller: variables in the Helmholtz equation are no longer separated, and the use of the uniform theory of diffraction can lead to uncontrollable errors far from the «lightshadow» boundary for the incident and reflected waves. So the G.D. Malyuzhinets’ method based on the functional equations for the Sommerfeld integral is the most preferable approach to solving the diffraction problem on an impedance wedge. 

In this paper, the reflection method formulated by P.Ya. Ufimtsev for a perfectly conducting wedge is generalized for the impedance boundary conditions. The rigorous solution for the diffraction on the impedance wedge by the reflection method is obtained both for non-uniform (with breaks in the vicinity of the «light- shadow» boundaries) and for uniform diffraction field.

To solve this problem, in G.D. Malyuzhinets’ solution the components associated with an incident and reflected wave are obtained. The generalized reflection coefficient that takes into account the influence of the surface impedance on the angular distribution of the diffraction field is received. The relation of the reflected fields with sheets of the Riemann surface is established. It is shown that the non-uniform solution based on the reflections method fully corresponds to the G.D. Malyuzhinets’ theory.

Akhiyarov V.V. Using the reflections method in the wedge diffraction theory. Radiotekhnika. 2021. V. 85. № 3.  P. 16−26. DOI: https://doi.org/10.18127/j00338486-202103-02 (In Russian).

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