A.L. Dzvonkovskaya, Yu.K Kalinin
The exact solution of scalar wave diffraction is obtained in case of wave incidence on a dielectric paraboloid along its axis of revolution. The solution is found using the conventional technique called separation of variables in paraboloidal coordinates (u, v). These coordinates correspond to cylindrical coordinates as following:
The obtained wave equations for the separated functions U(u) and V(ν) have the same structure inside and outside the paraboloid of revolution but they differ by scales.
where t is the separation parameter. The solutions are parabolic functions derived from the integrals of elementary functions. The main problem is to fulfil the boundary conditions on the parabolid's surface and it can be overcome using a new inversion formula based on the parabolic functions. These functions are presented similarly to hypergeometric functions and give the asymptotic solution in case of the main paraboloid size is significantly bigger than the incident wavelength.
The obtained relations are used to solve the planar wave diffraction problem for the paraboloid of revolution. Following these solutions, the decameter wave radar cross section (RCS) of ionosphere F2-layer inhomogenuity caused by hypersound moving electrons is estimated. The RCS σ in case of a "huge" electrical paraboloid with the size bigger than the wavelength can be expressed by the Fresnel's planar reflection coefficient Rф and the paraboloid's RCS with the refraction index approaching the infinity
The wave corrections are found for this relation. It is noticed that the obtained results can be applied in modelling for other wavelength bands.