Synthesis of an anisotropic surface, that reflects two incident plane waves in two given directions on ortogonal polarizations

In the paper, a two-dimensional problem of synthesis of the non-uniform anisotropic impedance surface that reflects two uniform plane waves of orthogonal polarization which simultaneously incident from the different directions, in two arbitrary chosen directions with the required orthogonal polarizations is solved for the first time. The impedance is presented as a dense grid of orthogonal stripes, which are arbitrarily oriented on the surface. The laws of distribution for impedance tensor components are received in an explicit form. Expressions for reflection coefficients are found. Scattering patterns are investigated. It is shown that in case of purely reactive impedance (reactance) in the reflected field, in addition to the given beams, there is still a system of specularly reflected plane waves on co-polarization. Analytical expressions for amplitudes of these waves are received. It is shown that the values of amplitudes of the waves which are reflected in a required and the mirror directions, are defined by a ratio between incidence angles and reflection angles and also types of polarization of these waves. Restrictions for a class of implementable scattering patterns are formulated. Appropriateness of the received theoretical expressions is confirmed with results of a rigorous solution of the analysis problem. Numerical results of synthesis are given.