Below, results of numeric calculations on a PC using the "ArrayGuides Rectangular" software are given.

Let’s consider the case where the AA period contains of one waveguide, the wide sheath of which has the size *a* and is oriented along the OX axis, the narrow sheath — size *b*, and the flat electromagnetic wave is polarized along the OY axis. The fig.2 shows the family of curves which reflects the change in the frequency band of impedance properties of the surfaces located at the distance of 0.08 ( — wavelength corresponding to the bottom frequency of the range) from the array aperture in the point x = y = 0. There are no dielectrics, the wave is normally incident to the AA surfaces, the waveguides are located in the nodes of the rectangular array.

Fig.2 Behavior of the imaginary part of the surface impedance above the array of supercritical rectangular waveguides from frequency (a: curve 1 - = 0.21, curve 2 — = 0.22, curve 3 — =0.23; b: curve 1 — = 0.18, curve 2 — = 0.19, curve 3 — = 0.2; c: curve 1 — *a* = 0.2, curve 2 — *a* = 0.19, curve 3 — *a* = 0.18; d: curve 1 — *b* = 0.17, curve 2 — *b* = 0.16, curve 3 — *b* = 0.15; e: curve 1 — = 0.08, curve 2 — = 0.07, curve 3 — = 0.06).

The given curves show how the outcome is affected by various structure parameters: array period (fig.2а) and (fig.2b), size of the wide (fig. 2c) and narrow (fig.2d) waveguide sheath and distance from the analyzed surface to the array aperture (fig.2e) to the value of the imaginary part of *Z*. The array geometry: = 0.21, = 0.18, waveguide: *a* = 0.2, *b* = 0.17. Since the waveguide is supercritical in the entire frequency range, the real part of *Z* is zero. The computation error specified using the internal convergence of the numerical procedure does not exceed 1…3% when to describe the field in the aperture of the rectangular waveguide, basis functions corresponding to the waves , , , are used. (Later on, to describe the results of the numerical experiment, those proper waves of the rectangular waveguide are specified, accounting for which provides the specified precision). Analyzing the curves shown at fig.2, the following conclusion can be made:

— the most significant effect on the value of impedance has change of the wide sheath of the waveguide and distance from the surface to the AA aperture;

— change of impedance to increasing in the bottom part of the range leads in all cases to shift to lower frequencies of resonance and therefore lowering the useful frequency range where .

The dotted line shows impedance determined using the formula:

where *a* = 0.2, *b* = 0.17, = 0.08. The specified formula corresponds to the zero approximation, and in it , — conductivity of the wave of the rectangular waveguide.

Also, the effect of the infinitely thin diaphragm located in the aperture of the supercritical waveguide was researched. It was determined that usage of the diaphragm does not allow obtaining the necessary surface impedance *Z* in the wide frequency range either.

Fig.3 Dependency between the surface impedance (a, 1 - module, 2 – real part, 3 – imaginary part) and the input resistance of RS (b, 1 – real part, 2 – imaginary part) and the frequency . RS is located on the surface with impedance (a).

Fig.3a displays curves of dependency *Z* above the AA of subcritical waveguides and the frequency in point x = y = 0. Array geometry — = = 0.2, rectangular array. Waveguide size — *a* = *b* = 0.19, dielectric filling = 7.2 (which corresponds to the wave slice frequency and ~0.98). The surface is located at the distance of = 0.125. The flat wave is normally incident to the AA surface. The following waves were taken into account in the waveguide: , , , , , , , .