# Axial-Symmetric Diffraction Radiation Antenna with a Very Narrow Funnel-Shaped Directional Diagram
## 4 Radial Emitters with a Narrow Funnel-Shaped Radiation Pattern
Radiation pattern \(D(\theta,k,\infty)\) in the frequency band \(3.1\leq k\leq 7.3\) and at possible operating frequencies \(k=k_{\text{oper}}=5.08\) and \(k=k_{\text{oper}}=6.01\) (\(f_{\text{oper}}\approx 0.242\) GHz and \(f_{\text{oper}}\approx 0.287\) GHz). pattern of the emitter, discussed earlier. This should also change the size \(l\) of the period of the grating, directing its fundamental spatial harmonic at an angle \(\theta\) close to zero. So, for the value \(k=3.9\), we obtain \(\overline{\chi}(k)=5.14\) (see Figure 3), \(\gamma(k)=\overline{\chi}(k)/k\approx 1.32\), and \(l=2\pi/k\gamma(k)\approx 1.22\). Having loaded the radial waveguide with a grating of a period \(l=1.2\) (\(d=1.0\), the parameters \(h\) and \(c\) remain the same) and having excited the structure with a pulsed \(TE_{01}\)-wave \(V_{1}(g,t):\ v_{1}\big{(}z:\ g\in\mathrm{L}^{+},t\big{)}=F_{1}(t),\widetilde{k }=3.9\), \(\Delta k=1.0\), \(\widetilde{T}=50\), and \(\overline{T}=100\), we arrive at the results presented in Figure 5. These results fully meet our expectations, but the minimum deviation of the beam corresponding to the zero spatial harmonic of the grating from the axis \(z\) has increased to \(3^{\circ}\). Obviously, this is due to a decrease in the number of grating periods that fit into the length \(L\), determining the dimensions of the emitter aperture. With the transition to a full-size aperture of the synthesized antenna, this indicator can be significantly improved. Figure 5: Radial diffraction radiation antenna. Radiation pattern \(D(\theta,k,\infty)\) in the frequency band \(2.9\leq k\leq 4.9\) and at frequencies \(k=k_{\mathrm{oper}}=3.9\) and \(k=k_{\mathrm{oper}}=3.98\) (\(f_{\mathrm{oper}}\approx 0.186\) GHz and \(f_{\mathrm{oper}}\approx 0.19\) GHz). As it has already been noted more than once [17; 20; 25], for the successful solution of the problem of synthesizing a real antenna of diffraction radiation, the energy parameters \(\eta(k)\) of prototype emitters and the ability to control their change by varying one of the parameters \(d\), \(h\), or \(c\), are important. In the case under consideration, \(\eta(k)=0.41\) at frequency \(k=3.9\), and \(\eta(k)=0.43\) at \(k=3.98\). Figure 6 shows how the radiation intensity changes with a change in the aiming distance \(c\), that is, the distance between the grating and the radial dielectric waveguide. When performing a specific technical task for the construction of a diffraction radiation antenna, similar dependences, calculated for all admissible (not leading to phase distortions of the surface wave field [17; 20; 25]) values \(c\) should be taken into account. An important issue in the construction of real antennas is the question of maximum simplification of their design without losses in the quality of the main electrodynamic characteristics of devices. In part, this also holds for the used periodic structures. The parameters of far from all gratings of classic geometry (gratings of the 'comb' type, for example) can be strictly maintained during their manufacture and operation in the wavelength ranges from 3.0 mm and less. A prototype of a diffractive radiation antenna, the main electrodynamic characteristics of which are presented in Figures 7 and 8, can be proposed as one of the options allowing to effectively solve the above problems. In this prototype, one of the planes of the radial dielectric waveguide is metallized, and the second one contains a concentric grating of 'thick' (\(h=0.08\)) narrow (\(l-d=0.2\), \(l=1.2\)) metal strips--its propagating spatial harmonics mainly form the radiation field. The structure is excited by a pulsed \(TE_{01}\)-wave \(V_{1}(g,t):\;v_{1}\big{(}z:\;g\in\mathrm{L}^{+},t\big{)}=F_{1}(t),\widetilde{k }=3.9\), \(\Delta k=1.0\), \(\widetilde{T}=50\), \(\overline{T}=100\), covering the frequency range \(2.9\leq k\leq 4.9\). For the expected value \(k=3.9\), the minimum deviation of the main lobe of the radiation pattern from the axis \(z\), equal to \(2^{\circ}\), is obtained for frequencies \(4.09\leq k\leq 4.15\).