# On the Use of Focused Incident Near-Field Beams in Microwave Imaging
## NF Beams and Results
### Interrogation of Objects by the Bessel Beam Launcher  
In the previous section, the idea of suppressing undesired scattering effects for MWI was studied using the NF plate. One limitation of this study lies in the fact that the OI and the undesired scatterer(s) are located on one line. This was due to the fact that the utilized NF plate provides 1D focusing. To consider more general cases, we have simulated the Bessel beam launcher presented in [48, 49] by the use of ANSYS HFSS so as to apply it to MWI applications. This Bessel beam launcher, shown in orange in Figures 11 and 12, is a planar structure capable of focusing electromagnetic fields into a 2D spot in front of the launcher and then maintains this focused beam over some distance away from the launcher. This distance is referred to as the non-diffracting zone of the launcher, after which the focused beam starts to diffract [48]. (The non-diffractive zone of this launcher is about 2.1\(\lambda\)[49].) This launcher utilizes a leaky radial waveguide in order to generate the Bessel beam [48]. This waveguide consists of a capacitive impedance sheet located over a ground plane (separated by 1 mm) which is fed by a coaxial cable. This capacitive impedance sheet is made of square patch elements (with the length of less than \(\lambda/10\) printed on both sides of a substrate with \(\epsilon_{r}=6.15\) and the height of \(h=0.127\) mm. The diameter of this launcher is about 6\(\lambda\) and its frequency of operation is 10 GHz [49]. The simulated Bessel beam launcher is capable of generating electric field whose normal  
Figure 10: Separation resolution study. Scattered NF data for (**a**) Configuration I and (**b**) Configuration II. Figure 9: Separation resolution study. The simulated NF plate (orange plane) setup with two dielectric objects (dark green dielectric boxes) separated by about 0.13\(\lambda\) from each other. (In the figure, this separation has been _exaggerated_ by a larger distance for illustration clarity.) The objects have the same size of \(\lambda/20\times\lambda/10\times\lambda/10\) along the \(x\)-, \(y\)-, and \(z\)-directions, and have the same relative permittivity of 1.50. The description of the excitation and receiver planes are the same as Figure 5.  
component, the \(\hat{y}\) direction in Figures 11 and 12, is a truncated zeroth-order Bessel function of the first kind, and has a first-null beamwidth of less than \(\lambda\). That is, theoretically, the incident field in the \(\hat{y}\)-direction will be in the form of [48]  
\[E_{y}=J_{0}(k_{xz}\sqrt{x^{2}+z^{2}})e^{-jy}y, \tag{5}\]  
where \(J_{0}\) is the zeroth-order Bessel function of the first kind, and \(k_{xz}^{2}+k_{y}^{2}=k_{b}^{2}\) where \(k_{xz}\) is the transverse wavenumber, \(k_{y}\) is the normal wavenumber, and \(k_{b}\) is the wavenumber in the background medium (free space in our case). Similar to the NF plate case, we consider two configurations. Configuration I uses the Bessel beam launcher to irradiate the objects. On the other hand, in Configuration II, a dipole antenna replaces the Bessel beam launcher to serve as our non-focused incident beam (see Figure A4 in Appendix A). For each of these configurations, we consider four case studies. In Case I, a rectangular dielectric box with the relative permittivity of two and the size of \(\lambda/2\times\lambda/4\times\lambda/3\) is placed at the center of the launcher and about \(\lambda\) away from the launcher (similarly, about \(\lambda\) away from the dipole antenna in Configuration II) as shown in Figure A3a. Case II not only considers the light green box as the OI, but also includes the two undesired scatterers, the dark green boxes in Figure 11, attached to the OI. These undesired scatterers have the same relative permittivity as the OI, each of which with the size of \(3\lambda/4\times\lambda/4\times\lambda/3\).