## 3 Results and Discussion
Further in Figure 3b, we present the radiation pattern of the horn used here (electric field, \(E/E_{0}\), as a function of \(\theta\) (\(\arctan[d/d_{0}]\))). The dot-dashed lines display the half power beam width (HPBW). The HPBW is defined as the angle between the two directions where the electric field decreases to \(E_{0}/\sqrt{2}\). Measured HPBW is (\(39.4\pm 3.8\))\({}^{\circ}\) for atom probe, again providing a more accurate measurement (HPBW\({}_{EMSS}=33.6\)\({}^{\circ}\)) than the metal probe (\(9.2\pm 2.2\))\({}^{\circ}\). We then analyze the symmetry of the near field of the microwave horn. Figure 4 displays the measurements of the normalized microwave electric field, \(\lg[E/E_{0}]\), as a function of \(|d|\) so that the symmetry of the near field of the horn can be addressed. We also plot the simulated electric field versus \(d\), which is the same for the sides, see black line in Figure 4. Short-dashed lines show the fittings to the experimental data using the equation \(y=a+b/(d_{0}^{2}+d^{2})\), with fitting parameters \(a\) and \(b\). Parameters \(a_{right}=-26.14\pm 1.10\), \(a_{left}=-26.12\pm 1.88\) and \(b_{right}=2.42\pm 0.13\), \(b_{left}=2.32\pm 0.23\) are obtained. The minor difference between these parameters for both sides demonstrates some asymmetry of the near field distribution. From Figures 3 and 4, it is seen that the simulated microwave electric field shows a symmetrical distribution of the near field. Measurements at larger \(d\) demonstrate some asymmetry. This is attributed to reflections of the microwave field from optics, and noise from the environment. Figure 4: (Color online) The measured electric field, \(\lg[E/E_{0}]\), as a function of distance from the center of the guide rail to the horn, \(d\), for both directions (\(d>0\) and \(d<0\)). The error bars for atomic measurements display a standard error of two measurements. Short-dashed lines are the fittings to the experimental data using an equation \(y=a+b/(a_{0}^{2}+d^{2})\) with parameters \(a\) and \(b\). The fitting parameters are \(a_{right}=-26.14\pm 1.10\), \(b_{right}=2.42\pm 0.13\) and \(a_{left}=-26.12\pm 1.88\), \(b_{left}=2.32\pm 0.23\), respectively. The minor difference in the fitting parameters for the data describing the right and left sides of the microwave distribution is symptomatic of a small asymmetry of the near field. The thin line denotes the simulation based on EMSS. Figure 3: (Color online) (**a**) Electric field amplitude \(\lg[E/E_{0}]\) (\(E_{0}\), microwave field at \(d=0\)) measured using an atomic probe (blue triangles) and a dipole metal probe (red circles). The error bars for atomic measurements display a standard error of two measurements. The solid line displays the simulation with the electromagnetic simulation software. The gray shadowed area corresponds to \(d=\pm 0.25\) m. The lower panel shows the residuals \(R\) between experiment and theory within this grey area. The root mean square (RMS) values of the residuals are 1.1 dB and 2.7 dB for the atomic and metal probe, respectively. (**b**) Comparison of the electric field, \([E/E_{0}]\) between measurements and electromagnetic simulated software (EMSS) simulation at near field. The major lobe of the emission is observed with measured half power beam width (HPBW) \((39.4\pm 3.8)^{\circ}\) for the atom probe and \((9.2\pm 2.2)^{\circ}\) for the metal probe. The microwave dressed Rydberg EIT-AT spectrum provides an optical readout of the microwave electric field that is employed to measure the near-field distribution of the horn. The microwave dressed AT spectrum reveals both the microwave field and polarization purity of the microwave horn. From Figure 3, we have well characterized the amplitude distribution and radiation pattern at the near field of a microwave horn using AT splitting of sensitive Rydberg states. From Figure 2d, we can also determine the purity of the microwave polarization by observing the presence and size of the central peak.