## 3 Results and Discussion
The frequency of the microwave field is 3.99 GHz driving the Rydberg transition \(|56D_{5/2}\rangle\rightarrow|57P_{3/2}\rangle\). The small peak at zero detuning originates from the component of the microwave field that is perpendicular to the laser polarization. **(d)** Measurements of microwave dressed EIT-AT spectra for the range of \(|d|\leq 0.39\) m. Microwave dressed AT line strength is displayed using a linear color scale. Two horizontal dashed lines are shown the case of **(b)** (red) and **(c)** (purple), respectively. inspection of the spectrum at \(d=0\) in Figure 2d reveals that the peak at 0-detuning (associated with polarization impurities) is small relative to Figure 2b,c, where the horn is at \(d=+0.24\) m and \(-0.09\) m. This demonstrates that the Rydberg atoms experience a microwave field with a relatively pure linear polarization parallel to the polarization of laser beams when the horn is at \(d=0\), and we clearly observe the two peak EIT-AT spectrum [22]. Meanwhile the AT spectrum at \(|d|\approx 0\) experiences a strong ac Stark effect, and causes additional splitting of the EIT feature which can be seen on the figure at small \(d\). The Lorentzian nature of the AT split peaks is also degraded by inhomogeneity of the microwave field across the cell. Rydberg atoms within the cell experience slightly different microwave fields, leading to a slightly different AT splittings [34]. We use multi-peak Lorentz fittings to fit all peaks, the averaged AT splitting (electric field) is considered as the microwave field at near \(d=0\). (iii) The microwave dressed AT splitting decreases with \(d\), whereas the strength of 0-detuning peak increases with \(d\), as the spectrum converges on the zero detuning case. The quality of the polarization also decreases at large \(d\), increasing this effect. In Figure 3a, we show measurements of microwave electric-field, \(\lg[E/E_{0}]\backsimeq\lg[\gamma_{AT}/\gamma_{AT}^{d=0}]\) with \(E_{0}\) (\(\gamma_{AT}^{d=0}\)) taken as the value the electric field (AT splitting) experienced by the atoms when the horn is positioned at \(d=0\). The Stark effect is largest at \(d=0\) and decreases with \(|d|\). For comparison, in Figure 3a we also plot measurements taken with a dipole metal probe and analyzed with a vector network analyzer (VNA). The metal probe was placed at the same position as the atomic cell. Measurements with the atomic probe are consistent with the dipole metal probe over the measurement range. To compare the measurements, we calculate the near field distribution using an EMSS based on electromagnetic theory, which is solved with Maxwell's equations and proper boundary conditions [35; 36]. The solid line of Figure 3a displays this simulation of the near field. The figure shows that both the atom- and metal-probe measurements are in agreement with the simulations. The atomic probe outperforms the metal probe; the measurements obtained therewith more accurately reproduce the simulated field. This is probably because the metal probe itself reflects the microwave field that perturbs the field under measurement. A grey box on Figure 3a highlights the data taken with our atomic probe that are in agreement with the simulations. Outside of this grey box, the field value is too small to be measured accurately. For \(d\gtrsim\pm 0.25\) m, the side lobes of the measured field do not vanish as rapidly as the simulations predict. Here, the measured field diverges from simulations. When \(d>>0\), the electric field experienced by the Rydberg atoms is weak, susceptible to interference from reflected microwaves and the environment. We display residuals \(R\) between experiment and simulation for the gray region in the lower panel of Figure 3a. Corresponding root mean square (RMS) values of residuals are respectively 1.1 dB and 2.7 dB for atom- and metal-probe measurements, the atom probe is, therefore a 1.6 dB improvement over measurements taken with the metal probe.