## 2 Experimental Setup  
Experiments were carried out in a caesium room-temperature vapor cell. A schematic of the experimental setup and relevant Rydberg EIT-AT four-level diagram is shown in Figure 1. The caesium ground state \(|6\mathrm{S}_{1/2},F=4\rangle\), excited state \(|6\mathrm{P}_{3/2},F^{\prime}=5\rangle\), and Rydberg state \(|56\mathrm{D}_{5/2}\rangle\) are used to define a cascaded three-level EIT system, see Figure 1a. The coupling laser is resonant with the \(|6\mathrm{P}_{3/2},F^{\prime}=5\rangle\to|56\mathrm{D}_{5/2}\rangle\) Rydberg transition. A probe laser couples the lower \(|6\mathrm{S}_{1/2},F=4\rangle\to|6\mathrm{P}_{3/2},F^{\prime}=5\rangle\) transition. The probe laser frequency is locked using polarization spectroscopy [32]. We scan the coupling laser across the transition, allowing us to obtain EIT spectroscopy without a Doppler background. A microwave electric field with a frequency \(\sim\)3.99 GHz couples the \(|56\mathrm{D}_{5/2}\rangle\to|57\mathrm{P}_{3/2}\rangle\) Rydberg transition, forming microwave dressed EIT-AT spectroscopy.  
Figure 1b displays the experimental scheme. A weak probe beam, with a \(1/e^{2}\) waist of 100 \(\upmu\)m and a wavelength of \(\lambda_{p}\) = 852 nm, and a strong coupling beam, with a \(1/e^{2}\) waist of 150 \(\upmu\)m and wavelength of \(\lambda_{c}\) = 510 nm, are overlapped and in a counter propagating geometry through a vapor cell with diameter 20 mm and length 50 mm. The probe and coupling beams are of the same linear polarization along \(z\)-axis. EIT microwave dressed AT splitting spectra are detected by measuring the transmission of the probe beam using a photodiode (PD) positioned after a dichroic mirror (DM). The power of probe and coupling lasers are 2.0 \(\upmu\)W and 29.8 mW, respectively, which yield an EIT spectrum with a linewidth \(2\pi\times 5.08\) MHz, as displayed in Figure 2a. The dominant peak at zero detuning corresponds to a double resonance, \(|6\mathrm{S}_{1/2},F=4\rangle\to|6\mathrm{P}_{3/2},F^{\prime}=5\rangle\to|56 \mathrm{D}_{5/2}\rangle\), while the  
small peak at \(-168\) MHz results from the hyperfine structure of an intermediate state \(|6\text{P}_{3/2},F^{\prime}=4\rangle\) resonance, that is used to calibrate the coupling laser frequency. Here, the distance between two hyperfine EIT peaks, 168 MHz, is attained by considering Doppler mismatch factor, \(\lambda_{p}/\lambda_{c}\) - 1 = 0.67, due to different wavelength of probe and coupling beams.  
A standard gain horn with center frequency of \(\sim\)4.0 GHz is placed on a commercial one-dimensional guide rail. The rail is placed parallel to the laser beams. The cell center is located along the perpendicular bisector of the rail with the distance \(d_{0}=0.3\) m, as shown in Figure 1b. The vertical center of the horn is positioned in the optical plane. We change the horn position \(d\) by moving it along the rail, and detect the microwave induced EIT-AT splitting. The strength of the splitting allows us to obtain the electric field value.  
A 3.99 GHz microwave electric field, produced with an analog signal generator (Agilent N5183B), is emitted by the horn. This field is incident upon the cell, transverse to the counter-propagating probe and coupling beams. The microwave field couples nearby Rydberg transition \(|56D_{5/2}\rangle\rightarrow|57P_{3/2}\rangle\) and splits the EIT peak. For investigating the near field feature of the horn, we fix the output of the microwave source at 13 dBm. At this power, EIT splitting is observable at all horn positions, \(d\in[-0.4\,\text{m},0.4\,\text{m}]\).