# Dual-Polarized Multi-Beam Fixed-Frequency Beam Scanning Leaky-Wave Antenna
## 2 Methods
One is the impedance surface with different notch depths, and the other is the impedance surface with the same notch depth but using devices with different capacitance values. It is noteworthy that the electric field direction excited by the two aforementioned impedance surfaces is perpendicular to each other, which is the fundamental idea behind our design of a dual-polarized fixed-frequency beam scanning LWA. The polarization characteristics are verified by observing the electric field distribution and cross-polarization patterns. As depicted in Figure 3, it can be observed that the electric field of the LWA with different notch depths varies linearly along the \(x\) direction that is perpendicular to the notch direction, while the electric field of the LWA with the same notch depth varies linearly along the \(y\) direction that is perpendicular to the capacitance slot direction. Furthermore, Slip symmetric branching has been utilized in the antenna array to enable flexible beam modulation and weaken the OSB effect that is typically present in periodic leaky antennas. To implement multibeam, the principle is based on Equation (1), which contains three modulation parameters, \(M\), \(p\), and \(Zs\), respectively. The period length \(p\) and the modulation factor \(M\) are changed by varying the number of cells contained in each modulation period. By tuning the varactor, different \(Zs\) can be obtained at a fixed frequency. Taking the first group of antennas as an example, the X-polarized SPPs antenna has six subwavelength cells in one modulation period. The periodic modulation caused by different depths of the slot cause the radiation of high-order harmonics. The Y-polarized SPPs antenna has six subwavelength cells in one modulation period, and its radiation principle is that the periodic alternate loading of varactor diodes and fixed capacitors causes the change of surface impedance, thus causing the radiation of high-order harmonics. Figure 2: The radiation schematic of the periodic LWA. The tool used for antenna simulation is CST MICROWAVE STUDIO, in which the eigenmode solver is used for the dispersion curves simulation, and the time domain solver is used for the S-parameters, gain, and radiation patterns simulation. For the unit of SPPs LWA, the most important performance is its dispersion characteristics. The dispersion curves of the X-polarized antenna unit and Y-polarized antenna unit are shown in Figure 4a,b, respectively, and it can be seen that when the slot depth of the X-polarized antenna unit increases, the cut-off frequency of the unit decreases. The depth of the slot of the Y-polarized antenna unit remains unchanged, and its dispersion curve varies with the loading capacitance. According to the dispersion curve of the antenna unit, the antenna can be designed to operate at a particular frequency. To complete the beam scanning at a fixed frequency, the wave number \(k_{x}\) of propagation direction can be tuned by impedance modulation. The dispersion curves for modulation periods of the antenna are presented in Figure 4c,d. The modulation period of the X-polarized antenna has dispersion curves shown in Figure 4c. The modulation period of the Y-polarized antenna can be explained by the triangular impedance modulation evolved from the sinusoidal impedance modulation. Its dispersion curves are presented in Figure 4d. From these results, it can be seen that beam scanning at a fixed frequency can be implemented by changing the capacitance of the loaded varactor diode. We have simulated the S-parameters and far-field radiation patterns of the LWA. The simulated reflection coefficients of the X-polarized and Y-polarized antennas are presented in Figure 5. It can be observed that the reflection coefficients of all six antennas in the operating frequency band of 3.3 to 3.8 GHz are consistently below \(-10\) dB. The simulated radiation patterns of the multi-beam antenna at 3.5 GHz have been presented in Figure 6, and the radiation angles of each group of x-polarized and y-polarized antennas remain identical.