# A Photonically-Excited Leaky-Wave Antenna Array at E-Band for 1-D Beam Steering
## 2 Leaky-Wave Antenna
### Radiating Section
For the unit-cell with one stub, note the typical open-stopband behavior around the frequency of broadside emission (\(\beta\)-1p/\(\pi=0\)) [19]. For \(\beta\)-1p/\(\pi\) equal exactly to 0, the wave is not radiated (\(\alpha\)/k\({}_{0}\) equals 0), and it is totally reflected (\(S_{11}>\) -1 dB in the stop-band frequencies when a sufficiently large structure is simulated). For the four-stub unit-cell with \(w=50\) um, the previous behavior is mitigated since the reflections from the stubs compensate to some degree, but it is still observed (in this case, \(S_{11}=\) -3 dB). Finally, for the designed unit-cell optimized using the approach explained before, the curves present a much smoother behavior, and the stopband effect is largely mitigated (S\({}_{11}<\) -12 dB). Since the antenna will be tested in a wireless link with a QO parabolic mirror of 10.16 cm focal, its phase center should remain constant over the operation band. Therefore, a compact design (far-field at 10.5 cm), with broadside directed radiation (for simpler alignment) was targeted. For that purpose, the row is truncated after four periods in a patch that radiates the remaining power, between 10% and 25%. The resonance frequency of the patch is fixed to 85 GHz, slightly higher than the central frequency (81 GHz), to compensate for the lower losses at the higher end of the operation band. It is worth mentioning that the narrowband patch used to truncate the antenna and make it compact degrades the patterns beyond its resonance frequency, and thus, it limits the antenna bandwidth. In line with the application discussed in Section 5, by including more periods in the row, the bandwidth upper limit would be increased, the side-lobes would be decreased, and also it would help to obtain a narrower beam for more pointing resolution. The above-described row is used to obtain the final planar array comprised of four rows. First, the row is duplicated to get a \(2\times 1\) array. Second, this \(2\times 1\) array is mirrored and excited in phase opposition, which leads to a significant reduction of the cross-polarization level and an E-plane pattern pointing at broadside. The final structure consists of an approximately square array with a simulated directivity between 18.5 and 20.0 dBi, side-lobe level (SLL) \(<\) -9 dB, a half power beam width (HPBW) \(<\) 13\({}^{\circ}\), and a radiation efficiency better than 75% in the 75-86 GHz frequency range. Figure 5a shows the \(S\)-parameters of the whole structure, and Figure 5b depicts the E- and H-plane cuts at broadside (81 GHz). The UTC-PDs are simulated as 50-\(\Omega\) lumped ports, which corresponds to the characteristic impedance of the output G-CPW of the photodiodes. In the future, one could envisage integration of the UTC-PD with a matching network, as in [24], whose output impedance is also 50 \(\Omega\). Figure 4: **(a)** Two consecutive periods along with representative geometrical parameters. **(b)** Optimized \(|S_{11}|\) and \(|S_{21}|\) for broadside emission as a function of the number of elements in the periodic structure (lines), and simulated values (dots). **(c)** Dispersion diagram and attenuation constant for three structures: the optimized one shown in **(a)** with 4 stubs per unit-cell and \(w\) = 450 μm (solid black lines), a 4-stub structure with \(w\) = 50 μm (solid grey lines), and a structure with a single stub per unit-cell with \(w\) = 50 μm (dashed grey lines).