**6. Comparison of plane wave and OAM wave propagation**

This section compares plane wave and OAM wave propagation using PWPA and OWPA designed at frequency 2.45 GHz. The electrical size of PWPA or OWPA at the center frequency is 0*:*9*λ*. The PWPA or OWPA is enclosed in radiating bounding box

of size 1 m 1 m 1m 8*<sup>λ</sup>* <sup>8</sup>*<sup>λ</sup>* <sup>8</sup>*λ*; 512*λ*<sup>3</sup> , as shown in **Figure 18(a)**. The extra open and added space radiating boundary ensures the far-field behavior in free space for both Tx–Rx antennas. The nature of the electric field, magnetic field, and power flow of individual PWPA, OWPA, and combined Tx–Rx pairs is monitored. Three cases simulated in the work are: (i) Tx–Rx: PWPA–PWPA, (ii) Tx–Rx: OWPA– OWPA, (iii) Tx–Rx–Rx: OWPA–PWPA–PWPA. In **Figure 18(a)**, two PWPA antennas, such as Tx and Rx, are separated by 1 m in their far-field distance.

Similarly, in the second case, **Figure 18(a)**, OWPA–OWPA Tx–Rx pair analysis is performed within the same boundary box as another simulation setup. **Figure 18(b)** illustrates the third case of OWPA–PWPA–PWPA configuration. The electric field carpet plots for individual PWPA and OWPA are depicted in **Figure 18(c)** and **(d)**, respectively. It clearly shows no field components along the z-axis for OWPA, whereas a maximum of the electric field for PWPA takes place along the z-axis. In fact, the OWPA electric field is skewed and is at an angle of 41° at x–z, y–z, and y–x plane. It also suggests that the Poynting vector for OWPA is not along the z-axis, but it is skewed along the z-axis.

It is evident that OWPA does not have a beam in direct LOS, so in **Figure 18(b)**, two PWPA at an angle of 41° are placed as a receiver antenna to pick up the signal from OWPA. This ensures a maximum reception of the signal from the OWPA antenna. The angle of 41° alignment is chosen as the main lobe direction of OWPA is at 41°. In this presentation, O1 is the OAM wave patch antenna, and P2 and P3 are the plane wave patch antennas. Moreover, the RF propagation path modeling for OWPA(O1)–PWPA(P2)–PWPA(P3) clearly shows the direction of power flow and the establishment of a communication path, as shown in **Figure 19(c)**. The OWPA– OWPA configuration depicted in **Figure 19(b)** shows that maximum energy reception does not happen if we consider choosing both Tx and Rx antennas as OWPA in direct line of sight (LOS). In contrast, this is not the case for plane wave propagation, as portrayed in **Figure 19(a)**.

It allows us to monitor the simulated and measured transmission and reflection in both plane wave and OAM wave propagation scenarios. Firstly, PWPA–PWPA simulated and measured reflection coefficients are shown in **Figure 20(a)**. Reflection coefficients are well below 20 dB for both Tx–Rx pairs, while the transmission coefficient is just above 30 dB. In **Figure 20(b)**, the results are presented for OWPA (O1)–PWPA (P2)–PWPA (P3) configurations, which are one of the desired arrangements for the OAM receiving scenario. Both simulated and measured transmission

#### **Figure 18.**

*(a) Far-field radiation condition in simulation to capture fields for PWPA–PWPA; (b) far-field radiation condition in simulation to capture fields for OWPA–PWPA–PWPA; (c) carpet plot of the electric field for PWPA and (d) OWPA on xz-plane gives visualization that PWPA has a maximum of propagation along the z-axis, whereas OWPA has no propagation along the z-axis. Propagation of OWPA is at an angle from the center of the z-axis.*

**Figure 19.**

*RF propagation path modeling for (a) PWPA–PWPA, (b) OWPA–OWPA, (c) OWPA (O1)–PWPA (P2)– PWPA (P3). All the antennas are at the far-field distances, E-field is considered in depiction where red indicates maximum value, and blue represents minimum value.*

#### **Figure 20.**

*Simulated and measured transmission and reflection coefficient of Tx–Rx pair (a) PWPA–PWPA and (b) OWPA (O1)–PWPA (P2)–PWPA (P3).*

parameters for O1–P2 and O1–P3 are just above 30 dB, whereas all the reflection parameters are below 20 dB for all O1, P2, and P3. The frequency shift between the measured and simulated results is approximately 5 MHz, whereas the magnitude difference is negligible. All the measured results follow as designed and expected through simulation. The power received from two PWPA is combined, and the phasedetection method has to be used further in the system to know the order of OAM [70].

Furthermore, a comprehensive measured comparison of different configurations OWPA–OWPA, OWPA–PWPA, and OWPA–PWHA is shown in **Figure 21**. Among all these configurations, one of the least received signals is observed in OWPA–OWPA and the RF propagation path model, whereas the most robust signal is received in the case of OWPA–PWHA at 30 dB. OWPA–PWPA configuration has received a signal level just above OWPA–OWPA at 50 dB, as depicted in **Figure 21**.

It is worth noting that the acquired transmission behavior in **Figure 21** clearly shows the pattern of two peaks with a valley for all configurations, forming the M-shape as the desired characteristics for vortex reception, which cannot be observed in the O1–P2–P3 reception configuration in **Figure 20(b)**. The signal received at individual two PWPA should go through further a signal power combining technique to get the desired OAM pattern. The measurement setup for two configurations, PWPA–PWPA and OWPA–PWHA, is presented in **Figure 22**. The rest configuration is adopted similarly in measurement.

*Orbital Angular Momentum Wave and Propagation DOI: http://dx.doi.org/10.5772/intechopen.104477*

**Figure 21.**

*Measured transmission and reflection coefficient of Tx–Rx pair OWPA–PWPA, OWPA–PWHA, OWPA– OWPA.*

**Figure 22.** *Measurement setup in SATIMO lab and for Tx–Rx configuration.*
