# A Low-Profile Dielectric Resonator Antenna Array for OAM Waves Generation at 5G NR Bands
## 3 Results and Discussion
### Mode Purity  
Generating OAM waves with mode purity is crucial to make sure the modes are orthogonal to one another. Mode purity is the main parameter to measure the consistency of information transmission using OAM waves. Several factors can be considered to generate high purity of OAM modes, such as the number of elements, transmitting antenna size, receiver size, and observation plane size [34; 35].  
In [36], the author verified the importance of a higher number of array elements in mode purity. Ripples will occur in the radiation pattern if the number of array elements is not enough to generate the desired OAM mode. The minimum number of elements required to generate a specific OAM mode can be found using the following equation:  
\[N\geq 2\left|l\right|+1 \tag{1}\]  
where \(N\) is the number of array elements and \(l\) is the mode number. As the number of elements in the array increases, the phase difference between the adjacent elements will be smaller, thus reducing the phase ambiguity effect. However, increasing the number of elements in the array will increase the size of the antenna, and the design will become more complex. Hence, special care during the simulation process needs to be taken to determine how many elements are required for a certain OAM mode to confirm that the mode has high purity. Another factor that can influence mode purity is the transmitting array antenna size and observation plane [36]. Decreasing the radius of the array will increase the mode purity. However, there is still the problem of mode divergence.  
In this paper, the phase distribution obtained from the CST simulation is used to analyze the mode purity by using Python programming. The mode purity of the OAM beams is calculated by using Fourier transform, as given by the following equations:  
\[\Psi(\O)=\frac{1}{\sqrt{2\pi}}\sum_{l=-\infty}^{\infty}A_{l^{\mu l\varnothing}} \tag{2}\]  
\[A_{l}=\frac{1}{2\pi}\int_{-\pi}^{\pi}\Psi(\O)e^{-jl\O}d\varnothing \tag{3}\]  
where \(\Psi(\O)\) is the angular distribution of the EM wave and \(A_{l}\) is the distribution of angular momentum of different OAM modes. Generally, generated OAM waves consist of multiple  
Figure 9: Far-field results at 3.56 GHz. (**a**) Simulated and measured 2D radiation patterns in \(E\) plane; (**b**) simulated 3D radiation pattern.  
OAM modes. The proposed DRA generated OAM mode +1 with a purity of 53.87%, as shown in Figure 10. The remaining 46.13% is distributed over other adjacent modes in the spectrum. The antenna was designed to produce OAM mode +1; hence, the ratio of purity is more for mode +1 when compared to the OAM wave as a whole.  
Table 2 compares the performance of the proposed design with some previous works on OAM antennas in terms of frequency, antenna dimension, gain, mode number, mode purity, and measurement of phase and intensity distributions. It is evident that the design of this paper has a small size, wide bandwidth, and high gain. Moreover, the proposed antenna manages to generate OAM at mode +1 with high mode purity. From the literature, it can be seen that all of the previous works disregarded the OAM mode purity information.