**3.4 Analyses summary**

The plots of the maximum and first EM cluster intensity distributions in **Figures 9(b)** and **(c)**, **10(b)**, **11(b)** and **(c)**, and **14** reveal important regions/points in the Vivaldi structure with high-density EM flow and associated first-order scattering, which contribute to the main EM energy proportion of the total radiation. As seen in **Figure 14**, the scattering degree at the transition positions can be evaluated primarily by 3–6.5 dB abrupt changes in magnitude. This scattering degree can also be assessed based on the cluster intensities in **Figure 16** and with a reference to the first-cluster intensities in **Figure 14**. The magnitude reduction along the Vivaldi edges in **Figure 14** indicates the EM energy transfer out of the antenna conducting element into the free space.

The propagation of EM first clusters in the structures can be observed and quantified in terms of field vector direction and magnitude of first clusters based on **Figures 10** and **11** and ToA of first clusters based on **Figures 12** or **13**. All three space distributions of field vector direction, magnitude, and ToA of first clusters in these figures provide adequate information of propagation of EM first clusters in the observed space, and the important features of the propagation can be recognized. For example, as seen in **Figures 10(b)**, **11** and **12(b)** and **(c)**, and also in **Figure 13**, the propagation process of first clusters on the metal plane of the Vivaldi antenna and the degree of local EM flows were revealed. These also revealed intensity of scattering fields at the antenna aperture, and geometric features of the field propagation were also revealed such as the flare effect of the EM flow propagating away from the Vivaldi patches at the aperture. This is a significant factor in the reduction of antenna directivity.

The propagation progress investigation on the main propagation path, such as the results shown in **Figures 15** and **16**, not only provides more details of propagation of the first clusters, but it also reveals formation of other clusters due to scattering at the detail elements of the structure. Additionally, features of the formed clusters are also observed and evaluated. Based on these information, higher-order scattering components and corresponding propagation paths can be recognized or inferred. For example, the H cluster formation in **Figure 16** reveals the higher-order scattering at the lateral edge and the Vivaldi edge, as illustrated in **Figure 17**. The scattering on the lateral edge causes partial radiation in unwanted directions and reduces the total directional characteristic.

Based on this knowledge about mechanism in propagation and radiation on the structure and influences of the structural detail elements, the solutions can be proposed to increase the advantage features and to reduce the disadvantage features of the propagation to improve the total responses of the antenna. For example, methods to reduce the flare effect at the Vivaldi antenna aperture are adjustment of the Vivaldi p-factor, introduction of a core element, conversion of the antenna into a double-slot structure in [11], and insertion of a material structure at the antenna aperture to adjust the directions and/or velocities of the local EM flows. The estimated results for magnitude, ToA, velocity, and direction of EM flows propagation at specific regions at conducting edges and/or in the radiating aperture support the effectiveness of these refined adjustment methods. Another example solution for the higher-order scattering on the lateral edge was proposed. By addition of 45<sup>0</sup> ripples on the lateral edge in [11], a part of this energy is redirected into the antenna end-fire direction. This improves the antenna gain in a certain frequency band.

It also reduces the EM energy portion coming back to the source, thereby improving the S11 characteristic.
