How to Obtain the Actual Current Components

The voltage spectrum of the incident wave taken over the finite array is shown in Fig. 4.5c. It contains mainbeams in the forward and specular directions corresponding to the Floquet currents only (see Fig. 4.4). 

Similarly, the voltage spectrum from the two semi-infinite arrays is shown in Fig. 4.5d. We observe two smaller beams at = 1, that is, in the endfire directions. Thus, the two semi-infinite arrays will try to propagate waves along the array structure. However, as illustrated in Fig. 4.2, many evanescent waves with different Tcxisx) are capable of propagating. They are distinguished by the magnitude of their scan impedance depicted in Fig. 4.2 and shown specifically in Fig. 4.5e. 

The discussion above served primarily to explain how surface waves are established on a finite periodic surface, namely as the ratio between the voltages induced by the two semi-infinite arrays and the impedances of possible surface waves. 

This is not necessarily the way we actually calculate the element currents. In fact this was done by direct calculations of the currents in the finite array in question by using the SPLAT program discussed in Chapter 3. Typical examples have already been presented in Figs. 1.3b and 1.3c. Clearly the currents in Fig. 1.3c are seen to be highly erratic. To find out what current components actually are contained in such a distribution, we simply ran a Fourier analysis and obtained the current spectrum shown in Fig. 4.5f. While the current spike at Tex = 0.707 is easy to associate with the Floquet currents obtained for an infinite array exposed to a plane wave incident at 45°, the two other spikes at Tex = 1.25 remained somewhat of a mystery until the explanation in Section 4.6 above was introduced. 

Finally, the Fourier analysis shows that we in addition to the Floquet and surface waves also obtain a small amount of additional currents at the edges of the array. They are usually associated with reflections of the two surface waves and the Floquet currents at the edges of the array. We have denoted them end currents.  

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