high‐gain mm‐wave antenna arrays can be realized over physically small areas because the associated wavelengths are small (recall that the gain of an aperture antenna – Gain = 4π Area/λ2). In fact, given the inherent high propagation losses of their radiated fields, high‐gain antennas are needed for virtually all mm‐wave communication systems. As a result, it has become imperative to develop mm‐wave beamforming networks to support multi‐beam mm‐wave antennas. In the current 3GPP standards for 5G mm‐wave, for example, user equipment (UE) or terminals are required to have an array antenna with between 8 and 64 elements [17].
1.6 THz Antennas
With 6G data rates promised to be even higher than those of 5G [1–3], a much wider spectrum is needed to accommodate 6G expectations. Unfortunately, a large currently unoccupied spectrum does not exist below 100 GHz. Consequently, it is widely expected that 6G will occupy a significant part of the THz spectrum [2]. Along with terrestrial‐based communication systems, it is anticipated that THz systems will also play a major role in space‐based communications [18, 19].
Currently, the most common definition of the THz band is that it consists of frequencies from 0.3 to 3.0 THz. Recall that the wavelength at 0.3 THz (300 GHz) is just 1.0 mm. Owing to the fact that THz wavelengths are even smaller than the mm‐wave ones, very narrow multiple beams with low probability of intercept (LPI) can be generated from very physically small areas. Beam steering and target tracking again will be indispensable features for THz antennas.
Referring to Figure 1.9, signal attenuation in the lower portion of the THz range is even more severe than in the mm‐wave band. Thus, high‐gain antenna arrays are even more necessary for anticipated 6G operations. Other important related THz technologies that must also be developed to address 6G expectations are high power sources and highly sensitive receivers [20]. Feeding a large array of THz antenna elements of 0.5λ in size using a corporate network is a daunting engineering task. Therefore, it has not been favoured to date. Instead, a more promising approach is to employ an electrically large lens fed by a simple radiating element such as a dipole or a slot or even a small array. To ease the problem of the precise alignment of the antenna and lens, one could integrate the antenna feed with the lens. Antennas with this characteristic are known as integrated lens antennas [20–22].
1.7 Lens Antennas
A number of different types of lens antennas operating in the mm‐wave and THz bands have been reported [21–25]. These include the elliptical lens, extended hemispherical lens, and Fresnel zone lens. Each has its own unique physical and performance characteristics.
A homogeneous elliptical lens has two focal points. It can transform the radiation pattern of a feed placed at one focal point into a plane wave exterior to it propagating in the direction of the second focal point. Assuming a represents the major semiaxis, b represents the minor semiaxis, L represents the distance between the focal point of the feed to the centre of the ellipsoid, and n is the index of refraction of the dielectric from which the lens is fabricated, one has the following relationships:
(1.1)
(1.2)
An integrated elliptical lens antenna is obtained by cutting off the part of the dielectric below the bottom focal point and placing the feeding antenna beneath it. As depicted in Figure 1.10, only rays that hit the surface of the elliptical lens above the plane of its maximum diameter, denoted herein as its waist, are collimated. The portion of the radiated fields intersecting the lens below its waist is not collimated, but rather propagates along undesired directions or excites surface wave modes, thus giving rise to side lobes or other perturbations in the lens’ radiation pattern [20]. One solution to solve this problem is to control the beamwidth of the feed in order that the majority of its radiated energy falls within the angular range above the waist of the lens.
Figure 1.10 Illustration of (a) an integrated elliptical lens antenna and (b) an extended hemispherical lens antenna.
Another issue arising from the internal reflections at the surface of an elliptical lens is the matching of the feed. One inherent characteristic of elliptical lenses is that all of the reflected rays that pass through the second focal point are reflected back to the first focal point. This reflected power causes a substantial mismatch to the feed impedance. A classical method to address this issue is to enclose the elliptical length with a matching shell that is a quarter‐wave thick. The shell dimensions are specified according to the following equations:
(1.3)
(1.4)
where n1, n2, and nmatch represent the refraction indexes of the lens, the air, and the matching shell. The main drawback of this approach is that the improved matching performance can only be maintained within a relatively narrow bandwidth. To improve the bandwidth, one can incorporate multiple consecutive matching layers to perform a gradual transition between the two dielectric constants across each interface.
Since the collimation from an elliptical lens only occurs for the portion of the wave front that impinges on its front surface, the part below its waist can be replaced with a cylinder. Furthermore, the top elliptical part, the hemi‐ellipse, can be approximated by a hemisphere. This modification significantly reduces the fabrication complexity. The difference in the height of the hemi‐ellipse and the hemisphere can be compensated by the height of the cylindrical extension. This new lens is known as an extended hemispherical lens. It turns out to be a rather good approximation to a true elliptical lens, although it tends to present a slightly lower directivity compared to one having the same diameter. The relationship between the radius of the hemisphere, R; the height of the cylinder under it, L; and the refraction index of the lens material, n, is given by
A lens similar to the extended hemispherical lens is known as a hyper hemispherical lens. In contrast to Eq. (1.5), the cylindrical extension length is now given by [23]:
The rays at the output of the hyper hemispherical lens are not collimated. Therefore, the beam that it generates is much broader than that of the extended hemispherical lens. Nevertheless, it does sharpen the beam radiated by the feed antenna and increases its gain by a factor of n2. However, unlike the collimating lenses, the directivity of this lens does not increase with the lens size, i.e., its aperture size. The hyper hemispherical length satisfies the Abbe sine condition so the lens itself is free from coma aberration when the feed is transversely displaced from the lens axis [25]. Therefore, it is well suited for beam steering.
It must be noted that Eqs. (1.5) and