Leaky-wave antennas (LWAs) are guiding structures  that radiate due to leakage caused by a small slit or cut on the mode guiding structure . As the wave travels on the guiding structure (see Fig. 3.22), it experiences exponential decay due to the aforementioned leakage. In general, the rate of energy leakage is very small along the guiding path, implying the need for long LWA antennas, viz. several periodic cells long. Early versions of LWAs were standard rectangular waveguides with a periodic set of slits on one of their faces . Each slit radiates a small portion of the waveguide mode’s energy as the mode travels, and its size, periodic arrangement, and orientation provide for bandwidth, beam, and radiation efficiency control. A key parameter is the propagation constant of the guided wave, p, and as noted in Fig. 3.22, в must be kept smaller than ko, the free-space wave number. Typically, we write the LWA's propagation constant in its complex form, к = b - ja . The attenuation constant represents the loss of energy due to radiation. For uniform waveguides, the leakage is usually exponential and a has a small value. But for other guiding structures, a can attain a larger value, implying stronger radiated fields. Typically, the beam direction of the LWA array changes with frequency, and this is because the phase delay or period length also changes with frequency. Consequently, LWAs can be scanned by changing the frequency of operation.
Figure 3.22 Operational principle of LWAs. Their radiation can be attributed to a complex propagation constant with radiation occurring when the LWA propagation constant is less than the free-space propagation wavenumber. Reprinted with permission from Ref. 41, Copyright 2007, McGraw Hill.
We can distinguish two types of LWAs. One class refers to uniform guided structures and another to LWA constructed of several periodic unit cells. A uniform LWA may be a waveguide that contains a longitudinal slot for radiation and supports a fast wave only. These antennas radiate as soon as the wave reaches the opening in the waveguide. Periodic LWAs can support forward and backward waves. Of course, the period and unit cell structure (see Fig. 3.23) can be adjusted to control radiation and frequency of operation. It is important to note that radiation from these LWAs is not due to the dominant DBE or MPC slow wave mode. Instead, it is necessary to also consider all harmonics of the dominant slow wave. These harmonics have the propagation constants
where p is the periodicity of the structure.
Figure 3.23 Coupled lines printed on a ferrite substrate having the material properties 4pMs = 1000 G, loss linewidth DH = 10 Oe, relative permittivity er = 14, and dielectric loss tangent tan de = 0.0002. The internal DC magnetic field Hi = 1450 Oe is assumed to be in -z-direction, normal to the ground plane. Unit cell dimensions are l1 = 120, l2 = 200, w1 = 60, w2 = 20, w3 = 30, s1 = 105, s2 = 10 (mils). Reprinted with permission from Ref. 43, Copyright 2013, IEEE.
As noted above, LWAs support both forward and backward waves. But this leads to multiple radiation beams, one for the forward and another for the backward mode. A way to suppress the backward mode is to employ a periodic cell that is anisotropic. More specifically, the MPC unit cell has this property. With this in mind, a non-reciprocal magnetic-biased LWA was proposed in Ref.  and demonstrated by Apaydin et al. . Non-reciprocity was achieved using the approach described in Fig. 3.9. That is, two non-identical transmission lines with magnetic biasing led to unequal coupling coefficients K1 П K2, which eventually provides non-reciprocal MPC modes. Figure 3.23 shows the unit cell design comprising a pair of CTLs on a biased ferrite substrate. The transmission lines are printed on a 100 mil thick commercially available CVG substrate. The material properties of the CVG, as specified by the manufacturer are as follows: saturation magnetization 4nMs = 1000G, loss linewidth DH = 10 Oe, relative permittivity e,. = 14, and dielectric loss tangent tan 8e = 0.0002. The narrow linewidth of the magnetic material was specifically chosen to minimize losses.
The unique feature of the MPC mode LWA antenna in Fig. 3.23 is its scanning capability via an external biasing voltage on the ferrite substrate. This external bias serves to change the effective constitutive parameters of the scanning angle versus frequency
. The dispersion diagram of the propagating modes by the subject LWA is given in Fig. 3.24 and includes several harmonics. One of them represents the fast/leaky-wave mode. Also, the black and blue curves refer to the n = ± 1 and n = -1 forward and backward propagating modes, respectively. We also observe the spectral asymmetry around the 3.7-3.78 GHz band. This is associated with the n = -1 fast wave.
To use the LWA as a transmitting antenna, as in Fig. 3.24, it can be fed at Ports 1 or 2 (Fig. 3.23) and terminated on Ports 3 or 4 with a matched load ZL = 50 W. As already noted, spectral asymmetry
suppresses backward radiation due to reflected waves (Д— > k0). But
in the receive mode, only forward waves are supported (Д+ < k0). These forward waves will, in turn, be guided with the leftover signal dissipated at the matched load termination ZL.
Figure 3.24 Dispersion diagram of the coupled microstrip lines unit cell in Fig. 3.23. Reprinted with permission from Ref. 43, Copyright 2013, IEEE.
Another important feature of the antenna is its capability of scanning at a fixed frequency by changing the external biasing magnetic field. The magnetic biasing can control the magnetic property of the ferrites and can shift the ш-fi diagram to higher or lower. As shown in Fig. 3.25, the antenna gain remained reasonably constant with respect to frequency change. Thus, frequency- independent operation of scanning with magnetic biasing is expected to be observed in these types of MPC-based LWAs.
Figure 3.25 Simulated versus measured TX/RX antenna gain as a function of frequency. Reprinted with permission from Ref. 43, Copyright 2013, IEEE.