techniques (laser and DRIE photolithography). On the other hand, since the top part of the lens is the most efficient in terms of reflection, we need a feed radiating in an infinite dielectric medium with very large directivity in order to illuminate properly this lens. For example, a lens with a solid angle of 20° will need a cosnθ feed with 19 dB directivity. Generating this type of radiation with low loss is challenging at high frequencies. In Ref. [25], a very directive lens feed, radiating most of the energy well below the air‐dielectric critical angle, with wide bandwidth and a very low‐loss at THz frequencies was proposed using a Fabry–Perot/leaky‐wave concept.
Figure 2.12 Sketch of the silicon lens antenna fed by a leaky‐wave feed geometry and its radiated field across the antenna.
Leaky wave antennas (LWAs) [38], also referred as electromagnetic band‐gap (EBG) antennas [39], Fabry–Perot Antennas (FPA) [40] or resonant cavity antennas [41], use a partially transmissive resonant structure that can be made of a thin dielectric superstrate [38] or by using frequency selective surfaces (FSS) [42] to increase the effective area of a small antenna. These antennas are used to achieve high directivity from a point source by the excitation of a pair of nearly degenerated TE1/ TM1 leaky‐wave modes. These modes propagate in the resonant region by means of multiple reflections between the ground plane and the superstrate, while partially leaking energy into the free space. The amount of energy radiated at each reflection is related to the LW attenuation constant and can be controlled by the FSS sheet‐impedance or the dielectric constant. At the resonant frequency, where the real part and imaginary part of the complex leaky‐wave wavenumber are similar, these antennas radiate a pencil beam. For the air cavity of thickness h0 and dielectric super‐layer of thickness hs, the maximum directivity at broadside is achieved at the resonant condition, i.e. the thickness of the resonant air cavity is h0 = λ0/2, and that of the super‐layer is
In a LWA, the maximum directivity is directly proportional to the super‐layer permittivity but inversely proportional to the relative bandwidth. This resonant behavior is well known as the main drawback of LWA and limits their use to narrowband applications. However, this drawback can be partially solved when the leaky‐wave antenna is radiating in a semi‐infinity medium [25]. Indeed the use of a resonant air gap cavity for small antennas radiating into a dense medium ensures a highly directive beam with most of the energy being radiated for angles smaller than the air‐dielectric critical angle over bandwidths ranging from 10% to 40% depending on the lens material [45].
2.4.1 Analysis of the Leaky‐wave Propagation Constant
In this section, we will analyze the propagation constant, kρlw, of the leaky waves propagating in the air cavity. For this evaluation the propagation constant, we will approximate the aperture field of Fabry–Perot leaky‐wave antennas as
If instead of a dielectric super‐layer stratification we consider an infinite layer of silicon, the impedance seen on top of the cavity is
Figure 2.13 Real and imaginary parts of the propagation constants klw of the leaky‐wave modes present in an air cavity (h = 275 μm) and infinite silicon dielectric medium. On the left axis, klw is normalized to the free space propagation constant, k0, whereas klw (shown in the right axis) is normalized to the propagation constant in the dielectric,
Figure 2.14 Input reflection coefficient of a waveguide loaded with a double‐slot iris in the presence of an air cavity (h = 275 μm) shown in [25]. The feed dimensions are: Rin = 109.7 μm, α = 50° and
