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Fundamentals of Terahertz Devices and Applications


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      As mentioned in Section 2.3, the amount of energy reflected inside of the lens depends on how the lens feed illuminates the lens surface. The top part of the lens is the most efficient part of the lens since it is where the transmitted energy is the highest, and the least efficient area is the lateral part, leading to high reflected energy. Thus, in order to have a highly efficient lens antenna, we need a feed that illuminates only the top part of the lens, a.k.a. a shallow dielectric lens.

      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 images, [38]. Under this condition, the couple of TE/TM leaky‐wave modes can propagate with same phase velocity, creating a nearly uniform phase distribution in the aperture. It has been seen that the generated aperture field is also very well polarized, due to a compensation effect between the TE and TM modal tangential field components [39]. However, this type of LWA also generates an undesired spurious TM0 leaky‐wave mode, conceptually associated with the transverse electromagnetic (TEM) mode of the perfectly conducting walls parallel plate waveguide [43]. This mode radiates near the Brewster angle creating spurious lobes in the E‐plane reducing the beam efficiency. An iris containing a double slot for single‐polarization or two double slots for dual‐polarization will suppress the spurious TM0 mode and provide the matching between the waveguide's fundamental modes and the silicon interface [44].

      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 images and use the approximate analytical equations provided in [46]. The value of this propagation constant depends on the impedance, ZL, seen from the top of the half‐wavelength cavity in the equivalent transmission line model. For a dielectric quartz (being images) super‐layer with a quarter wavelength thickness, this impedance is images. The pointing direction of the leaky‐wave modes is in this case 17°. If we need a more directive antenna, a lower ZL is required in order to achieve less attenuated mode, implying stronger multiple‐reflections (i.e. more resonant), and thus, less bandwidth.

Graphs depict the 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, kd=k0r.