Читать книгу Fundamentals of Terahertz Devices and Applications - Группа авторов - Страница 32

The fabricated surface of the lens can be analyzed independently of the rest of the antenna by the accurate characterization of the actual fabricated surface. Surface profilometers are used to map the 3D profile of the lens surface with high resolution. The basic parameters of this surface in terms of radius R, diameter of the aperture D, height H are computed with an optimization procedure using, for example, the optimization toolbox in Matlab and a basic cost function to minimize. The cost function compares the fabricated surface and an ideal spherical surface until it finds the best fitting sphere. By evaluating the error between both surfaces we can have a sense of how spherical the fabricated lens is, and identify flaws that can improve the fabrication process. For example, Figure 2.25a shows the profile of a fabricated shallow lens of D = 2.6 mm measured with a profilometer and its error surface obtained when compared with a perfect sphere. In this case, since the edges of the lens did not provide a good fit with the sphere, an improvement of the performance could be achieved by adjusting the illumination to minimize the lens area illuminated. This adjustment can be achieved by decreasing the lens thickness W, which will decrease the illumination of the lens edges, i.e. increase the edge field taper.

Figure 2.25 (a) Surface measured of the fabricated lens of D = 2.6 mm. The error surface defined as the difference between the measured surface and a perfect sphere is shown underneath. (b) Computed radiation pattern of the measured lens surface and the measured radiation pattern of the whole lens antenna at 1.9 THz from [26].

One can have an estimation of the effects of the aberrations in the radiation pattern by translating the error surface into a phase error surface. We can assume that the field distribution on top of the aperture has a Gaussian field distribution of a certain taper, for example −14 dB, with a phase of , where is the distance from the phase center of the waveguide feed to the fabricated lens surface and is the distance from the fabricated lens surface to the lens aperture plane. The resulting radiation pattern is obtained by calculating the Fourier transform of this resulting field distribution. From these fields, the directivity and Gaussicity loss can be computed to have a sense of how our antenna would perform. In this example, the small lens of 2.6 mm aperture would result in a directivity loss of 0.2 dB and a Gaussicity loss close to 2%. Figure 2.25b shows the radiation patterns of the fabricated lens at 1.9 THz for a 2.6 mm diameter lens using the method explained compared with the measured radiation pattern.

Figure 2.26 Photographs of different lens antenna prototypes fed by leaky‐wave feeds (a) at 550 GHz with lens laser micro‐machined [33].

Source: Alonso‐DelPino et al. [33]; IEEE.

(b) At 550 GHz with lens fabricated using DRIE silicon micromachining [25].

Source: Llombart et al. [25]; IEEE.

(c) At 1.9 THz integrated with tripler all in silicon micromachining package [26].

Source: Alonso‐delPino et al. [26]; IEEE.

(d) At 550 GHz integrated with a piezo‐electric motor in order to perform beam‐scanning [48].

Source: Alonso‐delPino et al. [48]; IEEE.