Fundamentals of Terahertz Devices and Applications. Группа авторов

Fundamentals of Terahertz Devices and Applications - Группа авторов


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rel="nofollow" href="#ulink_14413124-b500-5198-822e-7f6b93e143c5">(2.22)equation

      For a feed placed in the center of the coordinate system, the propagation vector see Figure 2.3b inside and outside of the lens are defined as:

      (2.23)equation

      (2.24)equation

      The normal vector to the lens surface defined in cylindrical coordinates for an elliptical lens is:

      (2.25)equation

      Then, the transmitted field can be expressed as:

Schematic illustration of (a) Scheme of the critical angle calculation on an elliptical lens. (b) Subtended critical angle vs permittivity of the elliptical lens.

      (2.31)equation

      As an example, Figure 2.4b shows θ0 as a function of the relative permittivity of the elliptical lens. It can be observed how the lower the permittivity, the smaller the angle is, and therefore, a more directive feed will be required to efficiently illuminate the lens above the critical angle.

      2.2.2.2 Spreading Factor S(Q)

      (2.32)equation

      (2.33)equation

      where Si represents the amplitude of the Poynting vector. The same can be done for the reflected power towards inside of the lens:

      (2.34)equation

      (2.35)equation

      and for the transmitted power:

      (2.36)equation

      (2.37)equation

      The relation between the incident, reflected and the transmitted power density is represented in Figure


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