Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 247

The Cerenkov radiation, also called the Cherenkov (or Cherenkov) radiation, in the DPS medium is generated from the charged particles traveling with a velocity faster than the velocity of the EM‐wave in that medium [B.12]. The radiation from a leaky‐wave antenna closely follows the radiation mechanism of Cerenkov radiation. Likewise, the planar transmission lines radiate the Cerenkov type radiation within a substrate resulting in high substrate loss [B.13]. It is discussed in subsection (9.7.3) of chapter 9. In a DPS medium the directions of the radiated power, i.e. the direction of the Poynting vector, and the wavevector are in the same direction. However, in a DNG medium, these directions are opposite to each other, giving inverse Cerenkov radiation [J.3]. Both Cerenkov radiation and inverse Cerenkov radiation are similar to the shock waves of supersonics generating the radiation cone.

Figure (5.15a) shows the generation of the radiation cone of the spherical wavefronts by a moving charge, with velocity V_c, in a DPS medium. The charged particle velocity V_c is greater than the phase velocity V_p of the EM‐wave in a DPS medium, i.e. V_c > V_p( = c/n). The positive refractive index is n, and c is the velocity of EM‐wave in free space. The locations P₀–P₄, on the positive x‐axis, are successive positions of the moving charge at time t₀–t₄. During the time interval T = (t₄ − t₀), the spherical wavefront acquires radius P₀N = V_pT = (c/n)T, while the charged particle travels a distance P₀P₄ = V_cT. Figure (5.15a) also shows other spherical wavefronts for the time sequence for t < T. Following the Huygens principle, the inclined tangential wavefront of the secondary radiation is NP₄. The wavevector (k), i.e. P₀N, is normal to the wavefront NP₄. It forms a Cerenkov angle ϕ_c at P₀ or angle θ_c at P₄. It is obtained from the triangle P₀N P₄:

(5.5.41)

Figure (5.15b) shows the directions of the wavevectors and Poynting vectors of the upper and lower radiation from the charged particle moving in the positive x‐direction. Cerenkov radiation is a linearly polarized EM‐wave with an electric field component parallel to the path of the charged particle, i.e. the x‐axis. Cerenkov radiation is directive in the forward direction within the cone angle 2ϕ_c. Similarly, a leaky‐wave antenna is highly directive. The beam becomes narrower for the higher value of the refractive index n.