Dielectric Concentrator for Cherenkov Radiation

We report on a dielectric target that concentrates Cherenkov radiation into a small spatial area. In contrast to traditional devices, this target can focus almost all of the radiation without using additional lenses or mirrors. We consider the case where radiation is produced by a point charge moving along the axis of a cylindrical channel inside an axially symmetrical target. The specific form of the target is determined using the laws of ray optics. The field is calculated using an aperture integration method that can determine the field near the focus. Typical field plots and the spatial distribution of the field outside the target are presented. We demonstrate that at terahertz frequencies, this concentrator can increase the field magnitude by up to at least 2 orders of magnitude relative to that on the surface of the target.

Figure 1

(a) Geometry of the problem: the target shape $r(\theta )$ is such that the target concentrates the CR onto the focus. (b) Geometry and rays of the “key” problem: CR from a charge moving in a cylindrical channel in an unbounded medium. (c) Geometry and rays of the “expanded” problem: a point source is placed at the focus, and the surface that transforms the divergent ray beam into a parallel beam is determined. (d) Final target that is extracted from the expanded target (c), two narrow rays (black solid) that converge to the focus point, and two multiple reflected rays (blue dashed) that do not converge to the focus.

Figure 2

Field behavior along the ray determined by the angle $\theta =170°$ calculated via the ray optics formulas (8) (RO) and the aperture integration approach (12) (AI). Problem parameters: $|q|=100\mathrm{pC}$, $ϵ=2+0.001i$, $\mu =1$ (Teflon), $\beta =0.8$, $x_{\max }=25\mathrm{cm}$, $z_{\mathrm{f}}=8.3\mathrm{cm}$, $f=5\mathrm{cm}$. The value $l=17.8\mathrm{cm}$ corresponds to the focus point.

Figure 3

Distribution of the absolute value of the field $|E_{\theta }|$ calculated using the aperture integration approach (12). The frequency $\omega =2\pi \times {10}^{12}{\mathrm{s}}^{-1}$, $a=0.03\mathrm{cm}$, and the other problem parameters are the same as in Fig. 2.