Anomalous Power Flow and “Ghost” Sources

It is demonstrated that EM radiation from complex sources can result in real power in restricted regions of space flowing back towards the sources, thereby mimicking “ghost” sources. This counterintuitive mechanism of radiation does not rely on backward waves, as ordinary waves carry the power. Ways to harness the effect by making it directional are presented, together with selected applications, of which deception is a prime example due to the nature of the phenomenon. The concept can be applied to other areas, such as mechanics, acoustics, etc., and can be realized with available technology.

Figure 1

Radiated power $P$ flow lines for an infinite array of sources aligned along $y$ (vertical). Only one cell is presented, and the filamentary source is located at the center of the area shown, which corresponds to a vertical extent $d=2.8\mathrm{cm}$, and horizontal ($x$-directed) coverage 3.8 cm. (a) 8 GHz, (b) 10 GHz, (c) 11 GHz, and (c) 15 GHz. At around 10 GHz, an anomalous power flow pattern develops, where power half a wavelength away from the array flows towards each source, and is accompanied by vortex formation. Away from 10 GHz, a “normal” power flow pattern exists.

Figure 2

Exact power flow $P_x$ for three dipole sources with $d=\lambda =1\mathrm{cm}$. (a) Unconstrained surface of $P_x$ on both sides of the array, (b) surface of $P_x\ge 0$. The hole and complementary dot locations are the places where backward power flow takes place.

Figure 3

Radiated power $P$ flow lines for an infinite array of filamentary sources in the presence of a 1 mm thick quartz slab of $\epsilon =4.0$. The sources are located on the left of the slab, 3 mm away from the face. Only one cell is shown, and the area corresponds to a vertical extent $d=2.8\mathrm{cm}$ and horizontal ($x$-directed) coverage 3.1 cm. (a) 8 GHz, (b) 9 GHz, (c) 10 GHz, and (c) 11 GHz. At around 9 GHz, an anomalous power flow pattern develops on the right-hand side, where power flows towards each source, and is accompanied by vortex formation. Away from 10 GHz, a “normal” power flow pattern exists. At 11 GHz, power reversal occurs on the side of the array, but in a less dramatic fashion, in the surroundings of the plane of the sources.

Figure 4

Phase of electric field radiated by a 9 GHz infinite array of filamentary sources in the presence of a 1 mm thick quartz slab of $\epsilon =4.0$. The sources are located on the left of the slab, 3 mm away from the face. Only one cell is shown, of area 2.8 cm (vertical) by 3.1 cm (horizontal). HFSS generated phase distribution indicates that backward power is not carried by backward wave means. The anomalous phase shown in the direction of anomalous power flow [see Fig. 3b] result in ordinary wave propagation everywhere.

Figure 5

Radiated power $P$ flow lines for a four element corporate feed with 0.5” separation between apertures. Operation is at (a) 21 GHz and (b) 22 GHz. The back power flow effect is apparent at 21 GHz, both from the external vector direction, and from the power unbalance on the different arms. At 20 GHz (not shown) and 22 GHz, the power distribution in the different arms is pretty much uniform. (c) Detail of the 21 GHz $P$ flow lines in the neighborhood of the central elements showing expected backward power regions plus an additional backward power region in the central plane, roughly a wavelength away from the aperture plane (note that the power in this region is pointing towards the aperture plane not towards the sources).

Figure 6

Potential applications of “ghost” sources. (a) Deception, making believe an observer that we are in the North when in reality we are in the South; (b) creating a “ghost” feed for a shaped reflector in order to create a high gain antenna. The R’s denote a number of properly designed radiating sources.