Information Carried by Electromagnetic Radiation Launched from Accelerated Polarization Currents

We show experimentally that a continuous, linear, dielectric antenna in which a superluminal polarization-current distribution accelerates can be used to transmit a broadband signal that is reproduced in a comprehensible form at a chosen target distance and angle. The requirement for this exact correspondence between broadcast and received signals is that each moving point in the polarization-current distribution approaches the target at the speed of light at all times during its transit along the antenna. This results in a one-to-one correspondence between the time at which each point on the moving polarization current enters the antenna and the time at which all of the radiation emitted by this particular point during its transit through the antenna arrives simultaneously at the target. This has the effect of reproducing the desired time dependence of the original broadcast signal. For other observer-detector positions, the time dependence of the signal is scrambled, due to the nontrivial relationship between emission (retarded) time and reception time. This technique represents a contrast to conventional radio transmission methods; in most examples of the latter, signals are broadcast with little or no directivity, selectivity of reception being achieved through the use of narrow frequency bands. In place of this, the current paper uses a spread of frequencies to transmit information to a particular location; the signal is weaker and has a scrambled time dependence elsewhere. We point out the possible relevance of this mechanism to 5G neighborhood networks and pulsar astronomy.

Figure 1

(a) Polarization-current antennas (PCAs) consist of a continuous series of elements made of a dielectric (white) sandwiched between pairs of electrodes (orange). The dielectric is polarized by applying a voltage difference $V_U-V_L$ between upper ($U$) and lower ($L$) electrodes; this is shown schematically for seven elements, the shading density representing the polarization strength. (b) The $V_U-V_L$ shown in (a) are applied to elements two further to the right, moving the polarized region. (c) The upper (green) trace shows $[V_U-V_L{]}_j=\sin [\omega (t-j\mathrm{\Delta }t)]$ versus $j$, where $j$ labels the antenna element, $\omega$ is an angular frequency, $t$ is time, and $\mathrm{\Delta }t$ is a time increment, at $t=0$. The lower (red) trace (offset vertically for clarity) shows $[V_U-V_L{]}_j$ at $t=\frac{103}{180}(2\pi /\omega )$; the effect of the timing differences is to move the “voltage wave” (and the induced polarization) along. In practice, fringing effects round off the stepped voltages, leading to a smoother waveform (fine liines).

Figure 2

(a) Front view of the passive antenna used in the demonstration experiment mounted on its turntable in the anechoic chamber. It has 32 elements spanning a total length of 0.64 m. The label indicates the cream-colored dielectric (alumina) that hosts the volume-distributed moving polarization current responsible for the emission of radio waves from the antenna. (b) Rear view of the antenna showing the 32-way splitter feeding 32 independent ATM P1214 mechanical phase shifters. The dials for adjusting the phase are visible on the lower left of the picture. The signal input on the top of the 32-way splitter is labeled.

Figure 3

(a) Experimental concept. An element of polarization current (red) moves along the dielectric antenna (dark yellow shading) such that the component of its velocity in the direction of the target [green cross at $(X_0,-Y_0)$] is always $c$, the speed of light. The center of the antenna is at $(0,0)$. (b) Notional time dependence of the polarization current $dP/dt$ sent along the antenna. (c) Derivative of the curve shown in (b) with respect to time $t$. The “arbitrary units” in (c) are equivalent to those in (b), the large scaling occurring because of the fast time dependences.

Figure 4

Each row shows the effect of moving the detector to positions $P$ 5 m from the antenna center (light green). In each row, the left panel gives position $P$, the center shows the arrival time $t_P$ of radiation emitted at time $t$ by a point accelerating along the antenna, and the right is the signal detected due to the polarization current of Fig. 3 being accelerated along the antenna. In all cases, the target (green cross) is 5 m from the antenna center at an angle of ${15}^{\circ }$ to the $x$ axis. Row (a): detector at target position. Row (b): detector placed on a line making an angle of ${30}^{\circ }$ with the $x$ axis. Row (c): detector placed ${10}^{\circ }$ to the other side of the $x$ axis.

Figure 5

(a) Launched $E$ field [$\propto (d^{2}P/d{t}^2)$], corresponding to a polarization current similar to that in Fig. 3, at three different times (denoted by red, green, and blue curves) during its transit along the antenna; note that the waveform “stretches out” due to the acceleration parameterized by Eqs. (3) and (6). (b) The corresponding detected $E$ field at the target point; colored lines linking (a),(b) show schematically the principle that radiation from a particular point on the traveling waveform arrives at the same time at the target. This is because the acceleration compensates exactly for the different distances between source point and detection locations [see Eq. (7) et seq.]. Hence, features in the launched $E$ field are reinforced in the correct time sequence in the detected signal. (c) The same principle is illustrated using Huyghens wavelets; colored dots in the antenna (dielectric outlined by black lines) represent the positions of a particular point on waveform (a) at different times during its transit of the antenna; semicircles of the same color show corresponding emittted Huyghens wavelets arriving at the focus point (orange diamond) simultaneously.

Figure 6

(a) Voltage measured by placing the dipole receiver 10 mm in front of the 16th antenna element as a function of time; in effect, this is the desired transmitted signal. (b) Fourier transform of the waveform in (a). Note the distinctive “triangular” pattern of harmonics of 0.9 GHz.

Figure 7

Time dependence of the signal received by the detector dipole for an antenna-to-detector distance of 3.0 m and for the azimuthal angles shown in the key. The shape of the transmitted waveform [Fig. 6] is only reproduced close to the “target” angle of ${11.6}^{\circ }$ (orange trace). Experimental traces are offset vertically for clarity.

Figure 8

Fourier transforms of the detector signal for azimuthal angles (shown in key) on either side of (green and black) and close to or at the target angle of ${11.6}^{\circ }$ (red) and at different antenna-to-detector distances: (a) 3.0 m, (b) 3.5 m, (c) 2.5 m, and (d) 2.0 m.

Figure 9

Fourier transforms of the detector signal plotted as contour plots versus frequency and azimuthal angle for different antenna-to-detector distances: (a) 3.0 m, (b) 2.5 m, (c) 3.5 m, and (d) 2.0 m.

Figure 10

Time dependence of the signal received by the detector dipole for azimuthal angle close to ${\mathrm{\Phi }}_0={11.6}^{\circ }$ and for different antenna-to-detector distances shown in the key. The shape of the transmitted waveform [Fig. 6] is only reproduced close to the “target” $R_0=3.0$ m (orange trace).

Figure 11

Simulation of a notional method for transmitting information only to a target point. The inset shows a “bit” (consisting of a Gaussian convoluted with a cosine) as it would appear in the time dependence of the broadcast $E$ field [compare with Fig. 3]. The main figure shows a calculation of the detected signal at a range of 5 m. This results from time spacing two of these “bits” by three periods of the cosine function and then subjecting them to the same acceleration scheme that is used to produce Fig. 4. At the target angle of ${15}^{\circ }$ (dark blue), the “bits” (labeled 1 and 2) may be easily resolved. However, as soon as the detector is moved to other angles (labeled by the colors in the key), the received signal is much weaker and the “bits” become virtually impossible to distinguish.