Observation of Locally Negative Velocity of the Electromagnetic Field in Free Space

Since the 1983 definition of the speed of light in vacuum as a fundamental constant with the exact value of $299792458\mathrm{m}/\mathrm{s}$ the question has remained as to what apart from the wave front travels at that speed. It is commonly assumed that the entire electromagnetic waveform in free space does. Here it is demonstrated, both theoretically and experimentally, that the near- and intermediate-field dynamics of the vectorial electromagnetic field is much more complex than simple outwards propagation. In particular, it is shown that there exists a region close to the source, where, while the wave front travels outwards at the speed of light, the main body of the waveform appears to go inwards or back in time. The same effect may also lead to apparent superluminal results in free space.

Figure 1

The near-field measurement setup with two identical vertically polarized dipole antennas placed at a varying distance along the measurement line.

Figure 2

Simulation of the electric field strength in the near- and itermediate-field zones of the point-dipole antenna fed by a sinusoidal current. Top image: space-time wave packet dynamics (see text); lower part of this image corresponds to the near-field zone, where the leftward bending indicates negative velocity; middle and top part—positive velocity approaching light cone behavior. Bottom plot: the first five near-field waveforms received at increasing distances from the source; the outer edges shift rightwards—normal (light cone) behavior; the inner part shift leftwards—negative velocity.

Figure 3

Experimental observation of the free-space negative waveform velocity. Top image: space-time waveform dynamics; the leftward bend in the lower part of the image indicates the negative velocity in the near-field. Bottom plot: details of the first five near-field waveforms with inner peaks traveling back in time.