Frequency spectrum of focused broadband pulses of electromagnetic radiation generated by polarization currents with superluminally rotating distribution patterns

Abstract

We investigate the spectral features of the emission from a superluminal polarization current whose distribution pattern rotates with an angular frequency ω and oscillates with an incommensurate frequency Ω > ω. This type of polarization current is found in recent practical machines designed to investigate superluminal emission. Although all of the processes involved are linear, we find that the broadband emission contains frequencies that are higher than Ω by a factor of the order of (Ω/ω)2 . This generation of frequencies not required for the creation of the source stems from mathematically rigorous consequences of the familiar classical expression for the retarded potential. The results suggest practical applications for superluminal polarization currents as broad-band radiofrequency and infrared sources.

Experimental observation of nonspherically-decaying radiation from a rotating superluminal source

“…Moreover, an additional conceptual barrier discouraged further work: even a massless particle cannot move faster than light in vacuo if it is charged, because if it did, it would give rise to an infinitely strong electromagnetic field on the envelope of the wave fronts that emanate from it. 11 Finally, theoretical treatments of a particular class of source of this type 12,13 were stimulated by the design and construction of the apparatus that is the subject of the current paper. The coordinated motion of aggregates of subluminally-moving charged particles can give rise to macroscopic polarization currents whose distribution patterns move superluminally.…”

“…6,12,13 (2) The above-mentioned cusps, which spiral upwards and outwards from the source into the far zone, 6,12,13 result from the centripetal acceleration of the source; without acceleration, the wave fronts would merely pile up on a two-dimensional envelope. The combined effect of the volume elements leads to a frequency-independent beaming in both the azimuthal and polar directions whose geometry is determined by the structure of the Čerenkov-like envelopes.…”

Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns

“…(57) and the latter, which follows from Eq. (40), was earlier calculated in [19]. The nonspherically decaying part of the radiation E ns is only emitted at the two frequencies µ ± ω, whereas the spherically decaying part E s has a discrete spectrum, comprising multiples nω of the rotation frequency, which extends as far as n ∼ (Ω/ω) 3 when Ω/ω (≫ 1) is different from an integer (see Table I).…”

“…At the higher of the two frequencies, i.e. at µ + ω = Ω + mω, the amplitude of E ns has the value |E ns µ+ | ∼ ) when Ω/ω is an interger and so n is exactly equal to µ + (see [19,25]). In a case where the emitting polarization current is parallel to the rotation axis, for instance, the ratio of the amplitudes of the two components of the radiation is given by …”

“…This contrasts with the spectrum of the spherically spreading part of the radiation which extends to frequencies of the order of Ω 3 /ω 2 when Ω/ω ≫ 1 (cf. [19]). The intensity of the radiation at the frequency Ω + mω is the same as its intensity at Ω − mω when either Ω/ω ≫ m or Ω/ω ≪ m. The radiation at one of these frequencies would have a much lower intensity, on the other hand, if Ω and mω are comparable in magnitude.…”