The 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 $\ddot{I}‰$ and oscillates with an incommensurate frequency $\hat{I}\text{c◯}>\ddot{I}‰$. 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 $\hat{I}\text{c◯}$ by a factor of the order of $(\hat{I}\text{c◯}/\ddot{I}‰{)}^2$. This generation of frequencies {\it 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.

26 pages, 10 figures