Abstract

The focusing of the radiation generated by a polarization current with a superluminally rotating distribution pattern is of a higher order in the plane of rotation than in other directions. Consequently, our previously published [J. Opt. Soc. Am. A 24, 2443 (2007) ] asymptotic approximation to the value of this field outside the equatorial plane breaks down as the line of sight approaches a direction normal to the rotation axis, i.e., is nonuniform with respect to the polar angle. Here we employ an alternative asymptotic expansion to show that, though having a rate of decay with frequency $\left(\mu \right)$ that is by a factor of order ${\mu }^{2∕3}$ slower, the equatorial radiation field has the same dependence on distance as the nonspherically decaying component of the generated field in other directions: It, too, diminishes as the inverse square root of the distance from its source. We also briefly discuss the relevance of these results to the giant pulses received from pulsars: The focused, nonspherically decaying pulses that arise from a superluminal polarization current in a highly magnetized plasma have a power-law spectrum (i.e., a flux density $S\propto {\mu }^{\alpha }$) whose index $\left(\alpha \right)$ is given by one of the values $-2∕3$, $-2$, $-8∕3$, or $-4$.

© 2008 Optical Society of America

Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source

Houshang Ardavan, Arzhang Ardavan, John Singleton, Joseph Fasel, and Andrea Schmidt
J. Opt. Soc. Am. A 24(8) 2443-2456 (2007)

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

Houshang Ardavan, Arzhang Ardavan, and John Singleton
J. Opt. Soc. Am. A 21(5) 858-872 (2004)

Morphology of the nonspherically decaying radiation generated by a rotating superluminal source: reply to comment

Houshang Ardavan, Arzhang Ardavan, John Singleton, Joseph Fasel, and Andrea Schmidt
J. Opt. Soc. Am. A 25(9) 2167-2169 (2008)

Fundamental role of the retarded potential in the electrodynamics of superluminal sources

Houshang Ardavan, Arzhang Ardavan, John Singleton, Joseph Fasel, and Andrea Schmidt
J. Opt. Soc. Am. A 25(3) 543-557 (2008)

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

J. H. Hannay
J. Opt. Soc. Am. A 23(6) 1530-1534 (2006)