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

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