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

TL;DR

This paper clarifies that a standard electrodynamics formula is not applicable to extended, superluminal rotating sources because it neglects boundary contributions crucial for accurate diffraction and radiation modeling.

Contribution

The authors demonstrate the importance of boundary terms in electromagnetic field calculations for superluminal sources, correcting misconceptions from previous comments.

Findings

Standard formulas neglect boundary contributions for superluminal sources.

Boundary terms are essential for accurate diffraction and radiation predictions.

Incorrect application of formulas can lead to impossible diffraction scenarios.

Abstract

The fact that the formula used by Hannay in his Comment is "from a standard text on electrodynamics" neither warrants that it is universally applicable, nor that it is unequivocally correct. We have explicitly shown [J. Opt. Soc. Am. A 25, 543 (2008)] that,since it does not include the boundary contribution toward the value of the field, the formula in question is not applicable when the source is extended and has a distribution pattern that rotates faster than light in vacuo. The neglected boundary term in the retarded solution to the wave equation governing the electromagnetic field forms the basis of diffraction theory. If this term were identically zero, for the reasons given by Hannay, the iffraction of electromagnetic waves through apertures on a surface enclosing a source would have been impossible. If this term were identically zero, for the reasons given by Hannay, the diffraction of electromagnetic waves through apertures on a surface enclosing a source would have been impossible.