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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 3 — Mar. 1, 2008
  • pp: 543–557

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

Houshang Ardavan, Arzhang Ardavan, John Singleton, Joseph Fasel, and Andrea Schmidt  »View Author Affiliations


JOSA A, Vol. 25, Issue 3, pp. 543-557 (2008)
http://dx.doi.org/10.1364/JOSAA.25.000543


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Abstract

We calculate the gradient of the radiation field generated by a polarization current with a superluminally rotating distribution pattern and show that the absolute value of this gradient increases as R 7 2 with distance R, within the sharply focused subbeams that constitute the overall radiation beam from such a source. In addition to supporting the earlier finding that the azimuthal and polar widths of these subbeams become narrower (as R 3 and R 1 , respectively) with distance from the source, this result implies that the boundary contribution to the solution of the wave equation governing the radiation field does not always vanish in the limit where the boundary tends to infinity (as is commonly assumed in textbooks and the published literature). While the boundary contribution to the retarded solution for the potential can always be rendered equal to zero by means of a gauge transformation that preserves the Lorenz condition, the boundary contribution to the retarded solution of the wave equation for the field may be neglected only if it diminishes with distance faster than the contribution of the source density. In the case of a rotating superluminal source, however, the boundary term in the retarded solution for the field is by a factor of the order of R 1 2 larger than the source term of this solution, in the limit where the boundary tends to infinity. This result explains why an argument based on the solution of the wave equation governing the field in which the boundary term is neglected [such as that presented by Hannay, J. Opt. Soc. A 23, 1530 (2006)] misses the nonspherical decay of the field that is generated by a rotating superluminal source. The only way one can calculate the free-space radiation field of an accelerated superluminal source is via the retarded solution for the potential. Our findings have implications also for the observations of the pulsar emission: The more distant a pulsar, the narrower and brighter its giant pulses should be.

© 2008 Optical Society of America

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(040.3060) Detectors : Infrared
(230.6080) Optical devices : Sources
(250.5530) Optoelectronics : Pulse propagation and temporal solitons
(260.2110) Physical optics : Electromagnetic optics
(350.1270) Other areas of optics : Astronomy and astrophysics

ToC Category:
Optical Devices

History
Original Manuscript: September 10, 2007
Revised Manuscript: December 3, 2007
Manuscript Accepted: December 5, 2007
Published: February 4, 2008

Citation
Houshang Ardavan, Arzhang Ardavan, John Singleton, Joseph Fasel, and Andrea Schmidt, "Fundamental role of the retarded potential in the electrodynamics of superluminal sources," J. Opt. Soc. Am. A 25, 543-557 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-3-543

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