Departmental Papers (ESE)


In this Letter the kernel of the integral transform that relates the field quantities over an observation flat plane to the corresponding quantities on another observation plane parallel with the first one is fractionalized for the two-dimensional (2-D) monochromatic wave propagation. It is shown that such fractionalized kernels, with fractionalization parameter ν between zero and unity, are the kernels of the integral transforms that provide the field quantities over the parallel planes between the two original planes. With proper choice of the first two planes, these fractional kernels can provide us with a natural way of interpreting the fields in the intermediate zones (i.e., the region between the near and the far zones) in certain electromagnetic problems. The evolution of these fractional kernels into the Fresnel and Fraunhofer diffraction kernels is addressed. The limit of these fractional kernels for the static case is also mentioned.

Document Type

Journal Article

Date of this Version

August 1999


Postprint version. Published in Microwave and Optical Technology Letters, Volume 22, Issue 4, August 20, 1999, pages 236-241.
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A portion of the preliminary findings of this work was presented by the author at the 1998 IEEE Antennas and Propagation Society (AP-S) International Symposium/USNC-URSI Radio Science Meeting in Atlanta, Georgia, June 21-26, 1998.


fractional kernels, fractional Calculus, fractional paradigm, intermediate zone, electromagnetic waves



Date Posted: 25 July 2007

This document has been peer reviewed.