On Fractional Paradigm and Intermediate Zones in Electromagnetism: I. Planar Observation

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fractional kernels
fractional Calculus
fractional paradigm
intermediate zone
electromagnetic waves
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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.

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Postprint version. Published in Microwave and Optical Technology Letters, Volume 22, Issue 4, August 20, 1999, pages 236-241. Publisher URL: http://www3.interscience.wiley.com/cgi-bin/jissue/62502278 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.
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