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On fractional paradigm and intermediate zones in electromagnetism: I—Planar observation
Author(s) -
Engheta Nader
Publication year - 1999
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/(sici)1098-2760(19990820)22:4<236::aid-mop6>3.0.co;2-8
Subject(s) - kernel (algebra) , plane (geometry) , monochromatic color , planar , electromagnetism , limit (mathematics) , integral transform , mathematics , physics , field (mathematics) , mathematical analysis , geometry , optics , pure mathematics , computer science , quantum mechanics , computer graphics (images)
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 to the first one is fractionalized for two‐dimensional (2‐D) monochromatic wave propagation. It is shown that such fractionalized kernels, with a 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 a 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 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. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 236–241, 1999.