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On Fractional Paradigm And Intermediate Zones In Electromagnetism: I. Planar Observation, Nader Engheta
On Fractional Paradigm And Intermediate Zones In Electromagnetism: I. Planar Observation, Nader Engheta
Nader Engheta
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 …
On Fractional Paradigm And Intermediate Zones In Electromagnetism: Ii. Cylindrical And Spherical Observations, Nader Engheta
On Fractional Paradigm And Intermediate Zones In Electromagnetism: Ii. Cylindrical And Spherical Observations, Nader Engheta
Nader Engheta
Extending our previous work for the planar case [1], in this Letter we present fractionalization of the kernels of integral transforms that link the field quantities over two coaxial cylindrical surfaces of observation for the two-dimensional (2-D) monochromatic wave propagation, and over two concentric spherical surfaces of observation for the three-dimensional (3-D) wave propagation. With the proper radial normalizations, we show that the fractionalized kernels, with fractionalization parameter ν that here could attain complex values between zero and unity, can effectively be regarded as the kernels of the integral transforms that provide the radially normalized field quantities over the coaxial …