Fractional Operators Approach in Reflection and Diffraction Problems

Ivakhnychenko, M.V.; Велиев, Е. И.

doi:10.1109/telsks.2007.4375985

Cited by 5 publications

(6 citation statements)

References 9 publications

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“…Fractional dual solutions obtained by fractional curl operator and corresponding sources were discussed in [5][6][7][8]. Then fractional field was analyzed in various electromagnetic problems: wave propagation in chiral media [9][10][11], waveguides [12], reflection and scattering problems [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Fractional Boundary Conditions in Plane Waves Diffraction on a Strip

Велиев¹,

Ivakhnychenko²,

Ahmedov³

2008

PIER

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Abstract-New fractional boundary conditions (FBC) on plane boundaries are introduced. FBC act as intermediate case between perfect electric conductor and perfect magnetic conductor. In certain sense FBC are analogue of commonly used impedance boundary conditions with pure imaginary impedance. The relation between fractional order and impedance is shown. Plane wave diffraction problem by a strip described by FBC is formulated and solved using new method which extends known methods. Numerical results for physical characteristics are presented. Analyzing the scattering properties of the fractional strip new features are observed. FBC has one important special case where the fractional order equals to 1/2. For this special case the solution of diffraction problem can be found in analytical form for any value of wavenumber. Also for small values of wavenumber monostatic radar cross section has new specific resonances which are absent for other values of fractional order.

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Section: Introductionmentioning

confidence: 99%

Fractional Boundary Conditions in Plane Waves Diffraction on a Strip

Велиев¹,

Ivakhnychenko²,

Ahmedov³

2008

PIER

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“…The two given geometries must be connected through the given ordinary operator. Frac-tional curl operator has been used to study various problems [7][8][9][10][11][12][13][14][15][16]. A linear operator may be fractionalized using recipe given in [4], which dictates that fractionalization of an operator means fractionalization of its eigenvalues.…”

Section: Grounded Chiral Nihility Slabmentioning

confidence: 99%

Planar Slab of Chiral Nihility Metamaterial Backed by Fractional Dual/Pemc Interface

Naqvi¹

2008

PIER

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Abstract-Fields inside the chiral nihility slab which is backed by perfect electric conductor are determined. It is noted that both electric and magnetic fields exist inside the grounded chiral nihility slab when it is excited by a plane wave. Electric field inside the slab disappears for excitation due to an electric line source. Magnetic field inside the slab disappears when geometry changes to corresponding dual geometry. Dual geometry means chiral nihility slab backed by perfect magnetic conductor and excited by a magnetic line source. Using fractional curl operator, fields are determined for fractional order geometries which may be regarded as intermediate step between the two geometries which are related through principle of duality. Discussion is extended for chiral nihility slab which is backed by perfect electromagnetic conductor (PEMC).

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“…Fractional calculus is found to be a good tool for presenting homogenous models for fractal boundaries in different physical problems including electromagnetic wave propagation [1,2]. This was the motivation for many researchers to introduce extensive studies of formulating and solving fractional dimensional problems in electromagnetics [3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Reflection and Transmission of Electromagnetic Wave Due to a Quasi-Fractional-Space Slab

Attiya

2011

PIER Letters

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A new method is introduced to construct a slab that has electric fields with propagation properties which are equivalent to a fractional-space wave equation in two-coordinate system. While its magnetic fields have propagation properties which are equivalent to the complementary fractional-space wave equation. Analytical forms for the reflection and transmission coefficients of this slab are derived. Results of these reflection and transmission coefficients show that such quasi-fractional-space slab has spatial and frequency selectivity properties.

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Fractional Operators Approach in Reflection and Diffraction Problems

Cited by 5 publications

References 9 publications

Fractional Boundary Conditions in Plane Waves Diffraction on a Strip

Fractional Boundary Conditions in Plane Waves Diffraction on a Strip

Planar Slab of Chiral Nihility Metamaterial Backed by Fractional Dual/Pemc Interface

Reflection and Transmission of Electromagnetic Wave Due to a Quasi-Fractional-Space Slab

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