Fractional Dual Solutions Research Articles

Analysis of the Goos-Hänchen shift for a planar dielectric-chiral interface excited by fractional dual fields

Fractional dual solutions to the Maxwell equations for a planar dielectric-chiral interface are determined using the fractional curl operator. Both ⊥ and ∥ modes are treated for this purpose. Behavior of absolute value of the reflection coefficients, their phases and GHS are depicted and analyzed taking specific values of the fractional parameter describing order of the fractional curl operator. Derived results are verified by comparing with published work and observing the canonical cases for the fractional duality.

Fractional dual fields to the Maxwell equations for a line source buried in dielectric half space

Fractional dual solutions to the Maxwell equations for a line source carrying time harmonic current and buried in planar dielectric half space geometry have been derived. Fractional dual solutions may be regarded as intermediate step between the two given canonical cases which are connected through the principle of duality. Original case is an electric line source buried in dielectric half space and dual to the original case is a magnetic line source buried in dielectric half space. For fractional dual situations, impedance of the interface separating the two half spaces has also been determined.

Fields in fractional dual DB', D'B and D'B' waveguides containing chiral nihility medium

In electromagnetics, a set of boundary conditions requiring vanishing of the normal components of the flux densities D and B (DB boundary) or their normal derivatives (DBboundary) have assumed great importance, recently. In the present study, we employ DB � , DBand DB boundary conditions to investigate the fields in a three layered fractional dual planar waveguide. Middle layer of the waveguide is filled with air and other two layers are filled with chiral nihility metamaterial. Fractional dual solutions for the waveguide are obtained using a fractional curl operator with a parameter ' α ' defining the fractional order of the operator. For limiting values of the parameter, i.e., α =0 and α =1 , the solutions to the Maxwell's equations correspond to the original and dual to the original solutions, respectively. Whereas, in general (0 <α< 1) , so called intermediate solutions are obtained. It has been noted that fields do exist in chiral nihility material backed by DB � , DBor DB boundary, and a circular wave behaviour of the fields is observed in the core of the waveguide. In this sense DB � ,DBa nd DB � chiral nihility waveguides behave identical to their DB counterpart.

Multiple Fractional Dual Solutions in PEMC Backed Chiral Nihility Slab

Inside a chiral nihility slab which is backed by perfect electromagnetic conductor, all valid fractional dual solutions are determined using the fractional curl operator. Fractional dual solutions may be regarded as intermediate step between the original and dual to the original solution. Corresponding fields outside the nihility slab for each case are also determined and analyzed. It is noted that only for one out of three cases the corresponding field outside chiral nihility slab is also fractional dual, while for other two cases, corresponding fields are not fractional dual. It is noted that time average power density vanishes inside the PEC‐backed chiral nihility slab, while it exists outside the nihility slab.

Fractional dual solutions to the Maxwell equations in chiral nihility medium

Solutions which seem as the dual solutions to the original solution of the Maxwell equations for chiral nihility medium are listed. Using operators composed of fractional curl, solutions to the Maxwell equations which may be regarded as intermediate step between the original solution and dual to the original solution are determined. Dual solutions which are not valid have been pointed out.

Fractional Dual Solutions in Grounded Chiral Nihility Slab and their Effect on Outside Fields

Inside the chiral nihility slab, three fractional dual solutions between the original and dual to original solutions are determined. Chiral nihility slab is backed by perfect electric conductor. Corresponding fields outside the nihility slab are determined and analyzed. It is noted that in only one case outside field is also fractional dual while for other two cases corresponding fields are not fractional dual.

Fractional Dual Solutions Using Calculus of Differential Forms

Fractional dual solutions to Maxwell equations are derived using differential forms formalism. Fractional dual solutions may be regarded as intermediate step between the original solutions and dual to the original solutions. Fractional differential operator has been used to obtain the fractional dual solutions.

Fractional Curl Operator and Fractional Chiro-waveguide

Fractional curl operator has been utilized to study the wave propagation through a fractional parallel plate chiro-waveguide. Chiro-waveguide is the waveguide filled with homogeneous, isotropic chiral material. Fractional dual solutions have been established for fractional chiro-waveguide. Using these solutions for electric and magnetic fields, impedance of the walls of the fractional chiro-waveguide has been determined. It is observed that waveguide with perfect electric conducting walls and waveguide with perfect magnetic conducting walls are the two limiting cases, while the solutions for non-integer values yield the waveguide with impedance walls. Impedance of walls of the fractional chiro-waveguide has been found periodic with respect to the fractional parameter α.

Fractional duality and metamaterials with negative permittivity and permeability

Fractional dual solutions for the source free Maxwell’s equations are determined for material with negative permittivity and permeability (DNG material). The fractional dual solutions for DNG materials are compared with the corresponding solutions for materials with positive permittivity and permeability (DPS material).

Fractional dual solutions to Maxwell equations in homogeneous chiral media

Fractional dual solutions to Maxwell equations in bi-isotropic medium are investigated using field decomposition approach. It is found that for homogeneous bi-isotropic media fractional dual solutions can be obtained using field decomposition approach. Fractional dual solutions in a chiral medium are determined and their behaviour is noted.

Fractional Dual Solutions and Corresponding Sources - Abstract

Fractional dual solutions to the Maxwell's equations for a TEM plane wave propagating in an arbitrary direction are derived. The results obtained are utilized to calculate fractional dual solutions for spectrum of plane waves radiated by a line source. It is shown that fractional dual field for a plate source and for a line source, in the far-zone along the axis of symmetry, are related via fractional order integral operator. Field that can be regarded as intermediate step between the fractional dual field for a plate source and for a line source is determined. Source distributions corresponding to the fractional dual solutions and intermediate fractional dual solutions are also derived.

Fractional Dual Solutions and Corresponding Sources

Fractional Dual Solutions and Corresponding Sources