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

Abstract

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.