Waves in Fractional Dual Planar Waveguides Containing Chiral Nihility Metamaterial

Abstract

Field expressions for guided waves in three-layered fractional dual planar waveguides are derived by virtue of fractional curl operator. Fractional dual waveguides may be regarded as intermediate steps of the two waveguides which are related through principle of duality. All layers are parallel to the walls of the guide. Middle layer of the waveguide is filled with air however other two layers are filled with chiral nihility metamaterial. Parameter α describes the order of the fractional curl operator. No electric field exists in the chiral nihility layers of the waveguide for α = 0, whereas no magnetic field exists in the chiral nihility layers for α = 1. That is, power flow is confined to only air region of the waveguide for integer values of fractional parameter and corresponding situations have been previously discussed in a published work. In present work, it is noted that, for 0 < α < 1, neither electric field and nor magnetic field is zero inside chiral nihility layers of the fractional dual waveguides. By varying the values of order of the fractional curl operator, one can observe how situation dealing with no electric field changes to situation dealing with no magnetic field. Behavior of fields and power flow in different regions of the fractional waveguides is discussed. It is concluded that, even for fractional dual waveguides, real part of power flow is zero in chiral nihility regions of the waveguides.