Fields in Fractional Parallel Plate D'B', Db' and D'B Waveguides

D′B′, DB′ and D′B boundary conditions are used to investigate the resulting field patterns inside a parallel plate waveguide. The D′B′ boundary conditions are accomodated by assigning the behavior of perfect magnetic conductor (PMC) for transverse electric mode (TE) and that of perfect electric conductor (PEC) for transverse magnetic (TM) mode, to the boundary, respectively. Likewise, DB′ boundary conditions are incorporated by assuming the behavior of boundary as PMC for both the TE mode and TM mode. Finally D′B boundary conditions are realized by assigning PEC characteristic to the boundary for both TE and TM modes. A general wave propagating inside the parallel plate waveguide is assumed and decomposed into TE and TM modes for the purpose of analysis. Fractional curl operator has been used to study the fractional parallel plate D′B′, DB′ and D′B waveguides for different values of fractional parameter α. Behavior of the field patterns in the waveguides are studied with respect to the fractional parameter α describing the order of the fractionalization.