Floquet-Mode Analysis of Two-Dimensional Electromagnetic Bandgap Waveguides Consisting of Circular Cylinders in Triangular Lattice

The electromagnetic fields propagating in the electromagnetic bandgap waveguides consisting of circular cylinders in triangular lattice are formulated using the periodic boundary conditions. The fields are expressed in the plane-wave and the cylindrical-wave expansions, and the transfer-matrix for one periodicity cell is derived with the help of the recursive transition-matrix algorithm. The Floquet-modes of the waveguides (not only the guided-modes but also the evanescent-modes) are calculated by the eigenvalue analysis of the transfer matrix. An adequate treatment of the boundary conditions at the cylinder surface makes us possible to decrease the truncation order while keeping accuracy.