The electric and magnetic fields in PPWG for TM modes for cylindrical symmetry are as follows :
0] denotes the Bessel function of any kind of order zero, z represents the coordinate of the height in PPWG, [k.
If the air gap of PPWG is such smaller that cutoff frequency of any high order mode is higher than the operating frequency, those modes cannot propagate and decay quickly in a small range when they are generated.
This work described a generalized multiple-scattering method for metal-stub structures and modal analysis for scattering coefficients (matrices) of a metal stub in PPWG.
A case study involving photonic band gap verifies that the dielectric-cylinder structure can be replaced with metal stubs in a PPWG.
The electric and magnetic fields in the PPWG for TM and TE modes are as follows :