Metal photonic band gap structures formed by triangular arrays

The finite-difference method is used to analyze the dispersion characteristics of two-dimensional photonic band gap (PBG) structures formed by triangular arrays of metal posts. The global band gaps for TE modes are derived. The method of designing PBG structures with specific eigen-frequency is obtained. It is shown that for the convenience of coupling the power out of the PBG cavity, the ratio of post radius to lattice constant should be as small as possible. The results also prove that it is possible to design a gyrotron with PBG cavities analogous to conventional cylindrical cavities.