Phenomenological construction of metal photonic topological insulators based on theory of characteristic modes

Dielectric photonic crystals are usually used to construct electromagnetic topological insulators, while metal photonic crystals are easier to be manufactured and compatible with microwave circuits. Characteristic mode analysis (CMA) can provide the mode eigenvalue curves of conductor structures, while energy band theory determines the dispersion features of periodic structures. The mode crossing avoidance in the theory of characteristic modes corresponds to the mode reversal at degeneracy points. Thus, in this paper, it is believed that, if the crossing avoidance modes of metal photonic crystal cells are annular, the metal photonic crystal should have the performance of photonic topological phase transitions (TPTs) in this band. Based on CMA, a spoof surface plasmon periodic structure is constructed to achieve electromagnetic TPTs with the photonic valley Hall effect. The CMA of metal photonic topological insulators essentially provides a novel phenomenological explanation for electromagnetic TPTs. We can intuitively construct topological protected edge states based on this phenomenological method.