Structure-independent flat bands induced by discontinuity plasma-air interface in photonic crystals

The band structures of transverse electric (TE) polarized dispersive photonic crystals are generally more complicated than those of transverse magnetic (TM) polarized photonic crystals. Here, by simplifying the governing equations of a TE polarized dispersion system and conducting the band structure analysis, we deduce the Hermitian eigenstates of the vector electric field. The results exhibit the double degeneracy eigenstates in the triangular lattice for lower eigenfrequencies and numerous plasmon-induced flat band modes in the interface of the plasma and air for higher eigenfrequencies. Moreover, we illustrate that the surface plasmon modes tend to present the quantized eigenfrequencies, which is due to the boundary condition imposed by the cylindrical geometry. However, when the eigenfrequency approaches the surface plasma frequency, the localization of the field on the boundary becomes stronger, which weakens the coupling between sites and reduces the dependence of the flat bands on the lattice structure. Unlike the generation mechanism of the lattice-induced flat bands, such plasma frequency-dependent localization at the interface enables a robust flat band characteristic immune to the lattice disorder and provides a novel degree of freedom to control the energy band. Our findings are expected to be useful for electromagnetic wave manipulation and field enhancement.