Study on complete band gap of two-dimensional photonic crystal with quadrangular rods

The plane wave expansion method (PWM) was employed to study the relation between the photonic band gap (PBG) of 2D triangular lattice photonic crystal (PC) and the shapes of rods and dielectric constant. It is shown that the PBG of PC with quadrangular rods is the widest one, compared with the other case with cross section shapes of triangular, circular and hexagon under the same filling ratio, and a peak value appears when the side length ratio of lx/ly is equal to 1.21 approximately to any filling ratio. In the aspect of the effects of dielectric constant, the PBG width does not increase monotonically with the increase permittivity ɛ2 of the background material to certain permittivity ɛ1 of the quadrangular rods, but has a peak value instead. However, the larger the permittivity ɛ1 is, the narrower the band width is and the lower the central frequency is, and the dispersion Δɛ = ɛ2 − ɛ1 is larger also.