The point defect and eigenfield distribution for two-dimensional function photonic crystal

Abstract

With the plane wave expansion method, we introduced the concept and theory of two-dimensional function photonic crystal, and compared the theoretical difference of two-dimensional function photonic crystal with the conventional photonic crystal. In Numerical calculation, with COMSOL software based on finite element method, we have studied the bandgap structure, defect mode and eigenfield distribution for the two-dimensional function photonic crystal with and without point defect. For the two-dimensional function photonic crystal, the dielectric constant of dielectric column is the space coordinate function, which can be realized by the electro-optic effect and the Kerr effect. In the paper, we studied the dielectric constant function form is [Formula: see text](r) = kr + b, and the parameters k and b can be adjusted by changing the electric field or light intensity applied to the dielectric column. By changing the parameters k or b of the dielectric column dielectric constant, we found the two-dimensional function photonic crystal transmission characteristics have the adjustability, i.e., the bandgap structure, the bandgap position and width, the defect mode position, width and number and the defect mode eigenfield distribution can be changed by adjusting the parameters k or b, which can be used to conveniently design the bandgap structure that we need. These conclusions will provide important theoretical basis and methods for optical devices design.