A Study on the Eigenmodes in the Photonic Crystal Waveguide with Dielectric Hole

The eigenmodes in the photonic crystal Waveguide with dielectric hole are investigated by finite element method. The relative permittivity of the dielectric hole and cladding is significantly lower than that of the core areas. The propagating wave is confined in the region of the high relative permittivity by Snell’s law. The space of the waveguide is divided into the elementary triangular mesh in the process of numerical calculation. The Krylov-Schur iteration method is performed to obtain several prominent and reliable eigenmodes. The eigenmode obtained from this calculation is determined as the transverse electro-magnetic modes because the photonic dielectric hole mixes the transverse magnetic and transverse electric characteristics. As results, eigenmodes composed with the vector electric field, three dimensional electric potential and two dimensional electric equipotential are shown in a simple schematic representation. These results will enable the implementation of more advanced communication fiber by utilizing the ideal properties of the photonic crystal waveguide.