Triangular mesh for hexagonal nanostructures using Finite-Difference Time-Domain method

Abstract

The hexagonal cavity confines the electromagnetic field inside the structure by total reflection and has high Q-factor caused by the whispering gallery modes or Quasi- whispering gallery modes However it is difficult to discriminate the degenerated modes with the same wavelength when the whole hexagonal structure is used in the simulation Hence according to the symmetry of the hexagonal cavity only a quarter of the hexagonal cavity with x-y axis symmetry can be used It can discriminate the degenerated modes and reduce the computational time Another issue found in the simulation is that the “stair case” will appear on the edge of the quarter hexagonal structure when square mesh is used The stair case will not correctly excitate the modes in low resolution In order to fix the problem a “triangular mesh” FDTD method is developed in this work The triangular mesh is used to simulate the hexagonal cavity of ZnO rod and graphene flakes ZnO rod is a dielectric 2D hexagonal structure The first 5~12th modes of the ZnO hexagonal cavity are successfully simulated and compared with previous results using square meshes The graphene flake’s hexagonal cavity modes are simulated using three dimensional triangular mesh In Cartesian mesh it is difficult to find the mode pattern with mode number higher than 10 The error caused by stair case can be easily solved in the triangular mesh

Date of Award	2019
Original language	English
Supervisor	Shih-hui Chang (Supervisor)