Finite Element Analysis of Photon Density of States for Two-dimensional Photonic Crystals with In-plane Light Propagation

摘要

In-plane light propagation in two-dimensional (2D) photonic crystals (PCs) has been investigated by using an adaptive finite element method (FEM). Conventionally, the band structures of 2D PCs were calculated by either the plane-wave expansion method (PWEM) or the finite difference time domain method. Here, we solve the eigenvalue equations for the band structures of the 2D PCs using the adaptive FEM in real space. We have carefully examined the convergence of this approach for the desired accuracy and efficiency. The calculated results show some discrepancies when compared to the results calculated by the PWEM. This may due to the accuracy of the PWEM limited by the discontinuous nature of the dieffectric functions. After acquiring the whole information of the dispersion relations within the irreducible Brillouin zone of the 2D PCs, the in-plane photon density of states can be calculated, accurately. These results are relevant to the spontaneous emission by an atom, or to dipole radiation in two-dimensional periodic structures.