| A 2-D photonic crystal cavity device is investigated in this thesis. A simplified flexible local approximation method (FLAME) is used to analyze the electromagnetic characteristics of the cavity.;The new method is applied to cavities based on NxN arrays of rods, from N=3 to 9. Good accuracy is achieved compared with the finite-element method (FEM), with an error of less than 0.001% in the resonant frequency for a density of 42.6 nodes per wavelength (when N=5), which shows better consistency than the previous FLAME. Further, the new method converges more quickly than the FEM with linear elements, as the node density is increased, though it is less accurate than the FEM with quadratic elements.;FLAME is a computational technique that is well suited to problems involving a large number of repeated structures. It has been used before to analyze photonic crystal cavities. In this thesis, an improved FLAME is developed, leading to a standard eigenproblem, which allows the use of sparse-matrix solution methods. Consequently, much larger problems can be solved. In addition, a graded perfectly matched layer (PML) is applied to absorb more effectively the out-going waves. |
