Abstract
Abstract In this thesis, we investigate the convergence of plane-wave-expansion method (PWEM) and transfer-matrix method (TMM). We calculate the bandstructure of photonic crystals and expand the eigenvalue of PWEM and TMM with power law method. The convergence is based on the x value of expansion. This thesis consists of four parts. First, we focus on the convergence of PWEM on different filling fractions. The results show that the convergence is the slowest when filling fraction is 0.5. Second, the boundary changes from discontinuous to continuous. And then, we find that the convergence on continuous boundary is faster than that on discontinuous boundary. Third, the convergence on the expansion of and are investigated. The results show that the convergence on expansion of is faster than that of . Finally, TMM can converges with the limited number of series expansion.