Numerical stable method for the analysis of Bloch waves in a general one-dimensional photonic crystal cavity

We present a numerical stable method to accurately solve band structures and the eigenvalues of a multilayer-basis photonic crystal cavity. We derive a set of band-edge equations to determine the band structures rather than use the cosine of the Bloch phase, which is traditionally used but may induce numerical instability. Moreover, two novel formulas are proposed to solve the eigenvalues for the cavity modes. The eigenvalues solved by the method are accurate without including the spurious solutions. Thus, it is not required to eliminate the spurious solutions from the results. Finally, numerical examples of binary and Fibonacci multilayers in each cell are studied to demonstrate that this method has better numerical stability in computing the band structure and cavity modes than traditional methods.