Determination of band structure in one-dimensional complex photonic crystals: A bandedge approach

We present a numerical stable method to easily compute bandgaps of one-dimensional complex basis photonic crystals using novel bandedge equations rather than the traditional dispersion equation. The bandedge equations are derived by the concept of scattering matrix and concisely expressed by the transport coefficients with operations of multiplication and addition only. It is not required to calculate the global transfer matrix or the cosine of Bloch phase to avoid numerical instability. Moreover, we present closed-form expressions to calculate the global scattering matrix without using recursive computation. Finally, numerical examples show that use of the derived bandedge equation has better numerical stability than using the traditional dispersion equation for the band structure analysis.