z-disp-rel

The dispersion relation for z-dispersive media can be computed in two ways:

1. Using the homogenized equations.
2. Using Floquet theory; see the paper of Lee & Yang.

This is a plot comparing the two:

The blue circles show the bandgap structure and are based on Floquet theory. The solid curves show the dispersion relation obtained from the homogenized equations including terms of increasing order.

Note that the homogenized dispersion relation predicts complex values above a certain threshold. It is not surprising that it cannot capture the correct behavior beyond the lower edge of the first bandgap. It does seem to accurately predict that lower edge.