Figure 7.

(a) Dispersion of the lowest branch of WBMs for a system of N=60 holes with radius $0.8\sin (\pi /60)$. The blue crosses (red circles) show the real (imaginary) parts of the complex frequencies calculated using the method outlined in this section, and the dashed line shows the asymptotic dispersion relation as calculated from (3.10) in §3. (b–d) The real part of the field u for modes with m=30,29,28, respectively, normalized to the colour bar shown. Note that the standing wave solution is antiperiodic (m=N/2) in this case.