Figure 3

Examples where cuts may cause coupling, but not necessarily mode splitting: (a) a symmetry-breaking magnetic perturbation (M-cut) that rotates the modes by 45° and causes coupling, with one rotated mode perturbed significantly while the other largely not, and the net effect being mode splitting; (b) a case similar to (a) but flipped as to affect a different mode, with same overall effects; (c) a cross cut that poses exactly the same kind of M-cuts to each mode, but no breaking of overall symmetry (degeneracy) and no mode splitting, while causing no/low coupling due to the local mode rotation near perturbation edges; and (d) a circular cut as another example where some coupling is observed due to local mode rotation at the cut’s boundary, but no mode splitting since symmetry is preserved. The rotated modes’ frequencies are denoted with primed symbols (f′₁ and f′₂). The shown curves are qualitative, to indicate the characteristic behaviours under discussion.