Fig. 4: Effective magnetic field, 2D dispersion, Berry curvature, and diabolical points.

a Total effective magnetic field for the system of two interacting cavity modes of Fig. 2c. The diabolical points (DP) occur where the magnetic field is cancelled and are positioned on a line on the \({k}_{x},{k}_{y}\) plane with a slope proportional to \({a}_{x}/{a}_{y}\). b Cross-section of the simulated dispersion from Fig. 2c. c Energy dispersion along the line connecting the diabolical points (\({k}_{{xy}}\) on the dashed line). The modes do not interact at the diabolical points and cross. d Energy dispersion along a line mirrored on the \({k}_{y}\) axis (\({k}_{{xy}}\) on the dotted line) where the two modes anti-cross. e Calculated Berry curvature \(\Omega\) showing two ill-defined divergent points for momentum values of the DP. f Same depiction as (e) at a logarithmic scale. g Absolute value of the Berry curvature on the \({k}_{x}\), \({k}_{y}\) plane, illustrating the divergence at the DP