Fig. 5: Numerical demonstration of FSR \(\propto {V}^{-\frac{1}{3}}\) scaling law of the monopole topological mode at large volumes.

a Resonance spectra from the cavities of core radius (R) from 0 to 10a. The frequency of the monopole topological mode ω0 remains almost constant in the middle of the bandgaps. b Free spectral range versus mode volume (normalized by λ0 = 2πc/ω0) relation fitted with the various scaling powers. The inset illustrates the cavity construction with the monopole core radius R.