TPTs driven by coupling strength. Transmission spectra as functions of wavelength λ and the parameter θ on coupling strength are shown, where θ is negatively correlated with the coupling strength and the amplitude transmittance of an MZI is cos( θ /2). The boundaries of non-trivial bandgaps in one FSR are indicated by purple dashed lines. Theoretical results are in good agreement with experimental results. Boundary states at bandgaps ❶ disappear with a continuous variation of θ near the critical point at θ = 0.272π, while edge modes in bandgaps ❷ and ❸ exist throughout the entire range of θ variation. The attenuation of light for large θ in experiment is due to resonant enhancement in rings, which increases the effective optical length and thus the loss.
