Due to their ability to confine light, optical resonators 1-3 are of great importance to science and technology, yet their performances are often limited by out-of-plane scattering losses from inevitable fabrication imperfections 4, 5 . Here, we theoretically propose and experimentally demonstrate a class of guided resonances in photonic crystal slabs, where out-of-plane scattering losses are strongly suppressed due to their topological nature. Specifically, these resonances arise when multiple bound states in the continuum -each carrying a topological charge 6 -merge in the momentum space and enhance the quality factors of all resonances nearby. We experimentally achieve quality factors as high as 4.9 × 10 5 based on these resonances in the telecommunication regime, which is 12-times higher than ordinary designs.We further show this enhancement is robust across the samples we fabricated. Our work paves the way for future explorations of topological photonics in systems with open boundary condition and their applications in improving optoelectronic devices in photonic integrated circuits.

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We extend the coupled-wave-theory (CWT) framework to a supercell lattice photonic crystal (PC) structure to model the radiation of high-Q resonances under structural fluctuations since they are inevitable in realistic devices. The comparison of CWT results and the finite-element-method (FEM) simulations confirm the validity of CWT. It is proved that the supercell model approaches a realistic finite-size PC device when the supercell size is large enough. The Q factors within fluctuated structures are constraint owing to the appearance of fractional orders of radiative waves, which are induced by structural fluctuations. For a large enough footprint size, the upper bound of the Q factor is determined by the fabrication precision, and further increasing the device size will no longer benefit the Q factor.

We investigate the extraordinary behavior of periodic photonic structures within radiation continuum from the perspective of interfering resonance. The coupled-channel equations of both TE-like and TM-like polarizations are reformulated into the similar forms of the quantum-defect theory that describes the interference of resonances belonging to different Coulombic quantum channels. The concepts of closed-channel, openchannel, coupling potential, and eigenvalues are well interpreted. Some iteration techniques, i.e., field-iteration and k-iteration, are proposed to obtain self-consistent solution of the coupled-channel equations. The iterations are important to guarantee quantitative accuracy for high-index-contrast structure, in which the strength of wave interactions is significantly enhanced compared with its low-index-contrast counterpart. The semianalytical results of resonance wavelength, transmissivity/reflectivity spectrum, and band structure agree well with the rigorous coupled-wave analysis (RCWA) and finite-difference time-domain (FDTD) simulation, confirming the accuracy of the iterations. The interfering resonance provides a clear and consistent picture to understand the periodic photonic structure within radiation continuum, and also reveals the intrinsic similarities between the photonic and quantum systems.