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.

Unidirectional radiation is important for a variety of optoelectronic applications. Many unidirectional emitters exist, but they all rely on the use of materials or structures that forbid outgoing waves, i.e. mirrors. Here, we theoretically propose and experimentally demonstrate a class of resonances in photonic crystal slabs, which only radiate towards a single side with no mirror placed on the other side-we call them "unidirectional bound states in the continuum". These resonances are found to emerge when a pair of half-integer topological charges in the polarization field bounce into each other in the momentum space. We experimentally demonstrate such resonances in the telecommunication regime, where we achieve single-sided quality factor as high as 1.6 × 10 5 , equivalent to a radiation asymmetry ratio of 27.7 dB. Our work represents a vivid example of applying topological principles to improve optoelectronic devices. Possible applications of our work include grating couplers, photoniccrystal surface-emitting lasers, and antennas for light detection and ranging. Topological defects 1 , characterized by quantized invariants, offer a general picture to un-1

Achieving topologically-protected robust transport in optical systems has recently been of great interest. Most studied topological photonic structures can be understood by solving the eigenvalue problem of Maxwell’s equations for static linear systems. Here, we extend topological phases into dynamically driven systems and achieve a Floquet Chern insulator of light in nonlinear photonic crystals (PhCs). Specifically, we start by presenting the Floquet eigenvalue problem in driven two-dimensional PhCs. We then define topological invariant associated with Floquet bands, and show that topological band gaps with non-zero Chern number can be opened by breaking time-reversal symmetry through the driving field. Finally, we numerically demonstrate the existence of chiral edge states at the interfaces between a Floquet Chern insulator and normal insulators, where the transport is non-reciprocal and uni-directional. Our work paves the way to further exploring topological phases in driven optical systems and their optoelectronic applications.

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Abstract. In this paper, we propose a two-grid finite element method for solving coupled partial differential equations, e.g., the Schrödinger-type equation. With this method, the solution of the coupled equations on a fine grid is reduced to the solution of coupled equations on a much coarser grid together with the solution of decoupled equations on the fine grid. It is shown, both theoretically and numerically, that the resulting solution still achieves asymptotically optimal accuracy.

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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.