We develop a formalism, based on the mode expansion method, to describe the guided resonances and bound states in the continuum (BICs) in photonic crystal slabs with one-dimensional periodicity. This approach provides analytic insights to the formation mechanisms of these states: the guided resonances arise from the transverse Fabry–Pérot condition, and the divergence of the resonance lifetimes at the BICs is explained by a destructive interference of radiation from different propagating components inside the slab. We show BICs at the center and on the edge of the Brillouin zone protected by symmetry, BICs at generic wave vectors not protected by symmetry, and the annihilation of BICs at low-symmetry wave vectors.

Optical fibers typically confine light through total internal reflection or through photonic bandgaps. Here we show that light can be perfectly guided in optical fibers through a different mechanism based on bound states in the continuum (BICs). In fibers with periodic Bragg gratings, we predict bona fide BICs in purepolarization modes, as well as quasi-BICs in hybrid-polarization modes. These guided modes exist robustly without the need for fine structural tuning, and they persist even with the very small grating index contrasts that are available in conventional fiber Bragg gratings. The suppression of radiation loss arises from the coupling between a weakly-radiating mode and a strongly-radiating one. This finding opens the possibility of guiding light with BICs in optical fibers and their applications in distributed fiber sensors, in-line fiber filters, and high-power fiber lasers.

With the development of wearable or flexible electronic products, there is a growing demand for electrochemical energy storage devices with high safety, low cost, and excellent performance. [1][2][3] Nowadays, most of the research focuses on the development of lithium-ion batteries and supercapacitors. However, the susceptibility of supercapacitors to electrolyte leakage and low charge/ discharge capacity have seriously hindered their development as energy storage devices. [4][5][6] Lithium-ion batteries typically exhibit long cycle life and high power tolerance, while they have fatal defects such as spontaneous combustion and insufficient lithium storage. [7][8][9][10] Among the rechargeable ion batteries, aqueous rechargeable zinc ion batteries (ZIBs) have been regarded as one of the most valuable energy storage devices because of their superior bulk energy density (5851 mAh cm À3 ), low manufacturing cost, relatively large theoretical capacity (819 mAh g À1 ), and superior stability in air environment. [11][12][13] However, aqueous ZIBs suffer from narrow window voltage, low matchable capacity of cathode, and irreversible by-products of zinc anode during cycling. In this case, the key factors of developing highperformance ZIBs are to break through the narrow electrochemical stability window of aqueous electrolytes, explore suitable cathode materials, and design zinc anodes with high electrochemical reversibility. [13][14][15][16][17] The main types of zinc-based batteries studied today include zinc-manganese batteries (Zn/MnO2), [17] zinc-nickel batteries (Zn/NiOOH), [18] zinc-air batteries (Zn/Air), [19] zinc-polyaniline batteries (Zn/PANI), [20] etc. As to the cathode materials of zinc-based batteries, MnO 2 is widely used because of its low cost, environment-friendly, fast charge/discharge, high theoretical specific capacity (%308 mAh g À1 ), and high discharge voltage platform of %1.4 V. [21,22] However, the expansion and contraction of the crystal structure during cycling will cause MnO 2 crushing and falling off from electrode, resulting in poor cycling performance. [23][24][25] In addition, its low conductivity also influences the total performance of ZIBs. [24] Much effort has been devoted to improve its conductivity, including doping metal compound, coating conductive surface layer, adding conductive agent with excellent performance, etc. [26][27][28][29][30][31] MXene is a new class of two-dimensional materials consisting of transition metal carbides or nitrides. [16] The expression is M nþ1 X n T x , where M represents transition metal atoms, X represents C or N atoms, and T represents oxygen, fluorine, and other functional groups on its surface. [17] Ti 3 C 2 T x is among the first discovered and the most extensively studied MXene materials.

We show that lasers near exceptional points have an oscillating population inversion that generates a frequency comb. We develop an ab-initio theory describing all steady-state properties of such lasers and validate it with FDTD.