Topologically enabled ultrahigh-Q guided resonances robust to out-of-plane scattering.

Because of their ability to confine light, optical resonators1-3 are of great importance to science and technology, but their performance is often limited by out-of-plane-scattering losses caused by inevitable fabrication imperfections4,5. Here we theoretically propose and experimentally demonstrate a class of guided resonances in photonic crystal slabs, in which out-of-plane-scattering losses are strongly suppressed by their topological nature. These resonances arise when multiple bound states in the continuum-each carrying a topological charge6-merge in momentum space and enhance the quality factors Q of all nearby resonances in the same band. Using such resonances in the telecommunication regime, we experimentally achieve quality factors as high as 4.9 × 105-12 times higher than those obtained with standard designs-and this enhancement remains robust for all of our samples. Our work paves the way for future explorations of topological photonics in systems with open boundary conditions and for their application to the improvement of optoelectronic devices in photonic integrated circuits.

Analytical and statistical investigation on structural fluctuations induced radiation in photonic crystal slabs.

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.

Mode splitting in high-index-contrast grating with mini-scale finite size.

The mode-splitting phenomenon within finite-size, mini-scale high-index-contrast gratings (HCGs) has been investigated theoretically and experimentally. The high-Q resonance splits into a series of in-plane modes due to the confinement of boundaries but can still survive even on a mini-scale footprint. Q factors up to ∼3300 and ∼2200 have been observed for the HCGs with footprints that are only 55 µm×300 µm and 27.5 µm×300 µm, which would be promising for realizing optical communication and sensing applications with compact footprint.

Understanding Chinese energy-environmental efficiency: performance, decomposition, and strategy.

Understanding energy-environmental efficiency is important for coordinating economic development and eco-environment protection through energy use; however, vague definitions and conflicting results confuse researchers and policymakers and impact China's high-quality development. After delimiting energy-environmental efficiency, this study employed the intermediate adjustment situation three-stage Slacks-Based Model Data Envelopment Analysis model to explore Chinese provincial energy-environmental efficiencies from 1995 to 2018, and discussed their impacts by regional strategies. The results illustrated that Chinese energy-environmental efficiencies were overestimated, and their national average value dropped from 0.573 to 0.361 after removing the influence of external environmental factors and random interference. Moreover, energy-environmental efficiencies in East China performed significantly better than other regions, with expanding gaps between regions existed. Moreover, China maintained low-scale efficiency and high pure energy-environmental efficiency, and the low-scale efficiency led to the worrisome energy-environmental efficiency. Fortunately, pure energy-environmental efficiencies were promising, but their downward trends that started in 2002 should be a warning. Unexpectedly, the regional strategies held various impacts, they benefitted overall energy-environmental efficiency and scale efficiency, but not help pure energy-environmental efficiency, and the impacts were weak and short time. Policymakers should improve scale efficiency and formulate regional strategies in a timely manner to maintain energy-environmental efficiency improvement.

Impact of carbon lock-in on green economic efficiency: Evidence from Chinese provincial data.

Carbon lock-in is a major obstacle to transforming carbon-based energy systems toward carbon peaking and neutralization, affecting the green economy. However, its impacts and paths on green development are unclear, and it is difficult to represent carbon lock-in using a single indicator. This study measures five types of carbon lock-ins and their comprehensive effect using the entropy index of 22 indirect indicators in 31 Chinese provinces during 1995-2021. Moreover, green economic efficiencies are measured using a fuzzy slacks-based model considering undesirable outputs. The panel Tobit models are used to test the impacts of carbon lock-ins on green economic efficiencies and their decompositions. Our results show that provincial carbon lock-ins in China range from 0.20 to 0.80, with notable type and regional differences. Overall carbon lock-in levels are similar, but the severity of different carbon lock-in types varies, with social behavior being the most serious. However, the overall trend of carbon lock-ins is declining. Low pure green economic efficiencies, rather than scale efficiencies, contribute to China's worrisome green economic efficiencies, but they are decreasing and accompanied by regional gaps. Carbon lock-in hinders green development, but a specific analysis is needed for different carbon lock-in types and development phases. It is biased to assume that all carbon lock-ins hinder sustainable development, as some are even necessary. The impacts of carbon lock-in on green economic efficiency depend more on its effect on technology than on scale change. Implementing various measures to unlock carbon and maintaining reasonable levels of carbon lock-in can promote high-quality development. This paper may promote the development of new unlocking CLI measures and sustainable development policies.