Advanced Optical Materials最新文献_第5页

Masthead: (Advanced Optical Materials 26/2024) 刊头：（先进光学材料 26/2024）

IF 8 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

Advanced Optical Materials

Pub Date : 2024-09-12 DOI: 10.1002/adom.202470082

引用次数: 0

Surface‐Enhanced Raman Scattering and Photothermal Effects on Optoplasmonic Nanofibers 光致发光纳米纤维的表面增强拉曼散射和光热效应

IF 9 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

Advanced Optical Materials

Pub Date : 2024-09-12 DOI: 10.1002/adom.202401640

Gregory Q. Wallace, Emilie Ringe, Karen Faulds, Duncan Graham, Jean‐François Masson

When decorated with plasmonic nanoparticles, pulled optical nanofibers are compatible with plasmonic techniques enabling the ability to probe microenvironments with high spatial and temporal resolution. Although the nanofibers exhibit excellent compatibility for biological samples including cells and tissues, the underlying interactions between the dielectric fiber, plasmonic nanoparticles, and the incident light have been minimally explored. It is shown that the complex coupling of optical and plasmonic properties within the nanofiber strongly influences both the surface‐enhanced Raman scattering (SERS) and photothermal capabilities. Through a combination of experimental results and simulated electric field distributions and spectra it is demonstrated that, although the nanofibers may be homogeneously decorated with gold nanoparticles, the optical effects spatially differ. Specifically, the SERS performance varies periodically based on the diameter of the nanofiber, which is associated with ring resonator modes, while the photothermal effects are more homogeneous over the same diameters, highlighting differences in optoplasmonic properties at this length scale. Through understanding these effects, it may become possible to control temperatures and SERS properties to evaluate processes with micrometric spatial resolution, such as the analytes secreted during temperature‐induced death of single cells.

用等离子纳米粒子装饰后，拉伸的光学纳米纤维与等离子技术兼容，能够以高空间和时间分辨率探测微环境。虽然这种纳米纤维对包括细胞和组织在内的生物样本具有极佳的兼容性，但对介质纤维、等离子纳米粒子和入射光之间的基本相互作用却很少进行探讨。研究表明，纳米纤维内光学和质子特性的复杂耦合会对表面增强拉曼散射（SERS）和光热能力产生强烈影响。通过实验结果与模拟电场分布和光谱的结合，可以证明虽然纳米纤维可以均匀地装饰金纳米粒子，但其光学效应在空间上是不同的。具体来说，SERS 性能根据纳米纤维直径的不同而周期性变化，这与环形谐振器模式有关，而光热效应在相同直径上更为均匀，这凸显了该长度尺度上的光电磁特性差异。通过了解这些效应，就有可能控制温度和 SERS 特性，从而以微米空间分辨率评估各种过程，例如在温度诱导单细胞死亡过程中分泌的分析物。

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引用次数: 0

Quantitative Dynamic Structural Color: Dual-Band Hyperchromatic Sensing with Mesoporous Metamaterials (Advanced Optical Materials 26/2024) 定量动态结构色彩：使用介孔超材料的双波段超变色传感（先进光学材料 26/2024）

IF 8 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

Advanced Optical Materials

Pub Date : 2024-09-12 DOI: 10.1002/adom.202470080

Nithesh Kumar, Estevao Marques Dos Santos, Tahmid H. Talukdar, Judson D. Ryckman

Quantitative Dynamic Structural Color

In article number 2401152 Nithesh Kumar, Judson D. Ryckman, and co-workers demonstrate an approach to overcome the limited sensitivity and often qualitative nature of structural-color-based sensors and indicators in a scheme referred to as ‘quantitative dynamic structural color’. As illustrated in this cover image, their scheme relies on a spectrally engineered mesoporous metamaterial combined with dichromatic laser illumination. The sensors achieve a well-defined and strongly enhanced color response toward refractometric stimuli including small molecules, vapors, and aerosols.

定量动态结构色在文章编号 2401152 中，Nithesh Kumar、Judson D. Ryckman 及其合作者展示了一种方法，该方法克服了基于结构色的传感器和指示器灵敏度有限和经常定性的问题，这种方法被称为 "定量动态结构色"。如封面图片所示，他们的方案依赖于光谱工程介孔超材料与双色激光照明的结合。这种传感器能对包括小分子、蒸汽和气溶胶在内的折射刺激产生明确且强烈的增强色彩响应。

引用次数: 0

Comprehensive Defect Suppression in Te-Doped Cs2ZrCl6 Perovskite Nanoparticles for Highly Efficient and Thermally Stable White Light-Emitting Diodes (Advanced Optical Materials 26/2024) 全面抑制 Te 掺杂 Cs2ZrCl6 包晶石纳米粒子中的缺陷，实现高效、热稳定的白色发光二极管（先进光学材料 26/2024）

IF 8 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

Advanced Optical Materials

Pub Date : 2024-09-12 DOI: 10.1002/adom.202470081

Chaojun Yang, Xiangdan Tian, Guangguang Huang, Xinyang Xiong, Kaiwei Sun, Bo Zhang, Shujie Wang, Zuliang Du

Defect Suppression in Te-Doped Cs₂ZrCl₆ Perovskite Nanoparticles

Lead-free Cs₂ZrCl₆:Te (CZCT) @ alkyl-terminated silica-oligomer (ASO) core/shell perovskite nanoparticles (PNCs) were designed and synthesized with the highest photoluminescence quantum yield (PLQY) of up to 96% and robust thermal tolerance simultaneously. The high PLQY was attributed to the comprehensive defect suppression through crystallization and surface control. The fabricated white light-emitting diodes based on the CZCT@ASO PNCs exhibit a color coordinate of (0.31, 0.33) and a color rendering index of 86. For further details, see article number 2303079 by Guangguang Huang, Shujie Wang, Zuliang Du, and co-workers from Henan University (the Iron Pagoda in the image representing its culture and spirit).

无铅 Cs2ZrCl6:Te (CZCT) @ 烷基端硅寡聚体 (ASO) 核/壳包晶纳米颗粒 (PNCs) 的设计与合成具有最高的光致发光量子产率 (PLQY)，高达 96%，并同时具有很强的耐热性。高光量子产率归功于通过结晶和表面控制对缺陷的全面抑制。基于 CZCT@ASO PNC 制成的白光发光二极管的色坐标为（0.31, 0.33），显色指数为 86。更多详情，请参阅河南大学黄光光、王淑杰、杜祖亮及合作者的 2303079 号文章（图片中的铁塔代表了河南大学的文化和精神）。

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引用次数: 0

Surface Defects Passivation of ZnSeTe/ZnSe/ZnS Quantum Dots by Iodine Ions for Highly Efficient Blue Light‐Emitting Diodes 碘离子钝化 ZnSeTe/ZnSe/ZnS 量子点表面缺陷，实现高效蓝色发光二极管

IF 9 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

Advanced Optical Materials

Pub Date : 2024-09-11 DOI: 10.1002/adom.202401884

Zhongyuan Guan, Yang Huang, Zhaojin Wang, Jiayun Sun, Chengwei Shan, Yiguo Xu, Dan Wu, Aiwei Tang, Xiao Wei Sun, Kai Wang

The development of cadmium‐free blue quantum dots (QDs) is of paramount importance to the display industry. In this study, high‐quality ZnSeTe/ZnSe/ZnS blue QDs, followed by surface treatment with ZnI2 are initially synthesized. The introduction of ZnI2 passivated the surface defects, resulting in an increase in the fluorescence quantum yield. The time‐resolved photoluminescence (TRPL) demonstrates a significant inhibition of non‐radiative recombination associated with the surface defect state. The density functional theory (DFT) calculation reveals that the binding energy between iodine ions and zinc ions is higher than that between oleate ions and zinc ions, providing a theoretical basis for the effective passivation of the suspended bonds of zinc ions on QDs' surface by iodine ions. Moreover, quantum dot light‐emitting diodes (QLEDs) are fabricated and UV photoelectron spectra (UPS) indicate the hole injection barrier between the hole transport layer and QDs decreases 0.12 eV after QDs being treated by ZnI2, facilitating hole injection. Finally, The ZnI2‐treated QLED demonstrates a 1.57‐fold and 1.82‐fold improvement in Lmax and EQEmax, respectively, reaching 6370 cd m−2 and 9.1%, compared to the pristine QLED. The work serves as a valuable reference for enhancing the performance of cadmium‐free blue QLED.

开发无镉蓝色量子点（QDs）对显示行业至关重要。本研究首先合成了高质量的 ZnSeTe/ZnSe/ZnS 蓝色量子点，然后用 ZnI2 进行表面处理。ZnI2 的引入钝化了表面缺陷，从而提高了荧光量子产率。时间分辨光致发光（TRPL）表明，与表面缺陷状态相关的非辐射重组受到了显著抑制。密度泛函理论（DFT）计算表明，碘离子与锌离子的结合能高于油酸根离子与锌离子的结合能，这为碘离子有效钝化量子点表面锌离子的悬浮键提供了理论依据。此外，还制备了量子点发光二极管（QLED），紫外光电子能谱（UPS）显示，经 ZnI2 处理后的 QDs 与空穴传输层之间的空穴注入势垒降低了 0.12 eV，从而促进了空穴注入。最后，与原始 QLED 相比，经过 ZnI2 处理的 QLED 的 Lmax 和 EQEmax 分别提高了 1.57 倍和 1.82 倍，达到 6370 cd m-2 和 9.1%。这项研究为提高无镉蓝色 QLED 的性能提供了宝贵的参考。

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引用次数: 0

Resonantly Enhanced Infrared Up‐Conversion in Double‐Step Asymmetric Subwavelength Grating Structure 双阶不对称亚波长光栅结构中的共振增强型红外上转换

IF 9 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

Advanced Optical Materials

Pub Date : 2024-09-11 DOI: 10.1002/adom.202401070

Lal Krishna Anitha Kumari Sreekantan Nair, Jyothsna Konkada Manattayil, Jayanta Deka, Rabindra Biswas, Varun Raghunathan

The design and experimental demonstration of double‐step, 1D amorphous germanium grating structures supporting quasi bound‐states‐in‐continuum (quasi‐BIC) resonance at 3.2 µm wavelength and its application to third‐order sum‐frequency generation‐based up‐conversion are reported. Linear transmission measurements on the fabricated metasurface with loosely focussed excitation spanning 0–3° angles show very good agreement with ideal plane‐wave excitation of the periodic photonic structure. TSFG measurements performed on the same structures with tightly focusing mid‐infrared signal and pump beams using a reflective‐type objective with 15–40° angular excitation show ≈375 times enhancement with significant blue‐shift in the resonance feature by ≈300 nm. To understand this excitation angle dependence of the resonance characteristics, a generalized plane‐wave expansion (PWE) model is developed by considering varying excitation angle plane‐waves incident on the metasurface with a discretized angular spectrum representation used to coherently combine the resultant electric and magnetic fields to obtain the linear transmission characteristics and nonlinear TSFG spectra. The PWE method is found to be particularly effective in modeling linear and nonlinear responses under realistic illumination conditions while ensuring optimal utilization of computational resources. Good agreement is obtained between the PWE simulations, linear transmission, and nonlinear TSFG measurements by considering appropriate angular excitation.

报告介绍了支持 3.2 µm 波长准连续束缚态（quasi-BIC）共振的双阶 1D 非晶锗光栅结构的设计和实验演示，以及它在基于三阶和频发生的上转换中的应用。利用 0-3° 角的松散聚焦激励对制造的元表面进行的线性传输测量显示，与周期性光子结构的理想平面波激励非常吻合。使用反射式物镜，以 15-40° 角激发中红外信号光束和泵浦光束，对相同结构进行的 TSFG 测量显示，共振特征的蓝移≈300 nm，增强了≈375 倍。为了理解共振特性的这种激励角度依赖性，我们开发了一个广义平面波扩展（PWE）模型，该模型考虑了入射到元表面上的不同激励角度平面波，并使用离散角频谱表示法将产生的电场和磁场相干地结合起来，从而获得线性传输特性和非线性 TSFG 光谱。研究发现，PWE 方法在模拟现实光照条件下的线性和非线性响应时特别有效，同时确保了计算资源的最佳利用。通过考虑适当的角度激励，PWE 模拟、线性传输和非线性 TSFG 测量之间获得了良好的一致性。

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引用次数: 0

Sb2Te3–Bi2Te3 Direct Photo–Thermoelectric Mid‐Infrared Detection Sb2Te3-Bi2Te3 直接光热电中红外探测器

IF 9 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

Advanced Optical Materials

Pub Date : 2024-09-10 DOI: 10.1002/adom.202401450

Simon Wredh, Mingjin Dai, Kenta Hamada, Md Abdur Rahman, Nur Qalishah Adanan, Golnoush Zamiri, Qing Yang Steve Wu, Wenhao Zhai, Nancy Wong Lai Mun, Zhaogang Dong, Wakana Kubo, Qi Jie Wang, Joel K.W. Yang, Robert E. Simpson

A compact and responsive thermoelectric photodetector is introduced for the mid‐infrared. By resonantly coupling mid‐infrared light to a Sb2Te3‐Bi2Te3 thermoelectric junction, a thermocouple is formed that is directly heated by narrow‐band mid‐infrared radiation. Near‐perfect absorption is achieved at this hot junction through the resonantly enhanced coupling of light to free‐electrons in the Bi2Te3 and Sb2Te3 materials. The fabricated devices operate at 3.6 µm and demonstrate a responsivity of 10.2 V W−1, a specific detectivity of 4.6 × 106 cm Hz1/2 W−1, and a bandwidth in the order of 1 kHz. The optimal detection wavelength can be spectrally tuned by changing the resonant cavity dimensions. This work shows a path toward miniaturized mid‐infrared detectors and spectrometers with high sensitivity, responsivity, and bandwidth. Importantly, the device presented here is ideal for industrial production, which it is hoped will provide wider access to mid‐infrared technologies for chemical sensing, medicine, and security.

本文介绍了一种结构紧凑、反应灵敏的中红外热电光电探测器。通过共振耦合中红外光到 Sb2Te3-Bi2Te3 热电结，形成一个热电偶，由窄波段中红外辐射直接加热。通过共振增强光与 Bi2Te3 和 Sb2Te3 材料中自由电子的耦合，热电结实现了近乎完美的吸收。所制造的器件工作波长为 3.6 µm，响应率为 10.2 V W-1，比检测率为 4.6 × 106 cm Hz1/2 W-1，带宽为 1 kHz。最佳探测波长可通过改变谐振腔尺寸进行光谱调谐。这项研究为实现具有高灵敏度、高响应度和高带宽的微型中红外探测器和光谱仪指明了道路。重要的是，这里介绍的装置非常适合工业化生产，希望它能为化学传感、医学和安全领域提供更广泛的中红外技术。

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引用次数: 0

Flexible Near‐Infrared Organic Photodetectors With Ultralow Dark Current by Layer‐by‐Layer Blade Coating 通过逐层叶片涂层实现具有超低暗电流的柔性近红外有机光电探测器

IF 9 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

Advanced Optical Materials

Pub Date : 2024-09-10 DOI: 10.1002/adom.202401891

Yingze Zhang, Wenliang Chen, Junhui Miao, Jun Liu, Lixiang Wang

Near‐infrared organic photodetector (NIR OPD) is promising for emerging wearable biosensing applications. However, their practical application is hindered by the high dark currents of devices that limit the detection of faint light. In this work, highly sensitive flexible NIR OPDs are presented with ultralow dark currents, fabricated using a layer‐by‐layer blade coating (LBL‐BC) technique. In the active layer, a fully fused‐ring molecule FM2, featuring a fixed molecular skeleton, is employed as an electron acceptor to reduce the trap density. The LBL‐BC method enhances the film order and phase purity of the active layer, significantly reduces the trap density of states, and optimizes the vertical phase separation structure of the thin film, thereby preventing reverse charge injection. As a result, a highly sensitive flexible NIR OPD is developed exhibiting an ultralow dark current density of 4.83 × 10−9 A cm−2 at −0.3 V bias and an extremely low noise current density of 7.65 × 10−15 A Hz−1/2 at 10 Hz, comparable to commercial silicon photodiodes. Furthermore, this flexible device is successfully applied for real‐time monitoring of human heartbeat rate, oxygen saturation, and motion recognition. These findings advance the development of highly sensitive NIR OPDs and their application in wearable biosensing technologies.

近红外有机光电探测器（NIR OPD）在新兴的可穿戴生物传感应用中大有可为。然而，这些器件的高暗电流限制了对微弱光线的检测，从而阻碍了它们的实际应用。本研究采用逐层刀片涂层（LBL-BC）技术制造出了具有超低暗电流的高灵敏度柔性近红外 OPD。在活性层中，采用了具有固定分子骨架的全熔环分子 FM2 作为电子受体，以降低陷阱密度。LBL-BC 方法提高了活性层的薄膜有序性和相纯度，显著降低了陷阱态密度，优化了薄膜的垂直相分离结构，从而防止了反向电荷注入。因此，这种高灵敏度的柔性近红外光电二极管在-0.3 V偏压下的暗电流密度为 4.83 × 10-9 A cm-2，在 10 Hz 下的噪声电流密度为 7.65 × 10-15 A Hz-1/2，与商用硅光电二极管相当。此外，这种灵活的器件还成功地应用于实时监测人体心跳率、血氧饱和度和运动识别。这些发现推动了高灵敏度近红外光电二极管的发展及其在可穿戴生物传感技术中的应用。

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引用次数: 0

Reconfigurable Hologram Response to Liquid via the Femtosecond Laser Direct Writing of 3D Micropillars 通过飞秒激光直接写入三维微柱实现对液体的可重构全息图响应

IF 9 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

Advanced Optical Materials

Pub Date : 2024-09-10 DOI: 10.1002/adom.202400612

Taoyong Li, Luqi Li, Lan Jiang, Peng Yi, Min Li, Songchang Li, Xibiao Li, Xiangyu Zhang, Andong Wang, Zhi Wang, Jiafang Li, Lingling Huang, Bing Han, Xiaowei Li

Reconfigurable and tunable holograms hold significant practical value in the fields of anti‐counterfeiting, optical security, and information display due to their ability to reprogram holographic patterns and create variable visual effects. However, current encryption techniques face challenges in achieving rapid encryption/decryption and ensuring consistent methods. In this study, a method for producing a reconfigurable encryption hologram utilizing the deformation and recovery properties of micropillars in response to liquid is demonstrated. Micron‐scale micropillars are fabricated using femtosecond laser two‐photon polymerization. By exploiting the rapid deformation and recovery capabilities of micropillars with specific pitches and aspect ratios in response to liquids, micropillar structures and holograms are combined to construct reconfigurable holograms. The encrypted pattern information in the reconfigurable holograms is only readable following immersion in alcohol and laser irradiation. The proposed method offers a facile, reversible, reusable, and practical solution for information encryption, with significant potential in anti‐counterfeiting and optical security.

可重构和可调谐全息图在防伪、光学安全和信息显示领域具有重要的实用价值，因为它们能够对全息图案进行重新编程，并创造出可变的视觉效果。然而，目前的加密技术在实现快速加密/解密和确保方法一致性方面面临挑战。本研究展示了一种利用微柱在液体作用下的变形和恢复特性制作可重新配置加密全息图的方法。微米级微柱是利用飞秒激光双光子聚合技术制造的。利用具有特定间距和长宽比的微柱在液体作用下的快速变形和恢复能力，将微柱结构和全息图结合起来，构建出可重新配置的全息图。可重构全息图中的加密图案信息只有在浸入酒精和激光照射后才能读取。所提出的方法为信息加密提供了一种简便、可逆、可重复使用的实用解决方案，在防伪和光学安全领域具有巨大潜力。

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引用次数: 0

Errata: A Comprehensive Multipolar Theory for Periodic Metasurfaces 勘误表周期性元曲面的综合多极理论

IF 9 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

Advanced Optical Materials

Pub Date : 2024-09-10 DOI: 10.1002/adom.202402267

Aso Rahimzadegan, Theodosios D. Karamanos, Rasoul Alaee, Aristeidis G. Lamprianidis, Dominik Beutel, Robert W. Boyd, Carsten Rockstuhl

<div>This correction refers to the article titled “A Comprehensive Multipolar Theory for Periodic Metasurfaces”[1] published in Advanced Optical Materials in March 2022. <ul><li>a) On page 12, in Equation (26), +rTE should be changed to −rTE. The correct equation is: <div><mjx-container ctxtmenu_counter="5" ctxtmenu_oldtabindex="1" display="true" jax="CHTML" role="application" sre-explorer- style="font-size: 103%; position: relative;" tabindex="0"><mjx-math aria-hidden="true" display="true" location="graphic/adom202402267-math-0001.png" style="margin-left: 0px; margin-right: 0px;"><mjx-semantics><mjx-mrow data-semantic-children="2,43,46" data-semantic-content="3,9" data-semantic- data-semantic-role="equality" data-semantic-speech="t Subscript upper T upper E Baseline equals 1 minus r Subscript upper T upper E Baseline equals 1 minus StartFraction 3 Over 4 pi normal upper Lamda overTilde squared EndFraction left parenthesis StartFraction 1 Over 1 divided by b 1 minus normal i upper C Subscript d d Baseline EndFraction right parenthesis" data-semantic-type="relseq"><mjx-msub data-semantic-children="0,1" data-semantic- data-semantic-parent="47" data-semantic-role="latinletter" data-semantic-type="subscript"><mjx-mi data-semantic-annotation="clearspeak:simple" data-semantic-font="italic" data-semantic- data-semantic-parent="2" data-semantic-role="latinletter" data-semantic-type="identifier"><mjx-c></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mi data-semantic-font="normal" data-semantic- data-semantic-parent="2" data-semantic-role="unknown" data-semantic-type="identifier" size="s"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator="relseq,=" data-semantic-parent="47" data-semantic-role="equality" data-semantic-type="relation" rspace="5" space="5"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children="4,8" data-semantic-content="5" data-semantic- data-semantic-parent="47" data-semantic-role="subtraction" data-semantic-type="infixop"><mjx-mn data-semantic-annotation="clearspeak:simple" data-semantic-font="normal" data-semantic- data-semantic-parent="43" data-semantic-role="integer" data-semantic-type="number"><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator="infixop,−" data-semantic-parent="43" data-semantic-role="subtraction" data-semantic-type="operator" rspace="4" space="4"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children="6,7" data-semantic- data-semantic-parent="43" data-semantic-role="latinletter" data-semantic-type="subscript"><mjx-mi data-semantic-annotation="clearspeak:simple" data-semantic-font="italic" data-semantic- data-semantic-parent="8" data-semantic-role="latinletter" data-semantic-type="identifier"><mjx-c></mjx

a) 第 12 页，公式 (26) 中的 +rTE 应改为 -rTE。正确的公式是：tTE=1-rTE=1-34πΛ∼2(11/b1-iCdd)$$begin{equation} t_{rm TE}= 1 - r_{rm TE} = 1 - frac{3}{4pi widetilde{Lambda }^2}{left(frac{1}{1/b_1-mathrm{i}C_{rm dd}}right)} end{equation}$$(1)b) 在第 3.5 节第二段中，归一化周期应从 1 变为 1.12。正确的公式是：Λ∼=Λ/λ=1.12$$begin{equation}（开始{equation}）。widetilde{Lambda }=Lambda /lambda =1.12 end{equation}$$(2)这个值在第 3.c 段中被正确地指出）在附录 B 中，方程 (B1a) 的左边不应该有斜线。正确的等式是：α¯¯jj′vv′=ζjζj′kj+j′+1α∼¯jj′vv′$$begin{equation}（开始{equation}）。bar{bar{alpha }}_{jj^{prime }}^{vv^{prime }}= frac{zeta _{j}zeta _{j^{prime }}}{k^{j+j^{prime }+1}}},bar{bar{widetilde{alpha }}}_{jj^{prime }}^{vv^{prime }}.end{equation}$(3)d) 在附录 F 的公式 (F3) 中，我们错误地表达了旋转矩阵 R¯$bar{bar{R}}$。(F3) 的正确表述是[θ̂ĵ]=R¯[x̂ŷẑ]=[cosθcosjcosθsinj-sinθ-sinjcosj0][x̂ŷẑ]$$begin{equation}{left[hspace{0.0pt}}}。defeqcellsep{&}begin{array}{c}hat{bm {theta }}.（[3pt]）hat{/bm {}phi }end{array}（hspace{0.0pt}）right]}hspace{0.0pt} = hspace{0.0pt}bar{bar{R}}, {left[hspace{0.0pt}defeqcellsep{&}begin{array}{c}hat{mathbf {x}}（[3pt]）hat{mathbf {y}（[3pt]）（{z}）end{array}hspace{0.0pt}[3pt] hat{mathbf {z}hspace{0.0pt} = hspace{0.0pt} {left[hspace{0.0pt }開始{array}{ccc}rm costheta ,{rm cos}phi & {rm cos}theta ,{rm sin}phi & -{rm sin}theta [3pt] -{rm sin}phi & {rm cos}phi & 0 end{array}hspace{0.0pt} - {rm sin}phi & {rm cos}phi & 0right]}hspace{0.0pt}{left[hspace{0.0pt}defeqcellsep{&}begin{array}{c}hat{mathbf {x}}（[3pt]）hat{mathbf {y}（[3pt]）（{z}）end{array}（hspace{-1.42262pt}）right]}end{equation}$$(4)These corrections do not affect the results or the figures, as the mistakes were only present in the manuscript's text.对于这些错字给读者带来的不便，我们深表歉意。

引用次数: 0