Research on surface plasmon refractive index sensing of gold nano cone array and gold film coupling structure

Wang Xiangxian; Chen Hanwen; Zhu Jiankai; Qi Yunping; Zhang Liping; Yang Hua; Yu Jianli

doi:10.12086/oee.2022.220135

Abstract

A surface plasmon resonance refractive index sensor based on the coupling structure of gold nano cones and a gold film with a SiO₂ film as spacer-layer is designed. The surface plasmon resonance modes in the composite structure are studied by using the Finite Difference Time Domain method. The composite structure can stimulate not only localized surface plasmon, but also propagating surface plasmon. The energy of the incident electromagnetic wave is partially coupled to the localized surface plasmon through a single gold nano cone, and partially coupled to the propagating surface plasmon through a grating of gold nano cone array. The reflection spectra of the composite structure are simulated in the refractive index range of 1.30 to 1.40. It is found that the resonance wavelength has a linear relationship with the refractive index of the analyte, and the reflectivity at the resonance is almost zero due to the strong resonance coupling between localized and propagating surface plasmon. In addition, the full width at half maximum of propagating surface plasmon resonance mode is very narrow when the geometric parameters of gold nano cone are optimized. The sensitivity and figure of merit reach 770 nm/RIU and 113 RIU⁻¹ respectively, and it has good refractive index sensing performance. The designed composite structure is expected to be widely used in the field of biochemical detection.

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1. 引　言

本文设计了金纳米锥与金薄膜耦合结构，并具体探究其所激发的表面等离子体效应，利用时域有限差分法对结构进行数值模拟研究，探究了结构的几何参数对折射率传感的影响。在光栅周期为800 nm，金纳米锥底面半径为140 nm，高度为200 nm时，耦合结构的折射率灵敏度可达770 nm/RIU。在900 nm~2000 nm的波长范围内，结构可以实现折射率范围1.30~1.40的传感，且可以通过改变结构周期或金纳米锥的几何参数来调谐共振波长。相比类似的折射率传感器件，所设计的结构在生物传感和检测方面具有较大的应用潜力。

在一定条件下，金属表面的自由电子经过入射光照射，入射光波中的光子与金属表面的自由电子相互作用产生的电磁振荡被称之为传播表面等离子体^[1-2](propagating surface plasmons, PSPs)。而当入射光作用于金属纳米颗粒上时，所产生的电磁振荡称为局域表面等离子体^[3-4](localized surface plasmons, LSPs)。在金属纳米颗粒和金属薄膜复合结构中，由于传播表面等离子体和局域表面等离子体的高效激发，使得微纳结构热点处的电磁场得到很大提高。这一特性也使得它在光催化^[5-7]、纳米光刻^[8-9]、生物传感^[10-13]、超表面^[14]、吸收器^[15-17]以及表面增强拉曼散射^[18-19]等领域得以广泛应用。

近几年，研究人员制备了不同形状、尺寸的纳米颗粒以及纳米颗粒与金属薄膜复合结构，使得这些微纳结构在应用方面的研究得到了广泛的关注。Qiang Fu^[20]等人通过银纳米立方体和银金属光栅的复合结构，实现了传播表面等离子体与局域表面等离子体的相互耦合。Chu^[21]等人研究了二维周期性金纳米盘阵列、二氧化硅间隔层和金薄膜组成的复合结构，通过改变金纳米盘的尺寸和阵列周期，发现共振条件下复合结构中单个金纳米盘的电场增强高达5000，远高于玻璃基片上单个金纳米盘的电场增强。此外，Kohandani^[22]等人通过在周期性二维纳米光栅(金纳米颗粒阵列)下方引入薄金层，实现了429 nm/RIU的灵敏度。Abutoama^[23]等人通过在薄金属膜上添加薄介质(Si₃N₄)光栅，在金属膜的两个边界处产生了两种表面等离子体，其中一种等离子体对分析物折射率敏感，其灵敏度达到580 nm/RIU。迄今，各种基于亚波长金属颗粒的表面等离子体折射率传感器已在实验或理论研究上均获得成功，如纳米球^[24-26]、纳米线^[27-31]及相互作用的颗粒集团等。随着微纳光刻技术的不断发展，通过颗粒阵列及薄膜结构耦合的方式来激发表面等离子体从而进一步提升折射率传感器的灵敏度、集成度及便携性仍然具有重要意义并表现出可观的应用潜力。

2. 理论分析

其次，当TM极化波垂直入射时，二维光栅激发的表面等离子体共振波长可表示为^[33-34]

当复合结构产生表面等离子体共振时，表面等离子体波对周围环境介质的变化十分敏感，故而共振波长的移动对应待测物的折射率变化。通过建立起待测物折射率与共振波长的曲线对应关系，即可达到折射率传感的目的。

其中：Δn为折射率(refractive index units，RIU)变化量，Δλ为Δn对应的共振波长偏离量。品质因数的定义为^[34]

该结构具有同时激发传播和局域表面等离子体共振的条件，入射电磁波能量通过单个金纳米锥可以激发局域表面等离子体共振，而金纳米锥组成的二维点阵可以激发传播表面等离子体共振。金纳米锥阵列作为一个二维点阵光栅提供额外的动量，从而将入射波能量耦合到传播表面等离激元中。补偿的额外动量^{[21, 32]}：

$FOM = \frac{S}{{FWHM}} ,$

传感器灵敏度(sensitivity，S)和品质因数(figure of merit，FOM)是描述传感器性能表现的两个物理参量，这两个参数值越高，则代表传感器性能越好。折射率灵敏度的定义为^[33]

其中：FWHM指的是用于折射率传感的共振峰的半高全宽(full width at half maximum，FWHM)。

${\lambda }_{{\rm{res}}}=\frac{P}{\sqrt{{n}^{2}+{m}^{2}}}\frac{\sqrt{\mathrm{Re}({\varepsilon }_{{\rm{metal}}}) \cdot {n}^{2}{}_{{\rm{analyte}}}}}{\sqrt{\mathrm{Re}({\varepsilon }_{{\rm{metal}}})+{n}^{2}{}_{{\rm{analyte}}}}} ,$

其中：n和m是衍射阶数，为整数，D为光栅常数(即阵列周期)。(n, m) = (1, 0)和(1, 1)代表低阶共振波长下的两种模式，而随着(n, m)的增大，共振频率会越来越高。

图1(a)是所设计的金纳米锥与金纳米薄膜耦合结构的三维示意图。复合结构以玻璃为基底，自下而上分别为金纳米薄膜、SiO₂纳米薄膜间隔层、金纳米锥二维阵列。金纳米锥以正方形阵列规则排列，整个阵列沿x方向和y方向周期性延展，结构由一个x方向偏振、z轴负方向传播的平面波激发其表面等离激元。其中，金纳米薄膜的厚度为120 nm，SiO₂纳米薄膜间隔层厚度为20 nm。设金纳米锥的底面半径为R，高度为H，且允许金纳米锥的尺寸在一定范围内变化。SiO₂薄膜使金纳米锥阵列和金纳米薄膜分离，以此激发结构的局域和传播表面等离子体共振。在分析研究中，使用时域有限差分法(finite difference time domain, FDTD)来计算结构的反射光谱和场强分布。由于复合结构是周期性的，我们只选择如图1(b)中一个金纳米锥与金薄膜耦合微元作为研究对象，并使用周期性边界条件探究其表面等离子体效应及折射率传感特性。

${{G}} = \frac{{2 {\text{π}} }}{D}\sqrt {{n^2} + {m^2}} ,$

$S = \frac{{\Delta \lambda }}{{\Delta n}} ,$

其中：n和m为衍射阶数，P为二维光栅的周期，n_analyte为分析物折射率，ɛ_metal为金属的复介电常数。光栅激发的表面等离子体共振波长与光栅周期有关，随着周期的增加，共振波长将发生红移。

Figure 1. (a) Three dimensional schematic diagram of the composite structure of Au nano cone and Au nano film; (b) A top-down view of the structure, and the red foursquare lattice is the calculation unit

Figure 1. Full-Size Img PowerPoint

(a) Three dimensional schematic diagram of the composite structure of Au nano cone and Au nano film; (b) A top-down view of the structure, and the red foursquare lattice is the calculation unit

3. 研究结果与讨论

最后，讨论模式1和模式2的传感特性，分析共振模式对结构传感器灵敏度及品质因数的影响。图5为以0.01为间隔，折射率从1.30变化到1.40时，不同折射率下复合结构的反射光谱，金纳米锥的底面半径为140 nm，高度为200 nm，光栅周期为800 nm (最优参数)。从反射光谱中可以看到，随着待测物折射率逐渐增大，两种模式的共振波长均发生红移，且反射率一直保持在0.1以下的较低范围。在不同待测物折射率下，同一模式所对应的共振峰半高全宽几乎不变，且模式1的半高全宽非常窄(FWHM=7 nm)，具有良好的折射率传感性能。

图6为不同待测物折射率下的反射光谱共振波长与折射率变化的关系曲线，金纳米锥的几何参数同上。其中，红色曲线为光栅激发的表面等离子体共振波长的理论值与背景折射率的关系曲线，黑色、蓝色曲线为复合结构两种共振模式下共振波长的数值模拟结果与背景折射率的关系曲线，可以看出模式1仿真结果与理论结果拟合良好。关系曲线的斜率即代表复合结构的折射率灵敏度，计算得到两种模式下折射率灵敏度(S)分别为770 nm/RIU (模式1)和225 nm/RIU (模式2)，两种模式的品质因数(figure of merit，FOM)分别为113 RIU⁻¹(模式1)和1.9 RIU⁻¹(模式2)。相较于Abutoama等人^[23]和Sharma^[35]等人提出的介质光栅与金薄膜耦合结构，本文的灵敏度均优于其所报道的580 nm/RIU和693.88 nm/RIU；品质因数也高于其他以往的研究报道^[1,36]。除此之外，本文所设计的金纳米锥与金薄膜耦合结构可同时激发传播和局域两种表面等离子体共振模式作为传感通道，实现双通道不同波段的折射率传感。

$Figure 6. Relationship curves of reflection spectrum resonance wavelength of the composite structure with refractive index change under different refractive index of object to be measured. The bottom radius of gold nano cone is 140 nm, the height is 200 nm, and the period is 800 nm$

Figure 6. Full-Size Img PowerPoint

Relationship curves of reflection spectrum resonance wavelength of the composite structure with refractive index change under different refractive index of object to be measured. The bottom radius of gold nano cone is 140 nm, the height is 200 nm, and the period is 800 nm

图4(c)为复合结构在不同周期下的反射光谱，背景折射率为1.30，金纳米锥底面半径为140 nm，高度为200 nm，光栅周期以50 nm为步长从700 nm变化到900 nm。从反射光谱中可以看到模式1的共振波长随周期的增加逐渐向长波长移动且反射率均保持在0.1以下的较低范围内，模式2共振波长基本保持不变但反射率谷值逐渐降低。这说明模式1是低阶的二维光栅引起的传播表面等离子体共振，而模式2主要是由局域表面等离子体共振引起的，表现为共振波长与周期无关。从图4(d)可以看出，根据式(2)计算得到的不同周期下模式1共振波长理论值与仿真值基本吻合。

通过以上研究可知，无论是灵敏度还是品质因数，模式2都要比模式1低很多且品质因数相差较大。模式1之所以具有较高的灵敏度，是因为其主要是由传播表面等离子体共振引起的，而模式2主要是由局域表面等离子体共振引起的。即模式1相较于模式2对环境电介质折射率的改变要更敏感，因此模式1有更高的折射率灵敏度。而品质因数的大小同时取决于灵敏度和半高全宽，模式1的灵敏度不仅要比模式2大很多，而且其半高全宽也小很多。

复合结构中两种共振模式下的电场分布如图3所示，3(a)和3(d)为复合结构在x-z平面上两种模式的电场分布，3(b)和3(e)为SiO₂间隔层下表面和金薄膜界面上两种模式的电场分布，3(c)和3(f)为分析物与SiO₂间隔层上表面上两种模式的电场分布；3(a)、3(b)、3(c)为模式1，3(d)、3(e)、3(f)为模式2。从图3(a)和3(b)可以看出，电场增强主要分布于待测物环境中和金薄膜的表面，这是入射电磁波在金薄膜上表面耦合形成传播表面等离子体共振的结果。从图3(e)和3(f)可以看出，电场强度分布主要局域于金纳米锥与SiO₂间隔层的界面处和SiO₂间隔层与金薄膜的界面处，而这是因为入射电磁波通过金纳米锥阵列耦合形成局域表面等离子体共振。需要注意的是，两种模式是由复合结构引起的传播和局域表面等离子体共振耦合的结果，金纳米锥颗粒周围激发的LSPs与金薄膜上的PSPs相互作用，从而导致SiO₂间隔层上表面的电场分布不同。它们的区别在于两种表面等离激元的贡献不同。模式1中占优势的为传播表面等离子体共振，而模式2中局域表面等离子体共振更占优势。

下面进一步研究在不同参数下金纳米锥复合结构的反射光谱，分析结构参数对共振模式的影响。图4(a)为金纳米锥在不同高度(H)下的反射光谱，固定待测物背景折射率为1.30，光栅周期为800 nm，金纳米锥的底面半径为140 nm，将金纳米锥的高度以10 nm为步长从200 nm变化到240 nm。从反射光谱可以看出，模式1的共振波长随金纳米锥高度的增大几乎没有变化，而模式2的共振波长表现出向长波长方向的移动。这说明模式1主要是由传播表面等离子体共振引起的，而模式2主要是由局域表面等离子体共振引起的。图4(b)为金纳米锥在不同底面半径(R)下的反射光谱，待测物背景折射率依然为1.30，光栅周期为800 nm，金纳米锥的高度为200 nm，将金纳米锥底面半径以20 nm为步长从100 nm变化到180 nm。从图中可以看到，模式1的共振波长随尺寸的增大也几乎没有变化，而模式2的共振波长随着尺寸的变化逐渐向长波长方向移动。再次说明模式1所引起的共振是非局域的，模式2主要是由局域表面等离子体共振引起的。此外，金纳米锥的耦合距离也会对局域表面等离子体共振模式(模式2)有一定影响。当复合结构的周期一定时，金纳米锥之间的耦合距离可以通过金纳米锥底面半径(R)调控。从图4(b)也可以看出，当金纳米锥底面半径(R)增大，即金纳米锥之间的耦合距离减小时，模式 2的共振波长会出现红移。

图2是用FDTD模拟计算的复合结构在900 nm~2000 nm波长范围内扫描得到的反射光谱。对应的几何结构参数：金纳米锥的底面半径(R)为140 nm，高度(H)为200 nm，阵列周期(D)为800 nm，背景折射率(待测物折射率)为1.30。复合结构的反射光谱主要表现出两种表面等离子体共振模式，两种共振模式分别位于波长1052 nm (模式1)和1553 nm (模式2)处。由此可以说明，金纳米锥与金薄膜耦合结构可以有效地激发传播和局域表面等离子体共振，两种模式相互耦合使得共振强度都较大。对比两种共振模式可见，反射光谱中模式1的半高全宽较窄，而模式2的半高全宽相对来说要宽很多。这是由于它们之间不同的激发特点，传播表面等离子体共振是由光栅衍射引起的，需严格满足光栅衍射条件和动量匹配条件，故而共振波长频域较小对应其半高全宽较窄；局域表面等离子体共振是当入射电磁波与金属纳米颗粒内部自由电子的本征振荡频率一致时，金属内部的自由电子发生集体振荡的行为，主要受金属纳米颗粒的几何形状、尺寸、金属薄膜厚度等因素影响，因其无需满足光栅衍射条件即可激发，故而共振波长频域较大对应其半高全宽较宽。

从金纳米锥复合结构在不同参数下的反射光谱可以看出，模式1主要受光栅周期的影响，所引起的共振主要是传播表面等离子体共振。而模式2受金纳米锥几何参数的影响更大，主要是由局域表面等离子体共振引起的。

$Figure 5. Reflection spectrum of the composite structure under different refractive index of analyte. The radius of Au nano cone is 140 nm, the height is 200 nm, and the period is 800 nm$

Figure 5. Full-Size Img PowerPoint

Reflection spectrum of the composite structure under different refractive index of analyte. The radius of Au nano cone is 140 nm, the height is 200 nm, and the period is 800 nm

$Figure 4. The background refractive index is 1.30, the reflection spectra of the composite structure under different parameters. (a) D 800 nm, R 140 nm, and H changes from 200 nm to 240 nm; (b) D 800 nm, H 200 nm, and R changes from 100 nm to 180 nm; (c) H 200 nm, R 140 nm, and D changes from 700 nm to 900 nm; (d) Simulation and theoretical values of mode 1 resonance wavelength at various period$

Figure 4. Full-Size Img PowerPoint

The background refractive index is 1.30, the reflection spectra of the composite structure under different parameters. (a) D 800 nm, R 140 nm, and H changes from 200 nm to 240 nm; (b) D 800 nm, H 200 nm, and R changes from 100 nm to 180 nm; (c) H 200 nm, R 140 nm, and D changes from 700 nm to 900 nm; (d) Simulation and theoretical values of mode 1 resonance wavelength at various period

$Figure 2. Reflection spectra of composite structure of gold nano cone and gold film. The bottom radius, the height and the period of the gold nano cone are 140 nm, 200 nm, 800 nm, and the background refractive index is 1.30$

Figure 2. Full-Size Img PowerPoint

Reflection spectra of composite structure of gold nano cone and gold film. The bottom radius, the height and the period of the gold nano cone are 140 nm, 200 nm, 800 nm, and the background refractive index is 1.30

$Figure 3. Electric field distributions of the composite structure at two modes resonance wavelengths. The bottom radius, the height and the period of gold nano cone are 140 nm, 200 nm and 800 nm. The background refractive index is 1.30. (a) and (d) are the electric field distribution on the x-z plane; (b) and (e) are the electric field distribution on the lower surface of the SiO2 spacer and the interface of the Au film; (c) and (f) are the electric field distribution on the surface above the analyte and the SiO2 spacer; (a), (b) and (c) are mode 1, (d), (e) and (f) are mode 2$

Figure 3. Full-Size Img PowerPoint

Electric field distributions of the composite structure at two modes resonance wavelengths. The bottom radius, the height and the period of gold nano cone are 140 nm, 200 nm and 800 nm. The background refractive index is 1.30. (a) and (d) are the electric field distribution on the x-z plane; (b) and (e) are the electric field distribution on the lower surface of the SiO₂ spacer and the interface of the Au film; (c) and (f) are the electric field distribution on the surface above the analyte and the SiO₂ spacer; (a), (b) and (c) are mode 1, (d), (e) and (f) are mode 2

4. 结　论

设计了基于SiO₂间隔的金纳米锥阵列与金薄膜耦合结构表面等离子体共振折射率传感器。从反射光谱和电场分布两个角度进行了理论分析和数值模拟研究，论证了复合结构可以有效激发表面等离子体共振。在确定的几何参数下，复合结构在模式1中主要形成传播表面等离子体共振，而在模式2中主要形成局域表面等离子体共振。在金纳米锥底面半径为140 nm，高度为200 nm，光栅周期为800 nm时，复合结构在共振峰处具有很低的反射率即具有很高的共振强度。在上述最优参数下，模式1的折射率灵敏度和品质因数分别为770 nm/RIU和113 RIU⁻¹，远高于模式2的灵敏度和品质因数。本文所设计的折射率传感器有望在生化检测领域得到应用。

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- Corresponding author: Wang Xiangxian, wangxx869@lut.edu.cn On this Site On Google Scholar
  wangxx869@lut.edu.cn
  - College of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
- Chen Hanwen, chenhw2039@163.com On this Site On Google Scholar
  - College of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
- Zhu Jiankai On this Site On Google Scholar
  - College of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
- Qi Yunping On this Site On Google Scholar
  - College of Physics and Eectronic Engineering, Northwest Normal University, Lanzhou, Gansu 730070, China
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  - College of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
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  - College of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
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  - School of Electronic Engineering, Chaohu University, Hefei, Anhui 238024, China

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DOI: 10.12086/oee.2022.220135

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Wang Xiangxian, Chen Hanwen, Zhu Jiankai, Qi Yunping, Zhang Liping, Yang Hua, Yu Jianli. Research on surface plasmon refractive index sensing of gold nano cone array and gold film coupling structure. Opto-Electronic Engineering 49, 220135 (2022). DOI: 10.12086/oee.2022.220135

Wang Xiangxian, Chen Hanwen, Zhu Jiankai, Qi Yunping, Zhang Liping, Yang Hua, Yu Jianli. Research on surface plasmon refractive index sensing of gold nano cone array and gold film coupling structure. Opto-Electronic Engineering 49, 220135 (2022). DOI: 10.12086/oee.2022.220135

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- Received Date June 19, 2022
- Revised Date September 25, 2022
- Accepted Date October 12, 2022
- Available Online December 01, 2022
- Published Date December 24, 2022
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[1]	Wang X X, Zhu J K, Tong H, et al. A theoretical study of a plasmonic sensor comprising a gold nano-disk array on gold film with a SiO₂ spacer[J]. Chin Phys B, 2019, 28(4): 044201. DOI: 10.1088/1674-1056/28/4/044201 CrossRef Google Scholar
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[7]	Gao H J, Zhao X X, Zhang H M, et al. Construction of 2D/0D/2D face-to-face contact g-C₃N₄@Au@Bi₄Ti₃O₁₂ heterojunction photocatalysts for degradation of rhodamine B[J]. J Electron Mater, 2020, 49(9): 5248−5259. DOI: 10.1007/s11664-020-08243-2 CrossRef Google Scholar
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[13]	张伟建, 曾祥龙, 杨傲, 等. 纳米金涂覆微纳光纤的倏逝场氨气检测研究[J]. 光电工程, 2021, 48(9): 200451. DOI: 10.12086/oee.2021.200451 Zhang W J, Zeng X L, Yang A, et al. Research on evanescent field ammonia detection with gold-nanosphere coated microfibers[J]. Opto-Electron Eng, 2021, 48(9): 200451. DOI: 10.12086/oee.2021.200451 CrossRef Google Scholar
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[16]	Yan Z D, Lu X, Du W, et al. Ultraviolet graphene ultranarrow absorption engineered by lattice Plasmon resonance[J]. Nanotechnology, 2021, 32(46): 465202. DOI: 10.1088/1361-6528/ac1af9 CrossRef Google Scholar
[17]	Wu X L, Zheng Y, Luo Y, et al. A four-band and polarization-independent BDS-based tunable absorber with high refractive index sensitivity[J]. Phys Chem Chem Phys, 2021, 23(47): 26864−26873. DOI: 10.1039/D1CP04568G CrossRef Google Scholar
[18]	Yu M D, Huang Z P, Liu Z Q, et al. Annealed gold nanoshells with highly-dense hotspots for large-area efficient Raman scattering substrates[J]. Sens Actuators B Chem, 2018, 262: 845−851. DOI: 10.1016/j.snb.2018.02.048 CrossRef Google Scholar
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Research on surface plasmon refractive index sensing of gold nano cone array and gold film coupling structure

Abstract

Keywords

1. 引　言

2. 理论分析

3. 研究结果与讨论

4. 结　论

利益冲突

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Corresponding author: Wang Xiangxian, wangxx869@lut.edu.cn On this Site On Google Scholar

Chen Hanwen, chenhw2039@163.com On this Site On Google Scholar

Zhu Jiankai On this Site On Google Scholar

Qi Yunping On this Site On Google Scholar

Zhang Liping On this Site On Google Scholar

Yang Hua On this Site On Google Scholar

Yu Jianli On this Site On Google Scholar

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Research on surface plasmon refractive index sensing of gold nano cone array and gold film coupling structure

Abstract

Keywords

1. 引 言

2. 理论分析

3. 研究结果与讨论

4. 结 论

利益冲突

References

Cited by

Periodical cited type(5)

Other cited types(1)

Author Information

Corresponding author: Wang Xiangxian, wangxx869@lut.edu.cn On this SiteOn Google Scholar

Chen Hanwen, chenhw2039@163.com On this SiteOn Google Scholar

Zhu Jiankai On this SiteOn Google Scholar

Qi Yunping On this SiteOn Google Scholar

Zhang Liping On this SiteOn Google Scholar

Yang Hua On this SiteOn Google Scholar

Yu Jianli On this SiteOn Google Scholar

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1. 引　言

4. 结　论

Corresponding author: Wang Xiangxian, wangxx869@lut.edu.cn On this Site On Google Scholar

Chen Hanwen, chenhw2039@163.com On this Site On Google Scholar

Zhu Jiankai On this Site On Google Scholar

Qi Yunping On this Site On Google Scholar

Zhang Liping On this Site On Google Scholar

Yang Hua On this Site On Google Scholar

Yu Jianli On this Site On Google Scholar