1.Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi’an 710129, China 2.CAS Key Laboratory of Spectral Imaging Technology, Xi’an Institute of Optics and Precision Mechanics of CAS, Xi’an 710119, China
Fund Project:Project supported by the National Key R&D Program of China (Grant No. 2017YFA0303800), the National Natural Science Foundation of China (Grant Nos. 11634010, 61675170, 11874050), the Open Research Fund of CAS Key Laboratory of Spectral Imaging Technology, China (Grant No. LSIT201913W), and the Fundamental Research Fund for the Central Universities, China (Grant Nos. 3102019JC008, 310201911fz049)
Received Date:13 February 2020
Accepted Date:01 May 2020
Available Online:07 June 2020
Published Online:20 September 2020
Abstract:Manipulating the core-shell structure with the optical force has been extensively studied, giving birth to applications such as particle sorting, biomarkers and drug delivery. Tailoring the optical force exerted on the core-shell above the metallic film remains unexplored, despite the obvious benefits for both fundamental research and applications including strong coupling, surface enhanced spectroscopy, nanolaser, and nanoscale sensing. In this work, we systematically investigate the optical force exerted on a dielectric/metal core-shell above a gold film by utilizing the Maxwell stress tensor formalism. It is found that at the present gold substrate, the optical force on the core-shell can be one order of magnitude larger than that on the individual core-shell due to the strong coupling between the core-shell and the gold film. Interestingly, the direction of the optical force can be reversed from positive to negative by distributing the local field from the upside of core-shell to the structure gap through changing the excitation wavelength. Furthermore, we demonstrate that the magnitude and peak wavelength of the optical force can be well controlled by altering the structure gap, the size and refractive index of the core. More specifically, it is found that the coupling strength between the core-shell and the gold film decreases with the gap size increasing. As a result, we observe the blue shift of bonding mode and the decrease of local field in the gap, which leads the force peak wavelength to be blue-shifted and the force peak magnitude to decrease, respectively. Also, by increasing the radius and refractive index of the core, a red shift of force peak is accompanied with the red shift of the bonding mode. In addition, the force peak magnitude follows the same trend as the total local field enhancement factor when the radius and refractive index of the core change. We hope that our results open the way to control the cavity size of particle on film structure, which would be beneficial for tailoring the light matter interaction even down to single molecular level and promises to have the applications in novel functional photonic devices. Keywords:optical force/ surface plasmons/ core-shell structure/ plasmon hybridization
这里, ε和μ为环境的介电常数和磁导率, E和H分别对应电场和磁场矢量, I为单位矩阵. 图3(a)中的红色实线给出了金膜衬底上核壳结构所受的纵向光学力Fz. 可以看出, 该纵向光学力Fz的幅值可达3.5 pN, 并且比无金薄膜时的核壳结构所受纵向光学力增大约一个数量级(图3(a)中的黑色实线). 此外, 核壳结构受到的纵向光学力的方向分别在波长600, 740和810 nm处发生反转. 特别地, 当激发波长处于散射峰540和790 nm时, 出现负Fz的峰值, 意味着核壳结构受到金膜的吸引力, 趋向金膜移动; 而当激发波长为670和830 nm时, 出现正Fz的峰值, 意味着核壳结构受到金薄膜的排斥力, 趋向远离金薄膜. 为解释光学力方向的反转机制, 进一步分析了Fz的正、负峰值波长处xz平面上结构周围的电场强度增强因子EF的分布(如图3(b)—(e)所示), 即局域场与入射场的光强比EF = |Eloc/Ein|2. 由图3(b)和图3(d)可知, 在共振波长为540和790 nm处, 核壳颗粒与金薄膜耦合强烈, 局域场被束缚在两者的间隙处. 由于梯度力指向光强最大处, 由此产生了负的Fz, 使得核壳结构向金薄膜移动. 相反, 如图3(c)和图3(e)所示, 当激发光波长远离共振波长时, 核壳结构与金薄膜耦合减弱, 局域场分布在核壳结构的上半侧, 此时产生正的Fz, 使核壳结构远离金薄膜. 值得注意的是, 在波长为790 nm处核壳结构所受纵向光学力是波长为540 nm时的5倍左右. 这是因为在波长为790 nm时, 核壳结构的共振类型为成键模式, 银壳内、外为同向电偶极模式的叠加, 产生了更强的净偶极矩. 由此, 核壳结构在金薄膜上诱导出更多的镜像电荷, 使间隙处的局域场增大, 产生更强的纵向光学力. 图 3 (a)核壳结构所受的纵向光学力Fz; 波长为(b) 540, (c) 670, (d) 790和(e) 830 nm时核壳结构周围电场强度增强因子EF的分布 Figure3. (a) Longitudinal optical force Fz exerted on the core-shell on gold film. The electric-field intensity enhancement factor map of the core-shell on gold film at wavelengths of (b) 540, (c) 670, (d) 790, and (e) 830 nm, respectively.
22.3.金膜衬底与核壳结构间距对光学力的影响 -->
2.3.金膜衬底与核壳结构间距对光学力的影响
核壳结构与金膜衬底间的模式耦合会影响核壳结构所受的光学力, 而模式间隙是决定等离激元模式耦合强弱的一个关键因素. 为此, 进一步保持核壳颗粒尺寸及材料不变, 分析金膜衬底与核壳结构间距对核壳结构纵向光学力的影响. 如图4(a)所示, 当间距h由6 nm增加到50 nm时, 核壳结构与金膜的耦合减弱, 其受到衬底的屏蔽效应也随之减弱, 导致表面等离激元共振的回复力增强, 促使散射光谱中反键模式和成键模式的峰位发生轻微蓝移. 相应地, 结构共振峰的蓝移也使得Fz的幅值峰位出现了蓝移, 如图4(b)所示. 此外, 随着h的增大, 反键模式散射强度相对于成键模式的散射强度减弱. 这是由于核壳结构与金膜耦合的减弱, 导致衬底上诱导的镜像电荷减少. 由此, 反键模式的净偶极矩减弱, 而成键模式的净偶极矩增强, 带来了对应光谱峰强度的变化. 如图4(c)中红色菱形所示, 核壳结构与衬底耦合减弱, 也使得结构间隙内的平均电场强度增强因子$\overline {EF}$(即间隙内总EF与间隙面积比)减弱, 造成纵向光学力Fz的幅值|Fz|max随间隙h增加而显著减弱(图4(c)中蓝色圆点). 图 4 核壳-金膜结构的(a)散射光谱、(b)光学力谱和(c)纵向光学力幅值及间隙的平均电场强度增强因子随结构间隙h的变化 Figure4. (a) Scattering spectra of the core-shell on gold film; (b) longitudinal optical force spectra of the core-shell on gold film; (c) maximum longitudinal optical force and the average electric-field intensity enhancement factor as a function of gap size for the core-shell on gold film.
22.4.不同内核尺寸对核壳所受光学力的影响 -->
2.4.不同内核尺寸对核壳所受光学力的影响
保持核壳颗粒的半径为70 nm, 核壳结构距离金膜衬底h = 10 nm, 分析不同内核尺寸对核壳结构的散射光谱及光学力的影响. 由图5(a)的散射光谱可以看出, 当介质核的半径Rc从50 nm减小到20 nm时, 成键模式的散射峰位逐渐蓝移, 并且与反键模式峰位的间距减小. 由等离激元杂化理论可知, 当内核尺寸减小, 银壳内、外层间的耦合作用减弱, 从而导致图5(a)中散射峰位的变化. 并且, 由于内核尺寸的减小, 银壳的损耗随其厚度增加而增大[36], 谱线的半高全宽也从25 nm增加到130 nm. 由图5(b)可知, 伴随着成键模式散射峰位的蓝移, 该模式对应的纵向光学力幅值的峰位也发生蓝移. 需要指出的是, 纵向光学力Fz的幅值|Fz|max取决于壳外的局域场[37]. 由图5(c)可以看出, 随着介质核半径的增大, |Fz|max (蓝色圆点)与间隙内的平均电场强度增强因子(红色菱形)表现出了相同的变化趋势. 图 5 核壳-金膜结构的(a)散射光谱、(b)纵向光学力谱和(c)纵向光学力幅值以及间隙内平均电场强度增强因子随内核尺寸Rc的变化 Figure5. (a) Scattering spectra of the core-shell on gold film; (b) longitudinal optical force spectra of the core-shell on gold film; (c) maximum longitudinal optical force as well as the average electric-field intensity enhancement factor as a function of dielectric core radius for the core-shell on gold film.
22.5.不同内核折射率对核壳所受光学力的影响 -->
2.5.不同内核折射率对核壳所受光学力的影响
最后, 保持内核半径Rc = 50 nm, 银壳厚度t = 20 nm, 核壳与金膜衬底间距h = 10 nm, 分析内核的折射率对核壳的散射光谱及光学力的影响. 从图6(a)的散射光谱可知, 当内核的折射率从3.5降到1时, 成键和反键模式的峰位均出现蓝移. 特别地, 成键模式的峰位从波长790 nm蓝移至590 nm. 这是由于随着内核的折射率减小, 其产生的屏蔽效应减弱, 银壳内表面产生的感应电荷数目增加, 模式的回复力增大, 从而导致成反键模式峰位的蓝移. 如图6(b)所示, 与成键模式的频移相对应, 内核的折射率减小将导致颗粒所受纵向光学力幅值峰位的蓝移. 为此, 进一步分析了内核折射率对核壳的光学力大小的影响. 由图6(c)可知, 纵向光学力幅值|Fz|max (蓝色圆点)随内核折射率的增大呈现出先增大后减小的趋势. 进而得到了不同内核折射率情况下间隙内平均电场强度增强因子(图6(c)中红色菱形). 可以看出, 随着内核折射率的增大, |Fz|max和$\overline {EF}$有着相同的变化趋势. 由此可知, 核壳结构所受光学力大小的变化, 源于折射率的增大引起核壳外局域场的改变, 导致了梯度力的改变. 图 6 核壳-金膜结构的(a)散射光谱、(b)光学力谱和(c)纵向光学力幅值及间隙的平均电场强度增强因子随内核折射率nc的变化 Figure6. (a) Scattering spectra of the core-shell on gold film; (b) longitudinal optical force spectra of the core-shell on gold film; (c) maximum longitudinal optical force and the average electric-field intensity enhancement factor as a function of index for the core-shell on gold film.
图 1 金膜衬底上介质/金属核壳结构的示意图
图 2 核壳-金薄膜结构的等离激元杂化示意图和散射光谱 (a)等离激元杂化示意图; (b)散射光谱, 插图为电场分量Ez在xy平面上的分布
图 3 (a)核壳结构所受的纵向光学力Fz; 波长为(b) 540, (c) 670, (d) 790和(e) 830 nm时核壳结构周围电场强度增强因子EF的分布
图 4 核壳-金膜结构的(a)散射光谱、(b)光学力谱和(c)纵向光学力幅值及间隙的平均电场强度增强因子随结构间隙h的变化
图 5 核壳-金膜结构的(a)散射光谱、(b)纵向光学力谱和(c)纵向光学力幅值以及间隙内平均电场强度增强因子随内核尺寸Rc的变化
图 6 核壳-金膜结构的(a)散射光谱、(b)光学力谱和(c)纵向光学力幅值及间隙的平均电场强度增强因子随内核折射率nc的变化