标题： 纳米粒子与石墨烯光栅之间的法向和侧向卡西米尔-利夫希茨力 显示英文标题

标题： Normal and lateral Casimir-Lifshitz forces between a nanoparticle and a graphene grating

摘要： 我们研究了纳米粒子与沉积在熔融石英板上的1D石墨烯光栅之间的卡西米尔-利夫希茨（CL）力的法向和侧向分量。 为此，采用了散射矩阵方法，并结合了增强的傅里叶模态方法与局部基函数。 我们发现，通过用石墨烯光栅覆盖熔融石英板，当光栅填充率为0.5时，小频率下的法向CL力谱增加了约100%，而当板完全被覆盖时，增加更多。 通常采用的加法近似（有和没有石墨烯涂层时力的加权平均）无法提供关于侧向CL力的任何信息，并且如我们所展示的，也无法对法向CL力提供准确估计。 当纳米粒子横向移动（$x_A$）时，法向CL力被调制并保持吸引力。 相反，侧向CL力在每个周期内改变符号两次，显示出一系列交替的稳定和不稳定侧向平衡位置，分别出现在石墨烯条带和光栅狭缝区域。 最后，我们表明侧向位移效应对几何因子$d/D$敏感（$d$是分离距离，$D$是光栅周期）。 我们识别出两个明显区域：一个区域（$d/D<1.0$）中侧向位移显著影响CL能量，另一个区域（$d/D \geq 1.0$）中这种效应可以忽略不计，在$d\approx D$处发生交叉。 我们的预测对纳米/微米尺度下纳米粒子与结构物体相互作用时的CL法向和侧向力的实验和应用具有相关意义，并且也直接适用于靠近这些纳米结构的原子。 显示英文摘要

摘要： We study the normal and lateral components of the Casimir-Lifshitz (CL) force between a nanoparticle and 1D graphene grating deposited on a fused silica slab. For this purpose, the scattering matrix approach together with the Fourier modal method augmented with local basis functions are used. We find that, by covering a fused silica slab by a graphene grating, the spectrum of the normal CL force at small frequencies is increased by about 100% for a grating filling fraction of 0.5, and even more when the slab is completely covered. The typically employed additive approximation (the weighted average of the force with and without the graphene coating) cannot provide any information on the lateral CL force, and, as we show, cannot provide accurate estimation for the normal CL force. When the nanoparticle is laterally shifted ($x_A$), the normal CL force is modulated and remains attractive. On the contrary, the lateral CL force changes sign twice in each period, showing a series of alternating stable and unstable lateral equilibrium positions, occurring in the graphene strips and of the grating slits regions, respectively. Finally, we show that the lateral shift effect is sensitive to the geometric factor $d/D$ ($d$ is the separation distance, and $D$ is the grating period). We identify two clear regions: a region ($d/D<1.0$) where the lateral shift significantly affects the CL energy, and a region ($d/D \geq 1.0$) where this effect is negligible, with a crossover at $d\approx D$. Our predictions can have relevant implications to experiments and applications of the CL normal and lateral forces acting on nanoparticles interacting with structured objects at the nano/micro scale, and are also directly valid for atoms close to these nanostructures.