We develop the theory of transportation and localization of a transparent dielectric spherical particle with the gradient forces in the interference field of orthogonally directed standing laser waves $E_z\left(\mathrm{c}\mathrm{o}\mathrm{s}kz\right)$ and $E_x\left(\mathrm{c}\mathrm{o}\mathrm{s}kx\right)$. It is shown that, when the waves $E_z$ and $E_x$ are coherent, the interference radiation field contains two harmonic components with the periods ${\mathrm{\Lambda }}_0=\pi /k$ and ${\mathrm{\Lambda }}_{\mathrm{\Delta }}=\pi /\left(k\mathrm{s}\mathrm{i}\mathrm{n}(\pi /4)\right)$. The amplitudes of the gradient force components depend on the ratio of the particle radius $R$ to the modulation periods due to inhomogeneity of radiation in the particle volume and are given by the Bessel functions $J_{3/2}(2\pi R/{\mathrm{\Lambda }}_0)$ and $J_{3/2}(2\pi R/{\mathrm{\Lambda }}_{\mathrm{\Delta }})$. We find the critical particle radii $R_0$ and ${R_{\mathrm{\Delta }}=\sqrt{2}R}_0$ defined by the Bessel functions zeros and corresponding to the vanishing components of the gradient forces. In particular, for the radiation with the wavelength ${\lambda }_0=1.064$ μm and a particle in water, the smallest critical radii are $R_0=0.286$ μm and 0.492 μm and $R_{\mathrm{\Delta }}=0.404$ μm and 0.696 μm, respectively. For a number of special cases, we obtain the analytical solutions of the Newton equations and the particle trajectories that depend on the ratio of wave intensities and the particle radius. The results can be used to study the dynamics of the “optical assembly” of a two-dimensional particles matrix which behaves as a molecular crystal [Mellor and Bain, Chem. Phys. Chem. 7 (2006) 329–332].

我们开发了在正交定向激光驻波干涉场中具有梯度力的透明电介质球形粒子的传输和定位理论 ${乙}_z\left(\mathrm{C}\mathrm{○}\mathrm{秒}克z\right)$ 和 ${乙}_X\left(\mathrm{C}\mathrm{○}\mathrm{秒}克X\right)$. 表明，当波${乙}_z$ 和 ${乙}_X$ 是相干的，干扰辐射场包含两个谐波分量，其周期为 ${\mathrm{\Lambda }}_0=\pi /克$ 和 ${\mathrm{\Lambda }}_{\mathrm{\Delta }}=\pi /\left(克\mathrm{秒}\mathrm{一世}\mathrm{n}(\pi /4)\right)$. 梯度力分量的幅值取决于粒子半径的比值$\mathrm{电阻}$ 由于粒子体积中辐射的不均匀性，调制周期由贝塞尔函数给出 $J_{3/2}(2\pi \mathrm{电阻}/{\mathrm{\Lambda }}_0)$ 和 $J_{3/2}(2\pi \mathrm{电阻}/{\mathrm{\Lambda }}_{\mathrm{\Delta }})$. 我们找到临界粒子半径${\mathrm{电阻}}_0$ 和 ${{\mathrm{电阻}}_{\mathrm{\Delta }}=\sqrt{2}\mathrm{电阻}}_0$由贝塞尔函数定义为零并对应于梯度力的消失分量。特别是对于波长为${\lambda }_0=1.064$ μm 和水中的粒子，最小临界半径为 ${\mathrm{电阻}}_0=0.286$ μm 和 0.492 μm 和 ${\mathrm{电阻}}_{\mathrm{\Delta }}=0.404$分别为 μm 和 0.696 μm。对于一些特殊情况，我们获得了牛顿方程和粒子轨迹的解析解，这取决于波强度和粒子半径的比率。结果可用于研究二维粒子矩阵的“光学组装”的动力学，该矩阵表现为分子晶体 [Mellor and Bain, Chem. 物理。化学 7 (2006) 329–332]。