Transportation dynamics of dielectric particles with the gradient forces in the field of orthogonal standing laser waves

•Analytical theory of a particle motion in the field of orthogonal standing waves.•Simple formulas for the critical radii corresponding to zero gradient forces.•Application to the optical assembly of crystal-like structures. 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 Ez(coskz) and Ex(coskx). It is shown that, when the waves Ez and Ex are coherent, the interference radiation field contains two harmonic components with the periods Λ0=π/k and ΛΔ=π/ksin(π/4). 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 J3/2(2πR/Λ0) and J3/2(2πR/ΛΔ). We find the critical particle radii R0 and RΔ=2R0 defined by the Bessel functions zeros and corresponding to the vanishing components of the gradient forces. In particular, for the radiation with the wavelength λ0=1.064 μm and a particle in water, the smallest critical radii are R0=0.286 μm and 0.492 μm and RΔ=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].