Narrow Results

The influence of the off-focus and off-axis distances on trapping of a metallic particle is investigated theoretically using vector diffraction and dipole approximation. Numerical results show that when the off-focus and off-axis distances of a metallic Rayleigh particle are smaller, typically smaller than 0.5$\lambda$, the particle can be three-dimensionally trapped to the focus by a highly focused real radially polarized beam. However, when the off-focus and off-axis distances are large, the particle can not be three-dimensionally trapped to the focus but it may be trapped to an annular region. The dependence of the trapping stability and trapping stiffness on the off-focus and off-axis distances are calculated. The effect of the beam parameter (the ratio of the radius of the lens to the beam waist) of the radially polarized light on optical trap is discussed.

We study the interaction of an atom with a one-dimensional nano-grating within the framework of macroscopic QED, with special emphasis on possible anisotropic contributions. To this end, we first derive the scattering Green’s tensor of the grating by means of a Rayleigh expansion and discuss its symmetry properties and asymptotes. We then determine the Casimir–Polder potential of an atom with the grating. In particular, we find that strong anisotropy can lead to a repulsive Casimir–Polder potential in the normal direction.

Scattering of sound by a target can be described as a wave radiated by virtual point sources inside the target. In the Rayleigh scattering regime, the strength of the virtual sources can be calculated analytically. When a target is located close to the ocean surface or another reflecting boundary, reflections of the incident and single-scattered waves from the boundary lead to multiple scattering from the target, with the target being insonified by nearby virtual sources. At low frequencies and for shallow targets, the distance from a virtual source to the target is not necessarily large compared to the acoustic wavelength or the target’s dimensions. Then, multiple orders of scattering make significant contributions and incident wave fields that cannot be approximated as a plane wave. This paper takes advantage of the virtual source concept and recently derived explicit analytic representations of 2D acoustic Green’s functions in unbounded fluids with inclusions of a circular cross-section, to develop a simple, intuitive, and numerically efficient model of multiple scattering. Scattering from soft, hard, and fluid targets is considered. The model is used to study the acoustic field in the vicinity of cylindrical targets near a pressure release surface or a hard bottom.

This paper fills the gap in the study of Rayleigh scattering near an interface. The structure of the near-field of the half-space Green’s function is analytically described. Explicit dependencies on range, distance to the boundary, and physical parameters of contacting media are obtained. These results are of applied value for modern ultrasonic cleaning techniques because they allow one to describe the action of the Bjerknes force on particles located near an interface.

Rayleigh scattering from a spherical object located near a planar rigid boundary at distances smaller than the wavelength is calculated. Low frequency analysis reduces a scattering problem to a sequence of potential problems. An analytical solution based on expansion in spherical solid harmonics and the use of addition theorem is presented. Analytical perturbation approach is validated by comparison with numerical calculations. The velocity of the center of the particle and the scattering amplitude are determined. In the lowest order in wavenumber, the scattering amplitude is expressed in terms of the monopole and dipole components. In contrast to the behavior of a bubble, under the same conditions, dipole oscillations of the particle in the direction normal to the boundary are not excited and the monopole component of the scattering amplitude does not depend on the location of the particle relative to the boundary.