Trapping and levitation of a dielectric sphere with off-centred Gaussian beams. II. GLMT analysis

Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam

Using the theory of electromagnetic scattering of a uniaxial anisotropic sphere, we derive the analytical expressions of the radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam. The beam's propagation direction is parallel to the primary optical axis of the anisotropic sphere. The effects of the permittivity tensor elements ε(t) and ε(z) on the axial radiation forces are numerically analyzed in detail. The two transverse components of radiation forces exerted on a uniaxial anisotropic sphere, which is distinct from that exerted on an isotropic sphere due to the two eigen waves in the uniaxial anisotropic sphere, are numerically studied as well. The characteristics of the axial and transverse radiation forces are discussed for different radii of the sphere, beam waist width, and distances from the sphere center to the beam center of an off-axis Gaussian beam. The theoretical predictions of radiation forces exerted on a uniaxial anisotropic sphere are hoped to provide effective ways to achieve the improvement of optical tweezers as well as the capture, suspension, and high-precision delivery of anisotropic particles.

Evaluation of trapping efficiency of optical tweezers by dielectrophoresis

A relatively new method for measuring optically induced forces on microparticles and cells, different from the conventional Brownian motion and viscous drag force calibration methods widely used, is introduced. It makes use of the phenomenon of dielectrophoresis for the calibration of optical tweezers through the dielectrophoretic force calculations. A pair of microelectrodes is fabricated by photolithography on a microscope slide and it is connected to a high-frequency generator. The calibration of the optical tweezers setup is performed by the manipulation of polystyrene beads and yeast cells. Calibration diagrams of the transverse forces versus power are deduced for different cell radii and numerical apertures of the objective lenses. The optical system and the related technique provide a fast and easy method for optical tweezers calibration.

Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration

Calculation of the radiation trapping force in laser tweezers by use of generalized Lorenz-Mie theory requires knowledge of the shape coefficients of the incident laser beam. The localized version of these coefficients has been developed and justified only for a moderately focused Gaussian beam polarized in the x direction and traveling in the positive z direction. Here the localized model is extended to a beam tightly focused and truncated by a high-numerical-aperture lens, aberrated by its transmission through the wall of the sample cell, and incident upon a spherical particle whose center is on the beam axis. We also consider polarization of the beam in the y direction and propagation in the negative z direction to be able to describe circularly polarized beams and reflected beams.

Electrically induced interactions between colloidal particles in the vicinity of a conducting plane

We address the problem of two-dimensional (2D) colloidal aggregation driven by an ac electrical field, by observing an aqueous dispersion of latex microspheres in contact with a conducting surface. Using micron-sized carboxylated polystyrene particles, we have systematically investigated the aggregation process, as a function of particle size and charge, and of the applied electric field amplitude and frequency. A low-density 2D phase is observed at high frequency (typically above 1 kHz), while at low frequency (below a "contact frequency" nu(c)) the collection of particles collapses into disconnected compact aggregates of crystalline (hexagonal) structure. We argue that this scenario is governed by the competition between an attractive force, of electrohydrodynamic nature, and a repulsive force, basically an electrical dipole-dipole interaction. Both contributions are revealed and analyzed in independent experiments on isolated particle pairs, using optical manipulation and dynamometry.

Pretransitional effects in dimyristoylphosphatidylcholine vesicle membranes: optical dynamometry study

We used micron-sized latex spheres to probe the phase state and the viscoelastic properties of dimyristoylphosphatidylcholine (DMPC) bilayers as a function of temperature. One or two particles were manipulated and stuck to a DMPC giant vesicle by means of an optical trap. Above the fluid-gel main transition temperature, T(m) congruent with 23.4 degrees C, the particles could move on the surface of the vesicle, spontaneously (Brownian motion) or driven by an external force, either gravity or the laser beam's radiation pressure. From the analysis of the particle motions, we deduced the values of the membrane hydrodynamic shear viscosity, eta(s), and found that it would increase considerably near T(m). Below T(m), the long-distance motion of the particles was blocked. We performed experiments with two particles stuck on the membrane. By optical dynamometry, we measured the elastic resistance of the membrane to a variation in the interparticle distance and found that it would decrease considerably (down to zero) when the temperature was increased to T(m). We propose an interpretation relating the elastic response to the membrane curvature modulus, k(C). In this scheme, the two-bead dynamometry experiments provide a direct measurement of k(C) in the P'(beta) phase of lipid bilayers.

Optical levitation particle delivery system for a dual beam fiber optic trap

We combine a radiation-pressure-based levitation system with a dual fiber, laser trapping system to demonstrate the potential of delivering single particles into the fiber trap. The forces versus position and the trajectory of the particle subjected to the laser beams are examined with an enhanced ray optics model. A sequence of video images taken from the experimental apparatus demonstrates the principle of particle delivery, trapping, and further manipulation.

Axial force acting on a dielectric sphere in a focused laser beam

We present the detailed behavior of the axial force acting on a dielectric sphere exerted by the optical pressure of a focused Gaussian laser beam. Comparison is made between the numerical results and those calculated from the radiation pressure cross section. There is also a discussion as to whether the expressions for the axial force given in this paper are consistent with the previously reported experimental results. Moreover, a simple experimental method to measure the axial force on a polystyrene sphere suspended in water is demonstrated, and fairly good agreement between theoretical and experimental results was obtained.

Simulated dynamic behavior of single and multiple spheres in the trap region of focused laser beams

An enhanced photon propagation method is used to calculate the forces and torque present on each sphere of a system of particles located in the vicinity of focused laser-trapping beams. Infinitesimal trajectory displacements are computed through classical mechanics and the new particle position used to define the next trapping system geometry considered. Repeated applications of the process, implemented as a computer program, enables full trajectory plotting and the dynamic behavior of the systems to be explored as a function of time.

Measurement of beam-shape coefficients in the generalized lorenz-mie theory for the on-axis case

The use of the generalized Lorenz-Mie theory that describes the interaction between a spherical particle and an arbitrarily shaped beam requires knowledge of the beam-shape coefficients (BSC's) that describe the illuminating beam. Classically, these BSC's are evaluated from an a priori mathematical description of the illuminating beam. We propose a method that relies on intensity measurements along the beam axis that permits one to measure directly the BSC's of an actual beam in the laboratory.

Improved standard beams with application to reverse radiation pressure

Recently a so-called standard beam description of Gaussian beams was introduced [J. Opt. Soc. Am. A 11, 2503 (1994)]. However, it was afterward observed [Appl. Opt.35, 2702 (1996)] that this description exhibits a finite radius of convergence, limiting its range of applicability. We introduce an improved standard beam description with an infinite radius of convergence. The utility of this improved description is illustrated by evaluation of radiation pressure forces under severe focusing conditions.

Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres

An efficient numerical procedure for computing the scattering coefficients of a multilayered sphere is discussed. The stability of the numerical scheme allows us to extend the feasible range of computations, both in size parameter and in number of layers for a given size, by several orders of magnitude with respect to previously published algorithms. Exemplifying results, such as scattering diagrams and cross-sectional curves, including the case of Gaussian beam illumination, are provided. Particular attention is paid to scattering at the rainbow angle for which approaches based on geometrical optics might fail to provide accurate enough results.

Prediction of reverse radiation pressure by generalized Lorenz-Mie theory

Radiation pressure exerted on a spherical particle by one extremely focused Gaussian beam is investigated by the use of generalized Lorenz-Mie theory (GLMT). Particular attention is devoted to reverse radiation pressure. GLMT predictions for different descriptions of the incident beam are compared with electrostriction predictions when the particle size is smaller than the wavelength and with geometric-optics predictions when the particle size is larger than the wavelength.