Trapping of low-index microparticles in an optical vortex

Abstract

The equilibrium position of a low-index particle in an optical-vortex trap was experimentally measured for two different systems: a buoyant hollow glass sphere in water and a density-matched water droplet in acetophenone. Vortex traps are the only known static, single-beam configurations allowing three-dimensional trapping of such particles in the size range of 2-50 m. The trap consists of a strongly focused Gaussian laser beam containing a holographically produced optical vortex. Using experimental and theoretical techniques, we also explored changes in the trapping efficiency owing to the vortex core size, the relative refractive index, and the numerical aperture of the focusing objective.

Controlled Shrinkage and Re-expansion of a Single Aqueous Droplet inside an Optical Vortex Trap

“…The radiation is then absorbed at a focal area of the particle section in a plane perpendicular to the axis of the laser beam. Thus one can write, for a spherical particle: 16,17 (3) Where G = πa 2 , the area of particle perpendicular to the axis of beam propagation, V is the volume of the particle, and Q abs is a factor of absorption that accounts for the intrinsic absorption of the droplet and the interface refraction; given by: 16-18 (4) where N = (n 2 + ik 2 )/(n 1 + ik 1 ), a complex index of refraction of the particle (subscript 2) with respect to the surrounding (subscript 1); and x = 2πa / λ, sometimes known as a wave or diffraction parameter. Defining the intrinsic absorption of the droplet as α 2 = 4πk 2 /λ, one can re-write: (5) where f is a correction factor to the intrinsic absorption coefficient given by: (6) Using the physical parameters listed in Table I, we computed that for water droplet surrounded by acetophenone, f = 0.67 .…”

“…With recent advances in optical vortex traps, which employ Laguerre-Gaussian (LG) beam profile, trapping low-index particles becomes possible. [3][4][5][6][7] LG profile is characterized by a dark focus in the center of the laser beam, which resembles a donut, and has found particular utility in trapping single femtoliter-volume aqueous droplets. [3][4][5][6][7] Aqueous droplets, when present in an immiscible phase that has a slight solubility for water, will shrink and concentrate their contents via passive diffusion and dissolution of water into the immiscible phase.…”

Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders

“…If the aim is to attract these particles towards the optical axis, it is well known that higher-order Gauss-Laguerre modes in 3D and Gauss-Hermite modes in 2D can be used [6,37]. The decomposition of the illuminating beam into a plane wave spectrum in the computational procedure, permits an efficient evaluation of the response of the structure to different illumination beams.…”

“…It becomes possible to attract and accelerate particles along the optical axis in the propagation direction of the illuminating laser beam for particles that have a higher index of refraction than the surrounding medium [5]. The particles are repelled from the optical axis if the index contrast is smaller than unity [6]. For particles much smaller than the wavelength, it is possible to find points in space where all the forces that act on the particle are equal and the object is stably trapped in three dimensions [7].…”

“…Due to conservation laws, the momentum in a system remains invariant, so the transfer of momentum between ray and particle can be calculated for each ray that is refracted. Summing up the momenta will result in a net force, which will accelerate the particle [6].…”