Shape-induced force fields in optical trapping

Abstract

Advances in optical tweezers, coupled with the proliferation of 2-photon polymerisation systems, mean that it is now becoming routine to fabricate and trap non-spherical particles. The shaping of both light beams and particles allows fine control over the flow of momentum from the optical to mechanical regimes. However, understanding and predicting the behaviour of such systems is highly complex in comparison with the traditional optically trapped microsphere. In this paper we present a conceptually new and simple approach, based on the nature of the optical force density. We illustrate the method through the design and fabrication of a shaped particle capable of acting as a passive force clamp; we demonstrate its use as an optically trapped probe for imaging surface topography. Further applications of the design rules highlighted here may lead to new sensors for probing bio-molecule mechanics, as well as to the development of optically actuated micro-machines.It is well known that the high intensity gradients generated in a tightly focused laser beam can be used to trap and manipulate micron-sized particles [1]. An optically trapped sphere is an elegant example of a microscopic harmonic oscillator, capable of measuring fN-scale forces, which has proved invaluable for the study of molecular motors and single biopolymer mechanics [2]. However, there are other desirable features of a force field that can only be introduced by modifying the particle shape or dielectric structure beyond that of a simple homogeneous sphere [3,4]. For example, optical torques can be applied to a particle whose symmetry has been lowered either by shape modification With increasing complexity of shape, the problem of predicting, and optimising, the 2 force profile of the trapped particle becomes ever more challenging. Although specialised software packages are available to compute the optical forces [13], their use is not routine.In this paper, therefore, we address this problem and describe a straightforward method for predicting the optical forces acting on extended dielectric particles of general shape. We support the description with rigorous 3-dimensional T-matrix calculations. To illustrate the approach, we describe the design and fabrication of a passive force clamp based on a tapered cylinder and capable of applying a constant force over displacements of several microns. We demonstrate its use in an optically-controlled scanning probe microscope for ultra-low force imaging. Potential future applications of this device may include the imaging of sensitive biological membranes. Results Background theory

‘Lissajous-like’ trajectories in optical tweezers

“…We note that in all of the simulations presented here, the probe particle remains within the linear Hookean restoring force regime: for example the probe is 5 µm in diameter, but only moves a maximum distance of ∼0.8 µm away from the trap centre [14]. In the schematics shown in Fig.…”

“…More generally, an understanding of the physics at work in low Reynolds number environments has helped our understanding of the connection between the form and the function of micro-scale biological systems. This understanding may also facilitate the development of artificial micro-swimmers and fluid pumps, and inform the growing field of microrobotics [11][12][13][14].…”

Quantitative optical trapping and optical manipulation of micro-sized objects

“…Bacterial dynamics are directly related to bacterial motility, and it can be observed in the trapping process [19,24]. The single cell level of E. coli can be damagefree trapped in the focus without any mechanical contact and tends to align itself along the optical axis [25]. This type of bacteria has two kinds of movements: Brownian motion and flagella-mediated propulsion.…”

Generalized phase contrast-enhanced diffractive coupling to light-driven microtools

“…25 This effect can be minimized by modifying the shape of the handles. 5,26 Figure 5(c) shows the output power fluctuations for the duration of our observation. We took the average power for both coupling cases and took the ratio to calculate the gain.…”