Position clamping of optically trapped microscopic non-spherical probes

We investigate the degree of control that can be exercised over an optically trapped microscopic non-spherical force probe. By position clamping translational and rotational modes in different ways, we are able to dramatically improve the position resolution of our probe with no reduction in sensitivity. We also demonstrate control over rotational-translational coupling, and exhibit a mechanism whereby the average centre of rotation of the probe can be displaced away from its centre

A compact holographic optical tweezers instrument

Holographic optical tweezers have found many applications including the construction of complex micron-scale 3D structures and the control of tools and probes for position, force, and viscosity measurement. We have developed a compact, stable, holographic optical tweezers instrument which can be easily transported and is compatible with a wide range of microscopy techniques, making it a valuable tool for collaborative research. The instrument measures approximately 30×30×35 cm and is designed around a custom inverted microscope, incorporating a fibre laser operating at 1070 nm. We designed the control software to be easily accessible for the non-specialist, and have further improved its ease of use with a multi-touch iPad interface. A high-speed camera allows multiple trapped objects to be tracked simultaneously. We demonstrate that the compact instrument is stable to 0.5 nm for a 10 s measurement time by plotting the Allan variance of the measured position of a trapped 2 μm silica bead. We also present a range of objects that have been successfully manipulated

Constructing 3D crystal templates for photonic band gap materials using holographic optical tweezers

A simple and robust method is presented for the construction of 3-dimensional crystals from silica and polystyrene microspheres. The crystals are suitable for use as templates in the production of three-dimensional photonic band gap (PBG) materials. Manipulation of the microspheres was achieved using a dynamic holographic assembler (DHA) consisting of computer controlled holographic optical tweezers. Attachment of the microspheres was achieved by adjusting their colloidal interactions during assembly. The method is demonstrated by constructing a variety of 3-dimensional crystals using spheres ranging in size from 3 µm down to 800 nm. A major advantage of the technique is that it may be used to build structures that cannot be made using self-assembly. This is illustrated through the construction of crystals in which line defects have been deliberately included, and by building simple cubic structures

Heat release by controlled continuous-time Markov jump processes

We derive the equations governing the protocols minimizing the heat released by a continuous-time Markov jump process on a one-dimensional countable state space during a transition between assigned initial and final probability distributions in a finite time horizon. In particular, we identify the hypotheses on the transition rates under which the optimal control strategy and the probability distribution of the Markov jump problem obey a system of differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh tends to zero, these equations converge to those satisfied by the diffusion process minimizing the heat released in the Langevin formulation of the same problem. We also show that in full analogy with the continuum case, heat minimization is equivalent to entropy production minimization. Thus, our results may be interpreted as a refined version of the second law of thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure

Bespoke optical springs and passive force clamps from shaped dielectric particles

By moulding optical fields, holographic optical tweezers are able to generate structured force fields with magnitudes and length scales of great utility for experiments in soft matter and biological physics. It has recently been noted that optically induced force fields are determined not only by the incident optical field, but by the shape and composition of the particles involved [Gluckstad J. Optical manipulation: sculpting the object. Nat Photonics 2011;5:7–8]. Indeed, there are desirable but simple attributes of a force field, such as orientational control, that cannot be introduced by sculpting optical fields alone. With this insight in mind, we show, theoretically, how relationships between force and displacement can be controlled by optimizing particle shapes. We exhibit a constant force optical spring, made from a tapered microrod and discuss methods by which it could be fabricated. In addition, we investigate the optical analogue of streamlining, and show how objects can be shaped so as to reduce the effects of radiation pressure, and hence switch from non-trapping to trapping regimes

Surface imaging using holographic optical tweezers

We present an imaging technique using an optically trapped cigar-shaped probe controlled using holographic optical tweezers. The probe is raster scanned over a surface, allowing an image to be taken in a manner analogous to scanning probe microscopy (SPM), with automatic closed loop feedback control provided by analysis of the probe position recorded using a high speed CMOS camera. The probe is held using two optical traps centred at least 10 µm from the ends, minimizing laser illumination of the tip, so reducing the chance of optical damage to delicate samples. The technique imparts less force on samples than contact SPM techniques, and allows highly curved and strongly scattering samples to be imaged, which present difficulties for imaging using photonic force microscopy. To calibrate our technique, we first image a known sample—the interface between two 8 µm polystyrene beads. We then demonstrate the advantages of this technique by imaging the surface of the soft alga <i>Pseudopediastrum</i>. The scattering force of our laser applied directly onto this sample is enough to remove it from the surface, but we can use our technique to image the algal surface with minimal disruption while it is alive, not adhered and in physiological conditions. The resolution is currently equivalent to confocal microscopy, but as our technique is not diffraction limited, there is scope for significant improvement by reducing the tip diameter and limiting the thermal moti

Force sensing with a shaped dielectric micro-tool

We analyse the thermal motion of a holographically trapped non-spherical force probe, capable of interrogating arbitrary samples with nanometer resolution. High speed video stereo-microscopy is used to track the translational and rotational coordinates of the micro-tool in three dimensions, and the complete 6 × 6 stiffness matrix for the system is determined using equipartition theorem. The Brownian motion of the extended structure is described in terms of a continuous distribution of thermal ellipsoids. A centre of optical stress, at which rotational and translational motion is uncoupled, is observed and controlled. Once calibrated, the micro-tool is deployed in two modes of operation: as a force sensor with <150 femto-Newton sensitivity, and in a novel form of photonic force microscopy

Optimizing the optical trapping stiffness of holographically trapped microrods using high-speed video tracking

Dielectric microrods can be trapped horizontally in pairs of holographically controlled optical traps. External forces acting on these microrods are registered via the rotational and translational displacement of the microrod relative to the traps. In the following paper we demonstrate accurate, real-time tracking of this displacement in two dimensions. The precision of the method is estimated and the translational and rotational stiffness coefficients of the trapped microrod are evaluated by analysing the thermal motion and the Stokes drag. The variation of these stiffness coefficients relative to the displacement of the traps from the ends of the microrods is measured, and optimal trapping conditions are located