Table of contents

Few would have predicted the impact the laser has had across all of the natural sciences. Laser technology in tandem with microscopy has fuelled a revolutionary advance in biology and chemistry. Microscopic methods permit imaging of cells, nanoparticles, atoms and single molecules. Without doubt, biophotonics has emerged in many guises as a major player on the international arena, and has spawned an industry with an explosive growth rate. Notably, the influence of light is not restricted to passive imaging—it may also move, trap and manoeuvre objects from single atoms right through to the size of a large cell with no damage whatsoever. Given the well-known uses of high power lasers in surgery and industrial cutting, this sounds like science fiction, but at the size scale of these objects it is science fact: it is the area of optical micromanipulation that is the subject of this special issue.

The field of optical micromanipulation has continued to impact right across the sciences in an unprecedented fashion, since its inception in the late 1960s. Excitingly the field has made an exceptional impact in single molecule biophysics and the physics of non-equilibrium systems largely due to the fact that an optical trap is an elegant and powerful force transducer. The field is also branching out into new directions: cell biology is benefiting from this advance. Trapping and microfluidics is an exciting combination within the broader remit of the field of optofluidics: methods of multiple traps using diffractive optics are permitting cell sorting, traps are aiding local viscosity measurements and novel biological studies are being performed. Combining traps with other spectroscopic methods and imaging modes is an interesting theme that poses interesting challenges but promises exciting new knowledge. All these areas are represented in this special issue, along with a number of contributions to quantitative modelling of optical fields suitable for trapping and of the motion of particles in these traps. The increasing sophistication and accuracy of these models allows for the optimization of the trapping process and shows how more and different information can be obtained.

Light certainly has taken hold!

Efforts at understanding the behaviour of complex materials at the micro scale have led to the development of many microrheological techniques capable of probing viscoelastic behaviour. Among these, optical tweezers have been extensively developed for biophysical applications: they offer several advantages over traditional techniques, and can be employed in both passive and active microrheology. In this report, we outline several methods that can be used with optical tweezers to measure the microrheological behaviour of materials such as glycerol, methylcellulose solutions, actin matrices, and cellular membranes. In addition, we quantify the effect that the index of refraction of the solution has on the stiffness of the optical trap. Our results indicate that optical tweezers force microscopy is a versatile tool for the exploration of viscoelastic behaviour in a range of substrates at the micro scale.

Most research on optical manipulation aims towards investigation and development of the system itself. In this paper we show how optical manipulation, imaging and microfluidics can be combined for investigations of single cells. Microfluidic systems have been fabricated and are used, in combination with optical tweezers, to enable environmental changes for single cells. The environment within the microfluidic system has been modelled to ensure control of the process. Three biological model systems have been studied with different combinations of optical manipulation, imaging techniques and microfluidics. In Saccharomyces cerevisiae, environmentally induced size modulations and spatial localization of proteins have been studied to elucidate various signalling pathways. In a similar manner the oxygenation cycle of single red blood cells was triggered and mapped using Raman spectroscopy. In the third experiment the forces between the endoplasmic reticulum and chloroplasts were studied in Pisum sativum and Arabidopsis thaliana. By combining different techniques we make advanced biological research possible, revealing information on a cellular level that is impossible to obtain with traditional techniques.

Expanding interest in microfluidic techniques for biomedical applications has driven the recent need for micro-integrated optics capable of both traditional characterization and emerging optical manipulation techniques. We discuss here how ultrafast laser micromachining can be used to create optical waveguides directly within microfluidic systems. We then utilize this fabrication approach to create a unique microfluidic platform for optical characterization and sorting of cells and particles. This new platform employs optically fabricated waveguides to scatter and refract light from individual particles, allowing accurate in situ size detection and sorting within a microfluidic channel.

The optical tweezers effect offers the potential for all-optical control of microfluidic and optofluidic devices. Several possible means for applying optical tweezers to optofluidics are described including the use of polymers to tether transversely trapped microspheres and eliminate the need for axial trapping. Also covered is the use of optically trapped cantilevers to make durable devices and to allow the optically actuated elements to be integrated into the devices during manufacture. Self-aligning fibre-optic confocal detection of backscattered light is used to measure the position of the trapped object with respect to the axis of the trap for application to force sensing.

Passive microfluidic sorting techniques based upon the interaction of particles with an optically defined potential energy landscape have possible advantages over active sorting techniques such as microfluorescence activated cell sorting (FACS), including ease of integration into lab-on-a-chip systems, reconfigurability, and scalability. Rather than analysing and deflecting a single-file stream of particles one by one, a passive approach intrinsically aimed at parallel processing may, ultimately, offer greater potential for high throughput. However attempts to sort many particles simultaneously in high density suspensions are inevitably limited by particle–particle interactions, which lead to a reduction in the efficiency of the sorting. In this paper we describe two different approaches aimed at reducing colloidal traffic flow problems. We find that continuous translation of the sorting lattice helps to reduce nearest neighbour particle spacing, providing promise for efficiency improvements in future high throughput applications, and that a flashing lattice yields a reduction in unwanted pile-up and spillover effects which otherwise limit the efficiency of sorting.

In this paper we discuss a state-of-the-art optical technique which combines Raman microspectroscopy and optical trapping. This technique permits one to study Raman spectra of aerosol particles, gas bubbles and cells that normally live in suspension and it opens the way to acquire information that otherwise would be inaccessible for this class of microparticles.

Technologies for the manipulation of single molecules have reached the resolution for the measurement of nanometre and sub-nanometre displacements and piconewton forces. In parallel with manipulation techniques, an array of single-molecule fluorescence detection methods have been developed to measure with great precision the position and/or the orientation of single biomolecules, as well as their conformational fluctuations. A new generation of instruments devoted to single-molecule biophysics is now emerging from the combination of two or more single-molecule techniques into one set-up. Particularly fruitful is the combination of manipulation techniques with single-molecule fluorescence techniques, allowing the detection of biomolecule position, conformation or biochemical state simultaneously with the measurement (or the external control) of mechanical output. Here we present the combination of optical tweezers and fluorescence imaging with nanometre accuracy (FIONA). The apparatus was tested on an actin filament labelled with a quantum dot and suspended in solution in a dumbbell configuration using the laser tweezers. This apparatus allows control of the mechanical conditions of a track (actin, microtubules, nucleic acids) while monitoring, by fluorescence, locomotion (and, possibly, biochemical state) of a motor on the track, thus being applicable to a large variety of biological systems.

Optical trapping of silver nanoparticles dispersed with rhodamine 6G (R6G) and NaCl in water gives surface-enhanced hyper-Raman scattering (SEHRS) of R6G. In this paper we have measured the SEHRS spectrum in the R6G concentration range between 10⁻⁷ and 10⁻¹¹ M. SEHRS intensity and signal-to-noise ratio show clear differences at the lower R6G concentrations than ∼10⁻⁹ M, indicating that the number of R6G in a trapped silver aggregate approaches the single-molecule level. This trapping SEHRS technique is applied for the detection of lysozyme molecules labelled with tetramethylrhodamine dye.

We report on the ability of holographic light fields to alter the normal growth patterns of filamentous fungi. The light fields are produced on a microscopic scale by borrowing methods from the field of optical tweezers, but without the aim of directly trapping or manipulating objects. Extended light fields are shown to redirect and constrict hyphal tip growth, and induce hyphal branching in a highly reproducible manner. The merits of using discrete and continuous light fields produced using a spatial light modulator are discussed and the use of three-dimensional 'pseudowalls' of light to control the growth patterns is reported. We also demonstrate the dependence of hyphal tip growth on the wavelength of light, finding that less power is needed at shorter wavelengths to effect changes in the growth dynamics of fungal hyphae.

The axial displacement of optically tweezed liquid aerosol droplets has been studied directly through the application of side imaging at 90° to the trapping laser beam. In conjunction with imaging in the plane of the optical trap and cavity-enhanced Raman spectroscopy (CERS), the optical forces experienced by a trapped aerosol have been interrogated. By varying the power of the trapping laser and observing changes in the axial position of a trapped particle it has been possible to examine the fine balance between the gradient and scattering forces, a key parameter in optical manipulation. Clear differences observed in sizing trapped particles from bright field microscopy and CERS have been reconciled. As a consequence, a novel technique for probing the evolving size of a single aerosol particle is proposed.

The limited working distance of the high numerical aperture microscope objectives used in conventional optical tweezers makes it difficult to trap objects at the liquid–air interface. Since with a weakly focused optical beam the gradient forces are not sufficient to overcome the axial scattering force, we investigated the possibility of the use of surface tension forces generated when the object is pushed against the liquid–air interface by a weakly focused optical beam to balance the axial scattering force. In contrast to the expected trapping of objects at the focal point of the trap beam the objects were observed to get trapped in an annular region about the trap beam. The experimental results and their analysis reveal that, apart from optical and surface tension forces, the laser-induced heating of the interface and the resulting thermocapillary effect are responsible for the observed trapping of objects.

We describe a toolbox, implemented in Matlab, for the computational modelling of optical tweezers. The toolbox is designed for the calculation of optical forces and torques, and can be used for both spherical and nonspherical particles, in both Gaussian and other beams. The toolbox might also be useful for light scattering using either Lorenz–Mie theory or the T-matrix method.

Conventional 19th century thermodynamics has limited our understanding of statistical physics to systems in the thermodynamic limit, at or near equilibrium. However, in the last decade two new theorems, collectively referred to as fluctuation theorems or FTs, were introduced that quantify the energy distributions of small systems that are driven out of equilibrium, possibly far from equilibrium, by an external field. As such the FTs represent a much needed extension of non-equilibrium thermodynamics that can potentially address systems of interest in the 21st century, including nano/micro-machines and single biomolecular function. Optical trapping has served as an ideal experimental technique for demonstrating these theorems. Measurement of picoNewton scale forces over nanometre-sized displacements of a trapped micron-sized particle allows us to measure the energies to a fraction of thermal energy along the particle's trajectory—precisely what is needed to demonstrate the predictions of the FTs. Here we review the fluctuation theorems, as cast by Evans and Searles (1994 Phys. Rev. E 50 1645; 2002 Adv. Phys.51 1529; 2004 Aust. J. Chem.57 1119) and Crooks (1999 Phys. Rev. E 60 2721), and provide a discussion of their importance and a comparison of their arguments. We further demonstrate an optical trap experiment that confirms the FTs. We have chosen to review an optical trapping experiment that is identical to a previously published experiment (Carberry et al 2004 Phys. Rev. Lett.92 140601), but where the solvent is viscoelastic rather than purely viscous. This represents the first experimental demonstration where dynamics of the colloidal particle are complex and not known a priori.

We present a modified analytical model describing optical forces acting on two spherical nanoparticles arranged longitudinally in two counter-propagating beams. These particles interact with light as Rayleigh particles and are approximated by dipoles. We focus on the key phenomena of longitudinal binding between these two objects and therefore we applied the general analytical solution to two counter-propagating beams with zero intensity gradients along their propagation (Bessel beams). Numerical results coincide with a numerical model based on the coupled dipoles method.

We extend the MDSA (Mie–Debye spherical aberration) theory of trapping forces in optical tweezers, previously developed for circularly polarized trapping beams, to linear polarization. Although it does not significantly affect the trap stiffness, linear polarization may introduce a strong axial asymmetry of the optical forces near the edge of a trapped microsphere, arising from Mie resonance effects.

In this paper we present a theory of optical forces on particles of arbitrary shape and size and with fields of arbitrary spatial profiles. This means the theory applies to particle–light interactions in every optical regime: Rayleigh, Mie and geometrical. The theory has the advantage of conceptual simplicity and can handle the real, focused Gaussian beams typically found in optical tweezer experiments. We present optical force calculations on spheres and cubes, and the results obtained with our theory agree well with benchmark calculations obtained using other techniques.

We study the transmitted intensity and induced photonic forces on interaction of light with a metallic disc containing a circular aperture. A procedure is used to calculate light transmission through the aperture, discussing the role of its morphological resonances. The resulting optical forces on metallic spheres placed in front of the aperture in the transmission side are analysed, observing that they yield a possible means of trapping, with particle size, position and composition discrimination, as a consequence of the force different signs and magnitudes as the wavelength varies.

At present, a major obstacle to the quantitative application of optical tweezers as a force spectrometer in living cells is the lack of a method to calibrate the tweezers. Calibration with approved methods such as the power spectrum method (Berg-Sørensen and Flyvbjerg 2004 Rev. Sci. Instrum.75 594; Berg-Sørensen et al 2006 Rev. Sci. Instrum.77 063106) is not possible as the viscoelastic properties of the bio-active medium are a priori unknown. Here, we present an approach that neither requires explicit assumptions about the size of the trapped particle nor about the viscoelastic properties of the medium. Instead, the interaction between the medium and the trapped particle is described in a general manner, through velocity and acceleration memory. Our method is applicable to general, at least locally homogeneous, viscoelastic media. The procedure combines active and passive approaches by the application of Onsager's regression hypothesis. It allows extraction of the trapping stiffness κ of the optical tweezers and of the response function χ(ω), which is the frequency-dependent effective inverse spring constant of the system. Finally, information about the viscoelastic properties of the medium may also be found. To test the method, we have performed simulations in which the system is driven sinusoidally. These simulations serve as an example of how to deal with real experimental data. For realistic parameters, we calibrate the trap stiffness κ with ∼1% stochastic error.

We studied experimentally how the beam retro-reflected from a planar interface (microscope slide) influences the axial stiffness of a single beam trap. Since the incident and retro-reflected beams interfere, weak intensity maxima and minima form a standing wave superposed on the axial single focused beam intensity envelope. Therefore there exists competition between the single beam trap and the weak standing wave traps. It results in microsphere hops to a new stable position at certain distances of the beam focus from the retro-reflecting surface. We analysed the behaviour of two polystyrene spheres of different sensitivities to the weak standing wave (diameters 690 and 820 nm) placed close to surfaces with different reflectivities (common glass R = 0.4% and reflective coating R = 13%). We used quadrant photodiode placed in a back focal plane of the microscope objective to track the position of the particle trapped in the single beam trap. Analyses of the thermal motion of trapped bead provided trap stiffnesses at different distances of the beam focus from the retro-reflecting surface and it also revealed a non-harmonic shape of the axial potential profile at the distances where the bead hops. We compared the experimental results with theoretical simulations based on Lorentz–Mie scattering theory.

Motivated by recent attempts to use parametric resonance to calibrate the spring constant of a Brownian particle in an optical trap, we have looked systematically at the effects of modulating laser power on the motion of the trapped particle. We predict and find experimentally an increase in the particle's position variance at low laser modulation frequencies, but we find no evidence for any resonant effects in the extremely overdamped motion of the trapped particle. Our results can serve as a guide for designing multiple traps by the 'time-sharing' method.

We compare the performance of a high-speed camera and a quadrant detector for measuring the displacement of micron-sized particles in optical tweezers. For trapping powers up to 100 mW, the standard deviation of the particle displacements measured by the two techniques shows excellent agreement. This comparison also provides a method for calibrating one technique against the other.

We provide a detailed account of the construction of a system of holographic optical tweezers. While a lot of information is available on the design, alignment and calibration of other optical trapping configurations, those based on holography are relatively poorly described. Inclusion of a spatial light modulator in the set-up gives rise to particular design trade-offs and constraints, and the system benefits from specific optimization strategies, which we discuss.

We present the results of experiments to parametrize the trapping forces on microbubbles held in scanning optical tweezers. We determine the dependence on microbubble and trap dimensions of the maximum axial trapping force, and the dependence on bubble size of the maximum transverse drag force for which the bubble remains trapped. We have also determined the spring constant of the optical trap in the radial direction, which is the first measurement of this important parameter for a low refractive index particle, or for any object in a time-averaged optical potential.