Active rotational and translational microrheology beyond the linear spring regime

Active particle tracking microrheometers have the potential to perform accurate broad-band measurements of viscoelasticity within microscopic systems. Generally, their largest possible precision is limited by Brownian motion and low frequency changes to the system. The signal to noise ratio is usually improved by increasing the size of the driven motion compared to the Brownian as well as averaging over repeated measurements. New theory is presented here which gives the complex shear modulus when the motion of a spherical particle is driven by non-linear forces. In some scenarios error can be further reduced by applying a variable transformation which linearises the equation of motion. This allows normalisation which eliminates low frequency drift in the particle's equilibrium position. Using this method will easily increase the signal strength enough to significantly reduce the measurement time for the same error. Thus the method is more conducive to measuring viscoelasticity in slowly changing microscopic systems, such as a living cell.Comment: 9 pages, 2 figure

Energy, momentum and propagation of non-paraxial high-order Gaussian beams in the presence of an aperture

Non-paraxial theories of wave propagation are essential to model the interaction of highly focused light with matter. Here we investigate the energy, momentum and propagation of the Laguerre–, Hermite– and Ince–Gaussian solutions (LG, HG, and IG) of the paraxial wave equation in an apertured non-paraxial regime. We investigate the far-field relationships between the LG, HG, and IG solutions and the vector spherical wave function (VSWF) solutions of the vector Helmholtz wave equation. We investigate the convergence of the VSWF and the various Gaussian solutions in the presence of an aperture. Finally, we investigate the differences in linear and angular momentum evaluated in the paraxial and non-paraxial regimes. The non-paraxial model we develop can be applied to calculations of the focusing of high-order Gaussian modes in high-resolution microscopes. We find that the addition of an aperture in high numerical aperture optical systems does not greatly affect far-field properties except when the beam is significantly clipped by an aperture. Diffraction from apertures causes large distortions in the near-field and will influence light–matter interactions. The method is not limited to a particular solution of the paraxial wave equation. Our model is constructed in a formalism that is commonly used in scattering calculations. It is thus applicable to optical trapping and other optical investigations of matter

Mapping the landscape of climate engineering.

In the absence of a governance framework for climate engineering technologies such as solar radiation management (SRM), the practices of scientific research and intellectual property acquisition can de facto shape the development of the field. It is therefore important to make visible emerging patterns of research and patenting, which we suggest can effectively be done using bibliometric methods. We explore the challenges in defining the boundary of climate engineering, and set out the research strategy taken in this study. A dataset of 825 scientific publications on climate engineering between 1971 and 2013 was identified, including 193 on SRM; these are analysed in terms of trends, institutions, authors and funders. For our patent dataset, we identified 143 first filings directly or indirectly related to climate engineering technologies-of which 28 were related to SRM technologies-linked to 910 family members. We analyse the main patterns discerned in patent trends, applicants and inventors. We compare our own findings with those of an earlier bibliometric study of climate engineering, and show how our method is consistent with the need for transparency and repeatability, and the need to adjust the method as the field develops. We conclude that bibliometric monitoring techniques can play an important role in the anticipatory governance of climate engineering

Phase-transition-like properties of double-beam optical tweezers

We report on double-beam optical tweezers that undergo previously unknown phase-transition-like behavior resulting in the formation of more optical traps than the number of beams used to create them. We classify the optical force fields which produce multiple traps for a double-beam system including the critical behavior. This effect is demonstrated experimentally in orthogonally polarized (noninterfering) dual-beam optical tweezers for a silica particle of 2.32  μm diameter. Phase transitions of multiple beam trapping systems have implications for hopping rates between traps and detection of forces between biomolecules using dual-beam optical tweezers. It is an example of a novel dynamic system with multiple states where force fields undergo a series of sign inversions as a function of parameters such as size and beam separation

Not just energy, but momentum and angular momentum too: Mechanical effects in scattering

We review the transport and transfer of momentum and angular momentum by electromagnetic waves, and applications of the mechanical effects of scattering

Optical tweezers toolbox: better, faster, cheaper; choose all three

Numerical computation of optical tweezers is one path to understanding the subtleties of their underlying mechanism—electromagnetic scattering. Electromagnetic scattering models of optical trapping can be used to find the properties of the optical forces and torques acting on trapped particles. These kinds of calculations can assist in predicting the outcomes of particular trapping configurations. Experimentally, looking at the parameter space is time consuming and in most cases unfruitful. Theoretically, the same limitations exist but are easier to troubleshoot and manage. Towards this end a new more usable optical tweezers toolbox has been written. Understanding of the underlying theory has been improved, as well as the regimes of applicability of the methods available to the toolbox. Here we discus the physical principles and carry out numerical comparisons of performance of the old toolbox with the new one and the reduced (but portable) code

Optical tweezers escape forces

With suitable calibration, optical tweezers can be used to measure forces. If the maximum force that can be exerted is of interest, calibration can be performed using viscous drag to remove a particle from the trap, typically by moving the stage. The stage velocity required to remove the particle then gives the escape force. However, the escape force can vary by up to 30% or more, depending on the particle trajectory. This can have significant quantitative impact on measurements. We describe the variation of escape force and escape trajectory, using both experimental measurements and simulations, and discuss implications for experimental measurement of forces

Computational modelling of optical tweezers with many degrees of freedom using dynamic simulation: cylinders, nanowires, and multiple particles

Computational tasks such as the calculation and characterization of the optical force acting on a sphere are relatively straightforward in a Gaussian beam trap. Resulting properties of the trap such as the trap strength, spring constants, and equilibrium position can be easily determined. More complex systems with non-spherical particles or multiple particles add many more degrees of freedom to the problem. Extension of the simple methods used for single spherical particles could result in required computational time of months or years. Thus, alternative methods must be used. One powerful tool is to use dynamic simulation: model the dynamics and motion of a particle or particles within the trap. We demonstrate the use of dynamic simulation for non-spherical particles and multi-particle systems. Using a hybrid discrete dipole approximation (DDA) and T-matrix method, we find plausible equilibrium positions and orientations of cylinders of varying size and aspect ratio. Orientation landscapes revealing different regimes of behaviour for micro-cylinders and nanowires with different refractive indices trapped with beams of differing polarization are also presented. This investigation provides a solid background in both the function and properties of micro-cylinders and nanowires trapped in optical tweezers. This method can also be applied to particles with other shapes. We also investigate multiple-particle trapping, which is quite different from single particle systems, as they can include effects such as optical binding. We show that equilibrium positions, and the strength of interactions between particles can be found in systems of two and more particles