Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring

We use a continuous acquisition, high-speed camera with integrated centroid tracking to simultaneously measure the positions of a ring of micron-sized particles held in holographic optical tweezers. Hydrodynamic coupling between the particles gives a set of eigenmodes, each one independently relaxing with a characteristic decay rate (eigenvalue) that can be measured using our positional data. Despite the finite particle size, we find an excellent agreement between the measured eigenvalues and those numerically predicted by Oseen theory applied to the two-dimensional (2D) ring geometry. Particle motions are also analyzed in terms of the alternative eigenmode set obtained by wrapping onto the ring the eigenmodes of a 1D periodic chain. We identify the modes for which the periodic chain is a good approximation to the ring and those for which it is not.

Liquid crystal multi-mode lenses and axicons based on electronic phase shift control

We report on the principle of operation, construction and testing of a liquid crystal lens which is controlled by distributing voltages across the control electrodes, which are in turn controlled by adjusting the phase of the applied voltages. As well as (positive and negative) defocus, then lenses can be used to control tip/tilt, astigmatism, and to create variable axicons.

Tuneable planar integrated optical systems

Planar integrated free-space optical systems are well suited for a variety of applications, such as optical interconnects and security devices. Here, we demonstrate for the first time dynamic functionality of such microoptical systems by the integration of adaptive liquid-crystal-devices.

Ray equation for a spatially variable uniaxial crystal and its use in the optical design of liquid-crystal lenses

To be able to design optical systems (e.g., variable focus or zoom lenses) made from liquid-crystal devices, it is necessary to be able to ray trace in a birefringent medium where the angle of the optical axis is a function of position in the device. To our knowledge, the theory required to achieve this has not previously been published, and we derive a suitable algorithm and give some examples of its use.

Colloidal interactions and transport in nematic liquid crystals

We describe a new nematic liquid-crystal colloid system which is characterized by both charge stabilization of the particles and an interaction force. We estimate the effective charge of the particles by electrophoretic measurements and find that in such systems the director anchoring energy W is very low and the particles have little director distortion around them. The interaction force is created by producing a radial distribution of the nematic order parameter around a locally isotropic region created by ir laser heating. We theoretically describe this as being due to the induced flexoelectric polarization, the quadrupolar symmetry of which provides the required long-range force acting on charged particles.

Direct measurement of the skew angle of the Poynting vector in a helically phased beam

We measure the local skew angle of the Poynting vector within a helically-phased, exp (il phi), beam using a Shack Hartmann wavefront sensor. It is the skew angle of the Poynting vector with respect to the beam axis that gives rise to the orbital angular momentum of a light beam. We confirm that this skew angle is l/kr, corresponding to an orbital angular momentum of l? per photon. Measurement of orbital angular momentum in this way is an alternative to interferometric techniques giving a non-ambiguous result to both the magnitude and sign of l from a single measurement, without any restriction on the optical bandwidth.

Modal liquid crystal devices in optical tweezing: 3D control and oscillating potential wells

We investigate the use of liquid crystal (LC) adaptive optics elements to provide full 3 dimensional particle control in an optical tweezer. These devices are suitable for single controllable traps, and so are less versatile than many of the competing technologies which can be used to control multiple particles. However, they have the advantages of simplicity and light efficiency. Furthermore, compared to binary holographic optical traps they have increased positional accuracy. The transmissive LC devices could be retro-fitted to an existing microscope system. An adaptive modal LC lens is used to vary the z-focal position over a range of up to 100 mum and an adaptive LC beam-steering device is used to deflect the beam (and trapped particle) in the x-y plane within an available radius of 10 mum. Furthermore, by modifying the polarisation of the incident light, these LC components also offer the opportunity for the creation of dual optical traps of controllable depth and separation.

Biomarker evidence for green and purple sulphur bacteria in a stratified Palaeoproterozoic sea

The disappearance of iron formations from the geological record approximately 1.8 billion years (Gyr) ago was the consequence of rising oxygen levels in the atmosphere starting 2.45-2.32 Gyr ago. It marks the end of a 2.5-Gyr period dominated by anoxic and iron-rich deep oceans. However, despite rising oxygen levels and a concomitant increase in marine sulphate concentration, related to enhanced sulphide oxidation during continental weathering, the chemistry of the oceans in the following mid-Proterozoic interval (approximately 1.8-0.8 Gyr ago) probably did not yet resemble our oxygen-rich modern oceans. Recent data indicate that marine oxygen and sulphate concentrations may have remained well below current levels during this period, with one model indicating that anoxic and sulphidic marine basins were widespread, and perhaps even globally distributed. Here we present hydrocarbon biomarkers (molecular fossils) from a 1.64-Gyr-old basin in northern Australia, revealing the ecological structure of mid-Proterozoic marine communities. The biomarkers signify a marine basin with anoxic, sulphidic, sulphate-poor and permanently stratified deep waters, hostile to eukaryotic algae. Phototrophic purple sulphur bacteria (Chromatiaceae) were detected in the geological record based on the new carotenoid biomarker okenane, and they seem to have co-existed with communities of green sulphur bacteria (Chlorobiaceae). Collectively, the biomarkers support mounting evidence for a long-lasting Proterozoic world in which oxygen levels remained well below modern levels.

Photic zone euxinia during the Permian-triassic superanoxic event

Carbon and sulfur isotopic data, together with biomarker and iron speciation analyses of the Hovea-3 core that was drilled in the Perth Basin, Western Australia, indicate that euxinic conditions prevailed in the paleowater column during the Permian-Triassic superanoxic event. Biomarkers diagnostic for anoxygenic photosynthesis by Chlorobiaceae are particularly abundant at the boundary and into the Early Triassic. Similar conditions prevailed in the contemporaneous seas off South China. Our evidence for widespread photiczone euxinic conditions suggests that sulfide toxicity was a driver of the extinction and a factor in the protracted recovery.

Laser beacon wave-front sensing without focal anisoplanatism

Wave-front sensing from artificial beacons is normally performed by formation of a focused spot in the atmosphere and sensing of the wave-front distortions produced during the beam's return passage. We propose an alternative method that senses the distortions produced during the outgoing path by forming an intensity pattern in the atmosphere that is then viewed from the ground. A key advantage of this method is that a parallel beam is used, and therefore the wave-front measurements will not suffer from the effects of focal anisoplanatism. We also envisage other geometries, all based on the concept of projecting a pupil pattern onto the atmosphere.

White-light performance of a polarization-independent liquid-crystal phase modulator

The broadband performance of a polarization-insensitive liquid-crystal phase modulator is analyzed, and its effect on an adaptive optics system is quantified.

Real-time optical aberration correction with a ferroelectric liquid-crystal spatial light modulator

Real-time correction of an optically aberrated wave front by use of a 10 x 10 ferroelectric liquid-crystal spatial light modulator as the correction device and a point-diffraction interferometer as the wave-front sensor is demonstrated. This type of interferometer requires no reference arm and so can be used, in theory, in an astronomical adaptive-optics system. We discuss some of the unusual features of the point-diffraction interferometer for wave-front sensing.

Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator

I describe a nematic liquid-crystal spatial light modulator that can be used as a high-precision wave-front control device. I present results showing the open-loop correction of wave-front aberrations and demonstrate wave-front shaping by the production and quantification of the first 15 significant Zernike terms.

Intensity-only modulation for atmospheric scintillation correction by liquid-crystal spatial light modulators

We consider the use of a ferroelectric liquid-crystal spatial light modulator (FLC SLM) to control the transmittance of a telescope pupil to compensate for the effects of scintillation. Our aim here is to prove the necessary and physically interesting result that it is possible to control the intensity of light by use of FLC SLM without inducing further phase aberrations. Furthermore, we show that system errors have only a small effect on the phase of the transmitted beam.

Binary adaptive optics: atmospheric wave-front correction with a half-wave phase shifter

We describe a binary approach to adaptive wave-front correction, especially suitable for narrow band applications, which would be simpler than conventional adaptive technology. Appropriate parts of the aberrant wave front are phase retarded by half a wavelength to ensure that none of the image-forming rays add together destructively. Simulations for monochromatic light show that the residual wave-front errors, in the absence of other errors, would result in Strehl ratios of ~40% with diffraction-limited widths at visible wavelengths. We simulate the imaging performance of such a system and describe a possible implementation that uses a ferroelectric liquid-crystal spatial light modulator.

Liquid-crystal prisms for tip-tilt adaptive optics

Results from an electrically addressed liquid-crystal cell producing continuous phase profiles are presented. The adaptive deflection of a beam of light for use in a tip-tilt adaptive optics system is demonstrated. We compare the optical performance of liquid-crystal prisms with experimental data on atmospheric seeing at the William Herschel Telescope.

Liquid-crystal phase modulator for unpolarized light

A simple method for phase modulating unpolarized light with a double pass through a nematic liquid crystal retarder is described.