Optical diffraction tomography of 3D microstructures using a low coherence source.

Optical diffraction tomography (ODT) is a label-free technique for three dimensional imaging of micron-sized objects. Coherence and limited sampling of 3D Fourier space are often responsible for the appearance of artifacts. Here we present an ODT microscope that uses low temporal coherence light and spatial light modulators to retrieve reliable 3D maps of the refractive index. A common-path interferometer, based on a spatial light modulator, measures the complex fields transmitted by a sample. Measured fields, acquired while scanning the illumination direction using a digital micro-mirror device, are fed into a Rytov reconstruction algorithm to obtain refractive index maps whose accuracy is directly evaluated on microfabricated 3D test objects. Even for challenging shapes such as pyramids, bridges, and dumbbells, we obtain volumetric reconstructions that compare very well with electron microscopy images.

Holographic tracking and sizing of optically trapped microprobes in diamond anvil cells.

We demonstrate that Digital Holographic Microscopy can be used for accurate 3D tracking and sizing of a colloidal probe trapped in a diamond anvil cell (DAC). Polystyrene beads were optically trapped in water up to Gigapascal pressures while simultaneously recording in-line holograms at 1 KHz frame rate. Using Lorenz-Mie scattering theory to fit interference patterns, we detected a 10% shrinking in the bead's radius due to the high applied pressure. Accurate bead sizing is crucial for obtaining reliable viscosity measurements and provides a convenient optical tool for the determination of the bulk modulus of probe material. Our technique may provide a new method for pressure measurements inside a DAC.

Self-Sustained Density Oscillations of Swimming Bacteria Confined in Microchambers.

We numerically study the dynamics of run-and-tumble particles confined in two chambers connected by thin channels. Two dominant dynamical behaviors emerge: (i) an oscillatory pumping state, in which particles periodically fill the two vessels, and (ii) a circulating flow state, dynamically maintaining a near constant population level in the containers when connected by two channels. We demonstrate that the oscillatory behavior arises from the combination of a narrow channel, preventing bacteria reorientation, and a density-dependent motility inside the chambers.

Hydrodynamic Trapping of Swimming Bacteria by Convex Walls.

Swimming bacteria display a remarkable tendency to move along flat surfaces for prolonged times. This behavior may have a biological importance but can also be exploited by using microfabricated structures to manipulate bacteria. The main physical mechanism behind the surface entrapment of swimming bacteria is, however, still an open question. By studying the swimming motion of Escherichia coli cells near microfabricated pillars of variable size, we show that cell entrapment is also present for convex walls of sufficiently low curvature. Entrapment is, however, markedly reduced below a characteristic radius. Using a simple hydrodynamic model, we predict that trapped cells swim at a finite angle with the wall and a precise relation exists between the swimming angle at a flat wall and the critical radius of curvature for entrapment. Both predictions are quantitatively verified by experimental data. Our results demonstrate that the main mechanism for wall entrapment is hydrodynamic in nature and show the possibility of inhibiting cell adhesion, and thus biofilm formation, using convex features of appropriate curvature.

Three-axis digital holographic microscopy for high speed volumetric imaging.

Digital Holographic Microscopy allows to numerically retrieve three dimensional information encoded in a single 2D snapshot of the coherent superposition of a reference and a scattered beam. Since no mechanical scans are involved, holographic techniques have a superior performance in terms of achievable frame rates. Unfortunately, numerical reconstructions of scattered field by back-propagation leads to a poor axial resolution. Here we show that overlapping the three numerical reconstructions obtained by tilted red, green and blue beams results in a great improvement over the axial resolution and sectioning capabilities of holographic microscopy. A strong reduction in the coherent background noise is also observed when combining the volumetric reconstructions of the light fields at the three different wavelengths. We discuss the performance of our technique with two test objects: an array of four glass beads that are stacked along the optical axis and a freely diffusing rod shaped E.coli bacterium.

Directed transport of active particles over asymmetric energy barriers.

We theoretically and numerically investigate the transport of active colloids to target regions, delimited by asymmetric energy barriers. We show that it is possible to introduce a generalized effective temperature that is related to the local variance of particle velocities. The stationary probability distributions can be derived from a simple diffusion equation in the presence of an inhomogeneous effective temperature resulting from the action of external force fields. In particular, transition rates over asymmetric energy barriers can be unbalanced by having different effective temperatures over the two slopes of the barrier. By varying the type of active noise, we find that equal values of diffusivity and persistence time may produce strongly varied effective temperatures and thus stationary distributions.

First-passage time of run-and-tumble particles.

We solve the problem of first-passage time for run-and-tumble particles in one dimension. Exact expression is derived for the mean first-passage time in the general case, considering external force fields and chemotactic fields, giving rise to space-dependent swim speed and tumble rate. Agreement between theoretical formulae and numerical simulations is obtained in the analyzed case studies --constant and sinusoidal force fields, constant gradient chemotactic field. Reported findings can be useful to get insights into very different phenomena involving active particles, such as bacterial motion in external fields, intracellular transport, cell migration, animal foraging.

Focusing and imaging with increased numerical apertures through multimode fibers with micro-fabricated optics.

The use of individual multimode optical fibers in endoscopy applications has the potential to provide highly miniaturized and noninvasive probes for microscopy and optical micromanipulation. A few different strategies have been proposed recently, but they all suffer from intrinsically low resolution related to the low numerical aperture of multimode fibers. Here, we show that two-photon polymerization allows for direct fabrication of micro-optics components on the fiber end, resulting in an increase of the numerical aperture to a value that is close to 1. Coupling light into the fiber through a spatial light modulator, we were able to optically scan a submicrometer spot (300 nm FWHM) over an extended region, facing the opposite fiber end. Fluorescence imaging with improved resolution is also demonstrated.

Stochastic hydrodynamic synchronization in rotating energy landscapes.

Hydrodynamic synchronization provides a general mechanism for the spontaneous emergence of coherent beating states in independently driven mesoscopic oscillators. A complete physical picture of those phenomena is of definite importance to the understanding of biological cooperative motions of cilia and flagella. Moreover, it can potentially suggest novel routes to exploit synchronization in technological applications of soft matter. We demonstrate that driving colloidal particles in rotating energy landscapes results in a strong tendency towards synchronization, favoring states where all beads rotate in phase. The resulting dynamics can be described in terms of activated jumps with transition rates that are strongly affected by hydrodynamics leading to an increased probability and lifetime of the synchronous states. Using holographic optical tweezers we quantitatively verify our predictions in a variety of spatial configurations of rotors.

Bacterial ratchet motors.

Self-propelling bacteria are a nanotechnology dream. These unicellular organisms are not just capable of living and reproducing, but they can swim very efficiently, sense the environment, and look for food, all packaged in a body measuring a few microns. Before such perfect machines can be artificially assembled, researchers are beginning to explore new ways to harness bacteria as propelling units for microdevices. Proposed strategies require the careful task of aligning and binding bacterial cells on synthetic surfaces in order to have them work cooperatively. Here we show that asymmetric environments can produce a spontaneous and unidirectional rotation of nanofabricated objects immersed in an active bacterial bath. The propulsion mechanism is provided by the self-assembly of motile Escherichia coli cells along the rotor boundaries. Our results highlight the technological implications of active matter's ability to overcome the restrictions imposed by the second law of thermodynamics on equilibrium passive fluids.

Hydrodynamic synchronization of light driven microrotors.

Hydrodynamic synchronization is a fundamental physical phenomenon by which self-sustained oscillators communicate through perturbations in the surrounding fluid and converge to a stable synchronized state. This is an important factor for the emergence of regular and coordinated patterns in the motions of cilia and flagella. When dealing with biological systems, however, it is always hard to disentangle internal signaling mechanisms from external purely physical couplings. We have used the combination of two-photon polymerization and holographic optical trapping to build a mesoscale model composed of chiral propellers rotated by radiation pressure. The two microrotors can be synchronized by hydrodynamic interactions alone although the relative torques have to be finely tuned. Dealing with a micron sized system we treat synchronization as a stochastic phenomenon and show that the phase lag between the two microrotors is distributed according to a stationary Fokker-Planck equation for an overdamped particle over a tilted periodic potential. Synchronized states correspond to minima in this potential whose locations are shown to depend critically on the detailed geometry of the propellers.

Probability distributions for the run-and-tumble bacterial dynamics: an analogy to the Lorentz model.

In this paper, we exploit an analogy of the run-and-tumble process for bacterial motility with the Lorentz model of electron conduction in order to obtain analytical results for the intermediate scattering function. This allows to obtain an analytical result for the van Hove function in real space for two-dimensional systems. We furthermore consider the 2D circling motion of bacteria close to solid boundaries with tumbling, and show that the analogy to electron conduction in a magnetic field allows to predict the effective diffusion coefficient of the bacteria. The latter is shown to be reduced by the circling motion of the bacteria.

Digital holographic tracking of microprobes for multipoint viscosity measurements.

Digital holographic microscopy provides an ideal tool for 3D tracking of microspheres while simultaneously allowing a full and accurate characterization of their main physical properties such as: radius and refractive index. We demonstrate that the combination of high resolution multipoint tracking and accurate optical sizing of tracers provides an ideal tool for precise multipoint viscosity measurements. We also report a detailed evaluation of the technique's accuracy and precision in relation to the primary sources of error.

Real-time digital holographic microscopy of multiple and arbitrarily oriented planes.

Digital holographic microscopy is used to numerically refocus a recorded hologram at an arbitrary axial distance. However, as a straightforward property of coherent light fields, image reconstruction on an arbitrary tilted plane could be directly obtained by a rotation in k-space. We demonstrate that this property allows the real-time microscopic inspection of particle distribution over three mutually orthogonal planes at the same time. As a straightforward application we use the proposed technique for real-time monitoring of fluid flow over the three cross sections of a microfluidic channel.

Three-dimensional to two-dimensional crossover in the hydrodynamic interactions between micron-scale rods.

Moving micron-scale objects are strongly coupled to each other by hydrodynamic interactions. The strength of this coupling decays with the inverse particle separation when the two objects are sufficiently far apart. It has been recently demonstrated that the reduced dimensionality of a thin fluid layer gives rise to longer-ranged, logarithmic coupling. Using holographic tweezers we show that microrods display both behaviors interacting like point particles in three dimensions at large distances and like point particles in two dimensions for distances shorter then their length. We derive a simple analytical expression that fits our data remarkably well and further validate it with finite element analysis.

Swimming with an image.

The hydrodynamic interactions of a swimming bacterium with a neighboring surface can cause it to swim in circles. For example, when E. coli is above a solid surface it had been observed to swim in a clockwise direction. By contrast we observe that, when swimming near a liquid-air interface, the sense of rotation is reversed. We quantitatively account for this through the hydrodynamic interaction of the bacterium with its own mirror image swimming on the opposite side of a perfect-slip boundary. The strength of the coupling is reduced for longer cells, where the torque is spread over a larger length, resulting in longer bacteria swimming in larger circles. We confirm this through precise video measurements of bacterial trajectories and orientations.

Effective interactions between colloidal particles suspended in a bath of swimming cells.

The dynamics of passive colloidal tracers in a bath of self-propelled particles is receiving a lot of attention in the context of nonequilibrium statistical mechanics. Here we demonstrate that active baths are also capable of mediating effective interactions between suspended bodies. In particular we observe that a bath of swimming bacteria gives rise to a short range attraction similar to depletion forces in equilibrium colloidal suspensions. Using numerical simulations and experiments we show how the features of this interaction arise from the combination of nonequilibrium dynamics (peculiar of bacterial baths) and excluded volume effects.

Comparison of Faxén's correction for a microsphere translating or rotating near a surface.

Boundary walls in microfluidic devices have a strong influence on the fluid flow and drag forces on moving objects. The Stokes drag force acting on a sphere translating in the fluid is increased by the presence of a neighboring wall by a factor given by Faxén's correction. A similar increase in the rotational drag is expected when spinning close to a wall. We use optical tweezers to confirm the translational drag correction and report the hitherto unmeasured rotational equivalent. We find that the corrections for the rotational motion is only required for particle-wall separations an order of magnitude shorter than that for the translational cases. These results are particularly significant in the use of optical tweezers for measuring viscosity on a picolitre scale.

Shear-banding phenomena and dynamical behavior in a Laponite suspension.

Shear localization in an aqueous clay suspension of Laponite is investigated through dynamic light scattering, which provides access both to the dynamics of the system (homodyne mode) and to the local velocity profile (heterodyne mode). When shear bands form, a relaxation of the dynamics typical of a gel phase is observed in both bands soon after the flow stops. Periodic oscillations of the flow behavior, typical of a stick-slip phenomenon, are also observed when shear localization occurs. Both results are discussed in the light of various theoretical models for soft glassy gels.

Hydrodynamic interactions in two dimensions.

We measure hydrodynamic interactions between colloidal particles confined in a thin sheet of fluid. The reduced dimensionality, compared to a bulk fluid, increases dramatically the range of couplings. Using optical tweezers we force a two body system along the eigenmodes of the mobility tensor and find that eigenmobilities change logarithmically with particle separation. At a hundred radii distance, the mobilities for rigid and relative motions differ by a factor of 2, whereas in bulk fluids, they would be practically indistinguishable. A two dimensional counterpart of Oseen hydrodynamic tensor quantitatively reproduces the observed behavior, once the relevant boundary conditions are recognized. These results highlight the importance of dimensionality for transport and interactions in colloidal systems and proteins in biological membranes.