Easily scalable multi-color DMD-based structured illumination microscopy.

Structured illumination microscopy (SIM) achieves super-resolution imaging using a series of phase-shifted sinusoidal illumination patterns to down-modulate high spatial-frequency information of samples. Digital micromirror devices (DMDs) have been increasingly used to generate SIM illumination patterns due to their high speed and moderate cost. However, a DMD micromirror array's blazed grating structure causes strong angular dispersion for different wavelengths of light, thus severely hampering its application in multicolor imaging. We developed a multi-color DMD-SIM setup that employs a diffraction grating to compensate the DMD's dispersion and demonstrate super-resolution SIM imaging of both fluorescent beads and live cells samples with four color channels. This simple but effective approach can be readily scaled to more color channels, thereby greatly expanding the application of SIM in the study of complex multi-component structures and dynamics in soft matter systems.

Three-dimensional optical trapping and orientation of microparticles for coherent X-ray diffraction imaging.

Optical trapping has been implemented in many areas of physics and biology as a noncontact sample manipulation technique to study the structure and dynamics of nano- and mesoscale objects. It provides a unique approach for manipulating microscopic objects without inducing undesired changes in structure. Combining optical trapping with hard X-ray microscopy techniques, such as coherent diffraction imaging and crystallography, provides a nonperturbing environment where electronic and structural dynamics of an individual particle in solution can be followed in situ. It was previously shown that optical trapping allows the manipulation of micrometer-sized objects for X-ray fluorescence imaging. However, questions remain over the ability of optical trapping to position objects for X-ray diffraction measurements, which have stringent requirements for angular stability. Our work demonstrates that dynamic holographic optical tweezers are capable of manipulating single micrometer-scale anisotropic particles in a microfluidic environment with the precision and stability required for X-ray Bragg diffraction experiments-thus functioning as an "optical goniometer." The methodology can be extended to a variety of X-ray experiments and the Bragg coherent diffractive imaging of individual particles in solution, as demonstrated here, will be markedly enhanced with the advent of brighter, coherent X-ray sources.

Snapshot multifocal light field microscopy.

Light field microscopy (LFM) is an emerging technology for high-speed wide-field 3D imaging by capturing 4D light field of 3D volumes. However, its 3D imaging capability comes at a cost of lateral resolution. In addition, the lateral resolution is not uniform across depth in the light field dconvolution reconstructions. To address these problems, here, we propose a snapshot multifocal light field microscopy (MFLFM) imaging method. The underlying concept of the MFLFM is to collect multiple focal shifted light fields simultaneously. We show that by focal stacking those focal shifted light fields, the depth-of-field (DOF) of the LFM can be further improved but without sacrificing the lateral resolution. Also, if all differently focused light fields are utilized together in the deconvolution, the MFLFM could achieve a high and uniform lateral resolution within a larger DOF. We present a house-built MFLFM system by placing a diffractive optical element at the Fourier plane of a conventional LFM. The optical performance of the MFLFM are analyzed and given. Both simulations and proof-of-principle experimental results are provided to demonstrate the effectiveness and benefits of the MFLFM. We believe that the proposed snapshot MFLFM has potential to enable high-speed and high resolution 3D imaging applications.

Excitation of Nonradiating Anapoles in Dielectric Nanospheres.

Although the study of nonradiating anapoles has long been part of fundamental physics, the dynamic anapole at optical frequencies was only recently experimentally demonstrated in a specialized silicon nanodisk structure. We report excitation of the electrodynamic anapole state in isotropic silicon nanospheres using radially polarized beam illumination. The superposition of equal and out-of-phase amplitudes of the Cartesian electric and toroidal dipoles produces a pronounced dip in the scattering spectra with the scattering intensity almost reaching zero-a signature of anapole excitation. The total scattering intensity associated with the anapole excitation is found to be more than 10 times weaker for illumination with radially vs linearly polarized beams. Our approach provides a simple, straightforward alternative path to realizing nonradiating anapole states at the optical frequencies.

Single-pixel interior filling function approach for detecting and correcting errors in particle tracking.

We present a general method for detecting and correcting biases in the outputs of particle-tracking experiments. Our approach is based on the histogram of estimated positions within pixels, which we term the single-pixel interior filling function (SPIFF). We use the deviation of the SPIFF from a uniform distribution to test the veracity of tracking analyses from different algorithms. Unbiased SPIFFs correspond to uniform pixel filling, whereas biased ones exhibit pixel locking, in which the estimated particle positions concentrate toward the centers of pixels. Although pixel locking is a well-known phenomenon, we go beyond existing methods to show how the SPIFF can be used to correct errors. The key is that the SPIFF aggregates statistical information from many single-particle images and localizations that are gathered over time or across an ensemble, and this information augments the single-particle data. We explicitly consider two cases that give rise to significant errors in estimated particle locations: undersampling the point spread function due to small emitter size and intensity overlap of proximal objects. In these situations, we show how errors in positions can be corrected essentially completely with little added computational cost. Additional situations and applications to experimental data are explored in SI Appendix In the presence of experimental-like shot noise, the precision of the SPIFF-based correction achieves (and can even exceed) the unbiased Cramér-Rao lower bound. We expect the SPIFF approach to be useful in a wide range of localization applications, including single-molecule imaging and particle tracking, in fields ranging from biology to materials science to astronomy.

Nanoscale Resolution 3D Snapshot Particle Tracking by Multifocal Microscopy.

Accurate, precise, and rapid particle tracking in three dimensions remains a challenge; yet, its achievement will significantly enhance our understanding of living systems. We developed a multifocal microscopy (MFM) that allows snapshot acquisition of the imaging data, and an associated image processing approach, that together allow simultaneous 3D tracking of many fluorescent particles with nanoscale resolution. The 3D tracking was validated by measuring a known trajectory of a fluorescent bead with an axial accuracy of 19 nm through an image depth (axial range) of 3 µm and 4 nm precision of axial localization through an image depth of 4 µm. A second test obtained a uniform axial probability distribution and Brownian dynamics of beads diffusing in solution. We also validated the MFM approach by imaging fluorescent beads immobilized in gels and comparing the 3D localizations to their "ground truth" positions obtained from a confocal microscopy z-stack of finely spaced images. Finally, we applied our MFM and image processing approach to obtain 3D trajectories of insulin granules in pseudoislets of MIN6 cells to demonstrate its compatibility with complex biological systems. Our study demonstrates that multifocal microscopy allows rapid (video rate) and simultaneous 3D tracking of many "particles" with nanoscale accuracy and precision in a wide range of systems, including over spatial scales relevant to whole live cells.

Controlling the Dynamics and Optical Binding of Nanoparticle Homodimers with Transverse Phase Gradients.

While transverse phase gradients enable studies of driven nonequilibrium phenomena in optical trapping, the behavior of electrodynamically interacting particles in a transverse phase gradient has not been explored in detail. In this Letter we study electrodynamically interacting pairs of identical nanoparticles (homodimers) in transverse phase gradients. We establish that the net driving force on homodimers is modulated by a separation-dependent interference effect for small phase gradients. By contrast, large phase gradients break the symmetry of the interaction between particles and profoundly change the electrodynamic interparticle energy landscape. Our findings are particularly important for understanding multiparticle dynamics during the self-assembly and rearrangement of optical matter.

Hierarchical Assembly of Plasmonic Nanoparticle Heterodimer Arrays with Tunable Sub-5 nm Nanogaps.

Nanoparticle assemblies have generated intense interest because of their novel optical, electronic, and magnetic properties that open up numerous opportunities in fundamental and applied nanophotonics, -electronics, and -magnetics. However, despite the great scientific and technological potential of these structures, it remains an outstanding challenge to reliably fabricate such assemblies with both nanometer-level structural control and precise spatial arrangements on a macroscopic scale. It is the combination of these two features that is key to realizing nanoparticle assemblies' potential, particular for device applications. To address this challenge, we propose a hierarchical assembly approach consisting of both template-particle and particle-particle interactions, whereby the former ensures precise addressability of assemblies on a surface and the latter provides nanometer-level structural control. Template-particle interactions are harnessed via chemical-pattern-directed assembly, and the particle-particle interactions are controlled using DNA-directed self-assembly. To demonstrate the potential of this hierarchical assembly approach, we demonstrate the fabrication of a particularly fascinating assembly: the nanoparticle heterodimer, which possesses a surprisingly rich set of plasmonic properties and is a promising candidate to enable a variety of imaging and sensing applications. Each heterodimer is placed on the surface at predetermined locations, and the precise control of the nanogaps is confirmed by far-field scattering measurements of individual dimers. We further demonstrate that the gap size can be effectively tuned by varying the DNA length. By correlating measured spectra with finite-difference time-domain (FDTD) simulations, we determine the gap sizes to be 4.2 and 5.0 nm-with subnm deviation-for the two DNA lengths investigated. This is one of the best gap uniformities ever demonstrated for surface-bound nanoparticle assemblies. The estimated surface-enhanced Raman scattering (SERS) enhancement factor of these heterodimers is on the order of 105-106 with high reproducibility and predictable polarization-dependence. This hierarchical fabrication technique-employing both template-particle and particle-particle interactions-constitutes a novel platform for the realization of functional nanoparticle assemblies on surfaces and thereby creates new opportunities to implement these structures in a variety of applications.

Dynamics of the Optically Directed Assembly and Disassembly of Gold Nanoplatelet Arrays.

The tremendous progress in nanoscience now allows the creation of static nanostructured materials for a broad range of applications. A further goal is to achieve dynamic and reconfigurable nanostructures. One approach involves nanoparticle-based optical matter, but so far, studies have only considered spherical constituents. A nontrivial issue is that nanoparticles with other shapes are expected to have different local electromagnetic field distributions and interactions with neighbors in optical-matter arrays. Therefore, one would expect their dynamics to be different as well. This paper reports the directed assembly of ordered arrays of gold nanoplatelets in optical line traps, demonstrating the reconfigurability of the array by altering the phase gradient via holographic-beam shaping. The weaker gradient forces and resultant slower motion of the nanoplatelets, as compared with plasmonic (Ag and Au) nanospheres, allow the precise study of their assembly and disassembly dynamics. Both temporal and spatial correlations are detected between particles separated by distances of hundreds of nanometers to several microns. Electrodynamics simulations reveal the presence of multipolar plasmon modes that induce short-range (near-field) and longer-range electrodynamic (e.g., optical binding) interactions. These interactions and the interferences between mutipolar plamon modes cause both the strong correlations and the nonuniform dynamics observed. Our study demonstrates new opportunities for the generation of complex addressable optical matter and the creation of novel active optical technology.

Design and simulation of a snapshot multi-focal interferometric microscope.

Realizing both high temporal and spatial resolution across a large volume is a key challenge for 3D fluorescent imaging. Towards achieving this objective, we introduce an interferometric multifocus microscopy (iMFM) system, a combination of multifocus microscopy (MFM) with two opposing objective lenses. We show that the proposed iMFM is capable of simultaneously producing multiple focal plane interferometry that provides axial super-resolution and hence isotropic 3D resolution with a single exposure. We design and simulate the iMFM microscope by employing two special diffractive optical elements. The point spread function of this new iMFM microscope is simulated and the image formation model is given. For reconstruction, we use the Richardson-Lucy deconvolution algorithm with total variation regularization for 3D extended object recovery, and a maximum likelihood estimator (MLE) for single molecule tracking. A method for determining an initial axial position of the molecule is also proposed to improve the convergence of the MLE. We demonstrate both theoretically and numerically that isotropic 3D nanoscopic localization accuracy is achievable with an axial imaging range of 2um when tracking a fluorescent molecule in three dimensions and that the diffraction limited axial resolution can be improved by 3-4 times in the single shot wide-field 3D extended object recovery. We believe that iMFM will be a useful tool in 3D dynamic event imaging that requires both high temporal and spatial resolution.

Particle tracking by repetitive phase-shift interferometric super resolution microscopy.

Accurate and rapid particle tracking is essential for addressing many research problems in single molecule and cellular biophysics and colloidal soft condensed matter physics. We developed a novel three-dimensional interferometric fluorescent particle tracking approach that does not require any sample scanning. By periodically shifting the interferometer phase, the information stored in the interference pattern of the emitted light allows localizing particles positions with nanometer resolution. This tracking protocol was demonstrated by measuring a known trajectory of a fluorescent bead with sub-5 nm axial localization error at 5 Hz. The interferometric microscopy was used to track the RecA protein in Bacillus subtilis bacteria to demonstrate its compatibility with biological systems.

Rotation and Negative Torque in Electrodynamically Bound Nanoparticle Dimers.

We examine the formation and concomitant rotation of electrodynamically bound dimers (EBD) of 150 nm diameter Ag nanoparticles trapped in circularly polarized focused Gaussian beams. The rotation frequency of an EBD increases linearly with the incident beam power, reaching mean values of ∼4 kHz for relatively low incident powers of 14 mW. Using a coupled-dipole/effective polarizability model, we reveal that retardation of the scattered fields and electrodynamic interactions can lead to a "negative torque" causing rotation of the EBD in the direction opposite to that of the circular polarization. This intriguing opposite-handed rotation due to negative torque is clearly demonstrated using electrodynamics-Langevin dynamics simulations by changing particle separations and thus varying the retardation effects. Finally, negative torque is also demonstrated in experiments from statistical analysis of the EBD trajectories. These results demonstrate novel rotational dynamics of nanoparticles in optical matter using circular polarization and open a new avenue to control orientational dynamics through coupling to interparticle separation.

Selective Induction of Optical Magnetism.

An extension of the Maxwell-Faraday law of electromagnetic induction to optical frequencies requires spatially appropriate materials and optical beams to create resonances and excitations with curl. Here we employ cylindrical vector beams with azimuthal polarization to create electric fields that selectively drive magnetic responses in dielectric core-metal nanoparticle "satellite" nanostructures. These optical frequency magnetic resonances are induced in materials that do not possess spin or orbital angular momentum. Multipole expansion analysis of the scattered fields obtained from electrodynamics simulations show that the excitation with azimuthally polarized beams selectively enhances magnetic vs electric dipole resonances by nearly 100-fold in experiments. Multipolar resonances (e.g., quadrupole and octupole) are enhanced 5-fold by focused azimuthally versus linearly polarized beams. We also selectively excite electric multipolar resonances in the same identical nanostructures with radially polarized light. This work opens new opportunities for spectroscopic investigation and control of "dark modes", Fano resonances, and magnetic modes in nanomaterials and engineered metamaterials.

Scaling laws governing stochastic growth and division of single bacterial cells.

Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈ 1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions.

Shape dynamics of growing cell walls.

We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape with the dynamics of growth and constriction. The model allows us to derive constraints on cell wall mechanical energy based on the observed dynamics of cell shape. We predict that exponential growth in cell size requires a constant amount of cell wall energy to be dissipated per unit volume. We use the model to understand and contrast growth in bacteria with different shapes such as spherical, ellipsoidal, cylindrical and toroidal morphologies. Coupling growth to cell wall constriction, we predict a discontinuous shape transformation, from partial constriction to cell division, as a function of the chemical potential driving cell wall synthesis. Our model for cell wall energy and shape dynamics relates growth kinetics with cell geometry, and provides a unified framework to describe the interplay between shape, growth and division in bacterial cells.

Intracellular transport of insulin granules is a subordinated random walk.

We quantitatively analyzed particle tracking data on insulin granules expressing fluorescent fusion proteins in MIN6 cells to better understand the motions contributing to intracellular transport and, more generally, the means for characterizing systems far from equilibrium. Care was taken to ensure that the statistics reflected intrinsic features of the individual granules rather than details of the measurement and overall cell state. We find anomalous diffusion. Interpreting such data conventionally requires assuming that a process is either ergodic with particles working against fluctuating obstacles (fractional brownian motion) or nonergodic with a broad distribution of dwell times for traps (continuous-time random walk). However, we find that statistical tests based on these two models give conflicting results. We resolve this issue by introducing a subordinated scheme in which particles in cages with random dwell times undergo correlated motions owing to interactions with a fluctuating environment. We relate this picture to the underlying microtubule structure by imaging in the presence of vinblastine. Our results provide a simple physical picture for how diverse pools of insulin granules and, in turn, biphasic secretion could arise.

Distribution of directional change as a signature of complex dynamics.

Analyses of random walks traditionally use the mean square displacement (MSD) as an order parameter characterizing dynamics. We show that the distribution of relative angles of motion between successive time intervals of random walks in two or more dimensions provides information about stochastic processes beyond the MSD. We illustrate the behavior of this measure for common models and apply it to experimental particle tracking data. For a colloidal system, the distribution of relative angles reports sensitively on caging as the density varies. For transport mediated by molecular motors on filament networks in vitro and in vivo, we discover self-similar properties that cannot be described by existing models and discuss possible scenarios that can lead to the elucidated statistical features.

Fabrication of a material assembly of silver nanoparticles using the phase gradients of optical tweezers.

Optical matter can be created using the intensity gradient and electrodynamic (e.g., optical binding) forces that nano- and microparticles experience in focused optical beams. Here we show that the force associated with phase gradient is also important. In fact, in optical line traps the phase gradient force is crucial in determining the structure and stability of optical matter arrays consisting of Ag nanoparticles (NPs). NP lattices can be repeatedly assembled and disassembled simply by changing the sign of the phase gradient. The phase gradient creates a compressive force (and thus a stress) in the optically bound Ag NP lattices, causing structural transitions (a stress response) from 1D "chains" to 2D lattices, and even to amorphous structures. The structural transitions and dynamics of driven transport are well described by electrodynamics simulations and modeling using a drift-diffusion Langevin equation.

Enhancing nanoparticle electrodynamics with gold nanoplate mirrors.

Mirrors and optical cavities can modify and enhance matter-radiation interactions. Here we report that chemically synthesized Au nanoplates can serve as micrometer-size mirrors that enhance electrodynamic interactions. Because of their plasmonic properties, the Au nanoplates enhance the brightness of scattered light from Ag nanoparticles near the nanoplate surface in dark-field microscopy. More importantly, enhanced optical trapping and optical binding of Ag nanoparticles are demonstrated in interferometric optical traps created from a single laser beam and its reflection from individual Au nanoplates. The enhancement of the interparticle force constant is ≈20-fold more than expected from the increased intensity due to standing wave interference. We show that the additional stability for optical binding arises from the restricted axial thermal motion of the nanoparticles that couples to and reduces the fluctuations in the lateral plane. This new mechanism greatly advances the photonic synthesis of ultrastable nanoparticle arrays and investigation of their properties.

Universality in stochastic exponential growth.

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.