Extended and knotted optical traps in three dimensions

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

Electromagnetic Forces and Torques: From Dielectrophoresis to Optical Tweezers

Electromagnetic forces and torques enable many key technologies, including optical tweezers or dielectrophoresis. Interestingly, both techniques rely on the same physical process: the interaction of an oscillating electric field with a particle of matter. This work provides a unified framework to understand this interaction both when considering fields oscillating at low frequencies─dielectrophoresis─and high frequencies─optical tweezers. We draw useful parallels between these two techniques, discuss the different and often unstated assumptions they are based upon, and illustrate key applications in the fields of physical and analytical chemistry, biosensing, and colloidal science.

Formation of Inverse Energy Flux in the Case of Diffraction of Linearly Polarized Radiation by Conventional and Generalized Spiral Phase Plates

Recently, there has been increased interest in the shaping of light fields with an inverse energy flux to guide optically trapped nano- and microparticles towards a radiation source. To generate inverse energy flux, non-uniformly polarized laser beams, especially higher-order cylindrical vector beams, are widely used. Here, we demonstrate the use of conventional and so-called generalized spiral phase plates for the formation of light fields with an inverse energy flux when they are illuminated with linearly polarized radiation. We present an analytical and numerical study of the longitudinal and transverse components of the Poynting vector. The conditions for maximizing the negative value of the real part of the longitudinal component of the Poynting vector are obtained.

Rapidly and accurately shaping the intensity and phase of light for optical nano-manipulation

Holographic optical tweezers can be applied to manipulate microscopic particles in various optical patterns, which classical optical tweezers cannot do. This ability relies on accurate computer-generated holography (CGH), yet most CGH techniques can only shape the intensity profiles while the phase distributions remain poor. Here, we introduce a new method for fast generation of holograms that allows for accurately shaping both the intensity and phase distributions of light. The method uses a discrete inverse Fourier transform formula to directly calculate a hologram in one step, in which a random phase factor is introduced into the formula to enable complete control of intensity and phase. Various optical patterns can be created, as demonstrated by the experimentally measured intensity and phase profiles projected from the holograms. The high-quality shaping of intensity and phase of light provides new opportunities for optical trapping and manipulation, such as controllable transportation of nanoparticles in optical trap networks with variable phase profiles.

Above and beyond: holographic tracking of axial displacements in holographic optical tweezers

How far a particle moves along the optical axis in a holographic optical trap is not simply dictated by the programmed motion of the trap, but rather depends on an interplay of the trap's changing shape and the particle's material properties. For the particular case of colloidal spheres in optical tweezers, holographic video microscopy reveals that trapped particles tend to move farther along the axial direction than the traps that are moving them and that different kinds of particles move by different amounts. These surprising and sizeable variations in axial placement can be explained by a dipole-order theory for optical forces. Their discovery highlights the need for real-time feedback to achieve precise control of colloidal assemblies in three dimensions and demonstrates that holographic microscopy can meet that need.

Programmable optical transport of particles in knot circuits and networks

A freestyle single-beam laser trap allows for multi-particle optical transport along arbitrary open or closed trajectories with independent control of the all-optical confinement and propulsion forces exerted over the particles. Here, exploiting this manipulation tool, we propose and experimentally demonstrate an optical dynamic routing technique to assist multi-particle transport in knot circuits and networks exhibiting multiple crossing paths. This new functionality for optical transport enables the particle circulation in such complex systems handling traffic jams and making possible particle separation/mixing in them. It is important for the development of programmable particle delivery and other automated optical transport operations of interest in colloidal physics, optofluidics, biophysics, etc.

Dynamic morphing of 3D curved laser traps for all-optical manipulation of particles

The development of optical manipulation techniques focused on the confinement and transport of micro/nano-particles has attracted increased interest in the last decades. In particular the combination of all-optical confinement and propelling forces, respectively arising from high intensity and phase gradients of a strongly focused laser beam, is promising for optical transport. The recently developed freestyle laser trap exploits this manipulation mechanism to achieve optical transport along arbitrary 3D curves. In practice, reconfigurable 3D optical transport of numerous particles is a challenging problem because it requires the ability to easily adapt the trajectory in real time. In this work, we introduce and experimentally demonstrate a strategy for on-task adaptive design of freestyle laser traps based on a dynamic morphing technique. This provides programmable smooth transformation of the 3D shape of the curved laser trap with independent control of the propelling forces along it, that can be configured according to the considered application. Dynamic morphing, proven here on the example of colloidal dielectric micro-particles, significantly simplifies the important problem of real-time reconfigurable 3D optical transport and opens up routes for other sophisticated optical manipulation tasks.

Vector polymorphic beam

A scalar polymorphic beam is designed with independent control of its intensity and phase along a strongly focused laser curve of arbitrary shape. This kind of beam has been found crucial in the creation of freestyle laser traps able to confine and drive the motion of micro/nano-particles along reconfigurable 3D trajectories in real time. Here, we present and experimentally prove the concept of vector polymorphic beam adding the benefit of independent design of the light polarization along arbitrary curves. In particular, we consider polarization shaped tangential and orthogonal to the curve that are of high interest in optical manipulation and laser micromachining. The vector polymorphic beam is described by a surprisingly simple closed-form expression and can be easily generated by using a computer generated hologram.

Creating Complex Optical Longitudinal Polarization Structures

In this Letter, we show that it is possible to structure the longitudinal polarization component of light. We illustrate our approach by demonstrating linked and knotted longitudinal vortex lines acquired upon nonparaxially propagating a tightly focused subwavelength beam. The remaining degrees of freedom in the transverse polarization components can be exploited to generate customized topological vector beams.

Active particle condensation by non-reciprocal and time-delayed interactions

We consider the flocking of self-propelling agents in two dimensions, each of which communicates with its neighbors within a limited vision-cone. Also, the communication occurs with some time-delay. The communication among the agents are modeled by Vicsek rules. In this study we explore the combined effect of non-reciprocal interaction (induced by limited vision-cone) among the agents and the presence of delay in the interactions on the dynamical pattern formation within the flock. We find that under these two influences, without any position-based attractive interactions or confining boundaries, the agents can spontaneously condense into "drops". Though the agents are in motion within the drop, the drop as a whole is pinned in space. We find that this novel state of the flock has a well-defined order and it is stabilized by the noise present in the system.

Drying-mediated optical assembly of silica spheres in a symmetrical metallic waveguide structure

We describe the optical trapping application of a simple metallic slab optical waveguide structure, and demonstrate the influence of the excited guided modes on the aggregation behavior of silica particles during the irreversible evaporation process. Periodic horizontal stripes are formed by the highly ordered assemblies of the silica spheres, which is explained via the interference effect between the forward propagating modes and its reflection at the solvent surface. Particularly, several layers consisting of high-density particles are discernible in the stripe zones due to the optical binding, while no particles locate between these stripes. Completely different from the self-assembly patterns in the evaporating solvent without excitation of optical modes, this Letter demonstrates the versatility in the possible patterns of the optical assembly by a coupling waveguide with more complex structures.

Accelerating incoherent hollow beams beyond the paraxial regime

We propose a non-paraxial hollow accelerating beam, which is formed by incoherently superposing two well-designed coherent accelerating beams. Very interestingly, this incoherent superposition does not hamper the acceleration dynamics pertaining to the coherent ones, but results in a hollow intensity pattern in the cross section transverse to the circular accelerating trajectory. By a simple optimization, this hollow cross section pattern can be effectively extended to an angle close to 90°. The magnitude and the phase of the angular spectrum of the beam are given followed by a suggested scheme to generate the beam in practice. Such highly self-bending hollow beams may find applications in some fields such as optical manipulation.

Structural correlations in diffusiophoretic colloidal mixtures with nonreciprocal interactions

Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio  =  reactio on coarse-grained length and time scales. Here we explore the statistical mechanics of Brownian particles with nonreciprocal effective interactions. Our model system is a binary fluid mixture of spherically symmetric, diffusiophoretic mesoscopic particles, and we focus on the time-averaged particle pair- and triplet-correlation functions. Based on the many-body Smoluchowski equation we develop a microscopic statistical theory for the particle correlations and test it by computer simulations. For model systems in two and three spatial dimensions, we show that nonreciprocity induces distinct nonequilibrium pair correlations. Our predictions can be tested in experiments with chemotactic colloidal suspensions.

Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram

An iterative beam shaping algorithm is proposed to simultaneously shape the amplitude and phase of an optical beam. The proposed algorithm consists of one input plane and two completely overlapped output planes which refer to the output plane in real space. The two output planes are imposed with both amplitude and phase constraints, and the constrained areas in the two output planes are complementary. As a result, both the amplitude and phase in the entire output plane are controllable and arbitrary target complex amplitudes can be achieved with the proposed algorithm. The computing result of the proposed algorithm is a phase-only distribution which can be conveniently realized with a spatial light modulator or a fabricated diffractive optical element. Both simulations and experiments have verified the high performance of the proposed algorithm.

Curved optical tubes in a 4Pi focusing system

We demonstrate the possibility of creating curved optical tubes in a 4Pi focusing system. The focal fields of such optical tubes have interesting properties: the energy is concentered in the neighborhood of a prescribed three-dimensional (3D) curve while the cross section is of hollow shape. The creation of these optical tubes is based on the annular focal spot of a vortex beam, which is employed as a building block. An optical tube is thus obtained by covering the central-axis curve of the tube by various such building blocks. Each building block has a certain orientation and position, realized by a rotation plus a certain translation. The spatial spectrum (the input field as well) of the optical tube is obtained by linearly superposing the spectrum of each transformed building block. The curve is rather arbitrary. Three examples of optical tubes: a torus, a solenoid and a trefoil knot are given, showing a good agreement with the expected results.

Direct evidence for three-dimensional off-axis trapping with single Laguerre-Gaussian beam

Optical tweezers are often applied to control the dynamics of objects by scanning light. However, there is a limitation that objects fail to track the scan when the drag exceeds the trapping force. In contrast, Laguerre-Gaussian (LG) beams can directly control the torque on objects and provide a typical model for nonequilibrium systems such as Brownian motion under external fields. Although stable “mid-water” trapping is essential for removing extrinsic hydrodynamic effects in such studies, three-dimensional trapping by LG beams has not yet been clearly established. Here we report the three-dimensional off-axis trapping of dielectric spheres using high-quality LG beams generated by a special holographic method. The trapping position was estimated as ~ half the wavelength behind the beam waist. These results establish the scientific groundwork of LG trapping and the technical basis of calibrating optical torque to provide powerful tools for studying energy-conversion mechanisms and the nonequilibrium nature of biological molecules under torque.

Shaping of light beams along curves in three dimensions

We present a method for efficient and versatile generation of beams whose intensity and phase are prescribed along arbitrary 3D curves. It comprises a non-iterative beam shaping technique that does not require solving inversion problems of light propagation. The generated beams have diffraction-limited focusing with high intensity and controlled phase gradients useful for applications such as laser micro-machining and optical trapping. Its performance and feasibility are experimentally demonstrated on several examples including multiple trapping of micron-sized particles.

Optical forces and torques in nonuniform beams of light

The spin angular momentum in an elliptically polarized beam of light plays several noteworthy roles in optical traps. It contributes to the linear momentum density in a nonuniform beam, and thus to the radiation pressure exerted on illuminated objects. It can be converted into orbital angular momentum, and thus can exert torques even on optically isotropic objects. Its curl, moreover, contributes to both forces and torques without spin-to-orbit conversion. We demonstrate these effects experimentally by tracking colloidal spheres diffusing in elliptically polarized optical tweezers. Clusters of spheres circulate deterministically about the beam's axis. A single sphere, by contrast, undergoes stochastic Brownian vortex circulation that maps out the optical force field.

Controlling the transverse momentum distribution of a light field via azimuth division of a hologram in holographic optical tweezers

This study proposes a method for creating a light field with controlled distribution of transverse momentum (TM) by displaying a hologram only in an azimuth region that centers at θ(0) and has a range of Δθ of a spatial light modulator in holographic optical tweezers. This study utilized ray optics to analyze the TM of the resultant field, revealing that the direction of the TM is determined by the center angle of the azimuth region and that the magnitude of the TM is proportional to sin(Δθ/2), without regarding the intensity. The relationship was verified experimentally. In addition, this study demonstrated moving particles along a designed path and depleting particles by the fields.

Response theory of optical forces in two-port photonics systems: a simplified framework for examining conservative and non-conservative forces

We extend the response theory of optical forces to general electromagnetic systems which can be treated as multi-port systems with multiple mechanical degrees of freedom. We demonstrate a fundamental link between the scattering properties of an optical system to its ability to produce conservative or non-conservative optical forces. Through the exploration of two nontrivial two-port systems, including an analytical Fabry-Perot interferometer and a more complex particle-in-a-waveguide structure, we show perfect agreement between the response theory and numerical first-principle calculations. We show that new insights into the origins of optical forces from the response theory provide clear means of understanding conservative and non-conservative forces in a regime where traditional gradient force picture fails.