Fabricable concentric-ring metalens with high focusing efficiency based on two-dimensional subwavelength unit splicing.

To address the challenges posed by computational resource consumption and data volume in the development of large-aperture metalenses, a design method for concentric-ring metalens based on two-dimensional unit splicing is proposed in this paper. In the method, the unit structure library is constructed through global traversal under the machining process constraints. The phase matching is performed for two polarization states with specific weights and the design of binary-height, concentric-ring structures with arbitrary polarization sensitivity is realized, whose focusing efficiency (the encircled power within 3×FWHM of the focal spot divided by the near-field outgoing power) is up to 90%. Based on this method, a polarization-insensitive metalens with a design wavelength of 10µm, diameter of 2 cm, and numerical aperture of 0.447 is obtained. The method combines the advantages of lower computation requirements for a building block array of a metalens and lower structure data for a concentric-ring metalens. Consequently, it becomes possible to reduce calculation and processing costs by several orders of magnitude during the development process of metalenses with diameters ranging from 103 to 105 wavelengths. The resulting focusing efficiency can approach the upper limit achievable through global structural optimization and significantly surpass that of binary-height Fresnel lenses.

Topologically optimized concentric-nanoring metalens with 1 mm diameter, 0.8†NA and 600†nm imaging resolution in the visible.

Metalenses can achieve diffraction-limited focusing via localized phase modification of the incoming light beam. However, the current metalenses face to the restrictions on simultaneously achieving large diameter, large numerical aperture, broad working bandwidth and the structure manufacturability. Herein, we present a kind of metalenses composed of concentric nanorings that can address these restrictions using topology optimization approach. Compared to existing inverse design approaches, the computational cost of our optimization method is greatly reduced for large-size metalenses. With its design flexibility, the achieved metalens can work in the whole visible range with millimeter size and a numerical aperture of 0.8 without involving high-aspect ratio structures and large refractive index materials. Electron-beam resist PMMA with a low refractive index is directly used as the material of the metalens, enabling a much more simplified manufacturing process. Experimental results show that the imaging performance of the fabricated metalens has a resolution better than 600 nm corresponding to the measured FWHM of 745 nm.

High-Efficiency Achromatic Metalens Topologically Optimized in the Visible.

Metalens, composed of arrays of nano-posts, is an ultrathin planar optical element used for constructing compact optical systems which can achieve high-performance optical imaging by wavefront modulating. However, the existing achromatic metalenses for circular polarization possess the problem of low focal efficiency, which is caused by the low polarization conversion efficiencies of the nano-posts. This problem hinders the practical application of the metalens. Topology optimization is an optimization-based design method that can effectively extend the degree of design freedom, allowing the phases and polarization conversion efficiencies of the nano-posts to be taken into account simultaneously in the optimization procedures. Therefore, it is used to find geometrical configurations of the nano-posts with suitable phase dispersions and maximized polarization conversion efficiencies. An achromatic metalens has a diameter of 40 µm. The average focal efficiency of this metalens is 53% in the spectrum of 531 nm to 780 nm by simulation, which is higher than the previously reported achromatic metalenses with average efficiencies of 20~36%. The result shows that the introduced method can effectively improve the focal efficiency of the broadband achromatic metalens.

The electrodynamics of rod-like microparticles based on optically induced dielectrophoresis.

Due to its characteristics of noncontact, non-damage, high flux, and easy-to-achieve flexible manipulation, optically induced dielectrophoresis (ODEP) technology has been employed to manipulate microspherical biological particles, including separation, enrichment, capture, arrangement, and fusion. However, in nature, biomolecules are morphologically diverse, and some of them are rodlike. In order to illustrate the electrodynamics of rodlike particles under the action of ODEP, a transient multi-physical field coupling model of ODEP chip under the hypothesis of electrical double layer thin layer was established in this paper. The arbitrary Lagrangian-Eulerian method is used to track single-rod particle in the strong coupled flow field and electric field simultaneously. The influence of several key factors, including the applied alternating current (AC) electric voltage, the width of optical bright area, and the initial position of particle, on the trajectory of particle center was analyzed in positive dielectrophoresis (DEP) action and negative DEP action, respectively. Especially, the planar motion process of rodlike particles was discussed together. The research results reveal the electrodynamics behavior of rodlike particles based on the action of ODEP, which may provide theoretical support for the further design of rodlike biological cells manipulation chip based on AC ODEP technology in the future.

The interaction between silica flat substrate and functional group-modified nanoparticles.

Inspired by nature, the research of functionalized nanoparticles and nanodevices has been in-depth developed in recent years. In this paper, we theoretically studied the interaction between functional polyelectrolyte brush layer-modified nanoparticles and a silica flat substrate. Based on the Poisson-Nernst-Planck equations, the mathematical model is established. The changes of the volume charge density and electric field energy density when the nanoparticle interacts with the silica flat substrate under multi-ions regulation were investigated. The results show that when there is a strong interaction between the silica flat substrate and nanoparticles, such as the distances between the nanoparticle and silica flat substrate, which are 2 or 5 nm, the isoelectric point shift under the influence of silica flat substrate and the total charge density in the brush layer is jointly controlled by the cations in the solution and the volume charge density of the brush layer. With the increase of the distances between the nanoparticle and silica flat substrate, the regulation of the volume charge density of the brush layer dominates. These results will provide guidance for the movement mechanism of functionalized nanoparticles in silica nanochannels.

Nanoantennas Inversely Designed to Couple Free Space and a Metal-Insulator-Metal Waveguide.

The metal-insulator-metal (MIM) waveguide, which can directly couple free space photons, acts as an important interface between conventional optics and subwavelength photoelectrons. The reason for the difficulty of this optical coupling is the mismatch between the large wave vector of the MIM plasmon mode and photons. With the increase in the wave vector, there is an increase in the field and Ohmic losses of the metal layer, and the strength of the MIM mode decreases accordingly. To solve those problems, this paper reports on inversely designed nanoantennas that can couple the free space and MIM waveguide and efficiently excite the MIM plasmon modes at multiple wavelengths and under oblique angles. This was achieved by implementing an inverse design procedure using a topology optimization approach. Simulation analysis shows that the coupling efficiency is enhanced 9.47-fold by the nanoantenna at the incident wavelength of 1338 nm. The topology optimization problem of the nanoantennas was analyzed by using a continuous adjoint method. The nanoantennas can be inversely designed with decreased dependence on the wavelength and oblique angle of the incident waves. A nanostructured interface on the subwavelength scale can be configured in order to control the refraction of a photonic wave, where the periodic unit of the interface is composed of two inversely designed nanoantennas that are decoupled and connected by an MIM waveguide.

Topologically optimized magnetic lens for magnetic resonance applications.

Improvements to the signal-to-noise ratio of magnetic resonance detection lead to a strong reduction in measurement time, yet as a sole optimization goal for resonator design, it would be an oversimplification of the problem at hand. Multiple constraints, for example for field homogeneity and sample shape, suggest the use of numerical optimization to obtain resonator designs that deliver the intended improvement. Here we consider the 2D Lenz lens to be a sufficiently broadband flux transforming interposer between the sample and a radiofrequency (RF) circuit and to be a flexible and easily manufacturable device family with which to mediate different design requirements. We report on a method to apply topology optimization to determine the optimal layout of a Lenz lens and demonstrate realizations for both low- (45 MHz) and high-frequency (500 MHz) nuclear magnetic resonance.

Electrokinetic Translocation of a Deformable Nanoparticle through a Nanopore.

The nanopore-based biosensing technology is built up on the fluctuation of the ionic current induced by the electrokinetic translation of a particle penetrating the nanopore. It is expected that the current change of a deformable bioparticle is dissimilar from that of a rigid one. This study theoretically investigated the transient translocation process of a deformable particle through a nanopore for the first time. The mathematical model considers the Poisson equation for the electric potential, the Nernst-Planck equations for the ionic transport, the Navier-Stokes equations for the flow field, and the stress-strain equation for the dynamics of the deformable bioparticle. The arbitrary Lagrangian-Eulerian method is used for the fully coupled particle-fluid dynamic interaction. Results show that the deformation degree of the particle, the velocity deviation, and the current is different from the rigid particle. The deformation degree of the particle will reach the maximum when the particle passes a nanopore. Because of the deformation of particles, the total force applied on deformable particles is larger than that of rigid particles, resulting in larger velocity deviation and current deviation. The influences of the ratio of the nanoparticle radius to the Debye length and surface charge density of the nanopore are also studied. The research results illustrate the translocation mechanism of a deformable nanoparticle in the nanopore, which can provide theoretical guidance for the biosensing technology based on the nanopore.

A new droplet breakup phenomenon in electrokinetic flow through a microchannel constriction.

A completely new droplet breakup phenomenon is reported for droplets passing through a constriction in an electrokinetic flow. The breakup occurs during the droplet shape recovery process past the constriction throat by the interplay of the dielectrophoretic stress release and the interface energy for droplets with smaller permittivity than that of the ambient fluid. There are conditions for constriction ratios and droplet size that the droplet breakup occurs. The numerical predictions provided here require experimental verification, and then can give rise to a novel microfluidic device design with novel droplet manipulations.

Self-Powered Intracellular Drug Delivery by a Biomechanical Energy-Driven Triboelectric Nanogenerator.

Nondestructive, high-efficiency, and on-demand intracellular drug/biomacromolecule delivery for therapeutic purposes remains a great challenge. Herein, a biomechanical-energy-powered triboelectric nanogenerator (TENG)-driven electroporation system is developed for intracellular drug delivery with high efficiency and minimal cell damage in vitro and in vivo. In the integrated system, a self-powered TENG as a stable voltage pulse source triggers the increase of plasma membrane potential and membrane permeability. Cooperatively, the silicon nanoneedle-array electrode minimizes cellular damage during electroporation via enhancing the localized electrical field at the nanoneedle-cell interface and also decreases plasma membrane fluidity for the enhancement of molecular influx. The integrated system achieves efficient delivery of exogenous materials (small molecules, macromolecules, and siRNA) into different types of cells, including hard-to-transfect primary cells, with delivery efficiency up to 90% and cell viability over 94%. Through simple finger friction or hand slapping of the wearable TENGs, it successfully realizes a transdermal biomolecule delivery with an over threefold depth enhancement in mice. This integrated and self-powered system for active electroporation drug delivery shows great prospect for self-tuning drug delivery and wearable medicine.

Dielectrophoretic choking phenomenon in a converging-diverging microchannel for Janus particles.

The dielectrophoretic (DEP) choking phenomenon is revisited for Janus particles that are transported electrokinetically through a microchannel constriction by a direct-current (DC) electric field. The negative DEP force that would block a particle with a diameter significantly smaller than that of the constriction at its inlet is seen to be relaxed by the rotation of the Janus particle in a direction that minimizes the magnitude of the DEP force. This allows the particle to pass through the constriction completely. An arbitrary Lagrangian-Eulerian (ALE) numerical method is used to solve the nonlinearly coupled electric field, flow field, and moving particle, and the DEP force is calculated by the Maxwell stress tensor (MST) method. The results show how Janus particles with non-uniform surface potentials overcome the DEP force and present new conditions for the DEP choking by a parametric study. Particle transportation through microchannel constrictions is ubiquitous, and particle surface properties are more likely to be non-uniform than not in practical applications. This study provides new insights of importance for non-uniform particles transported electrokinetically in a microdevice.

Topology Optimization of Passive Micromixers Based on Lagrangian Mapping Method.

This paper presents an optimization-based design method of passive micromixers for immiscible fluids, which means that the Peclet number infinitely large. Based on topology optimization method, an optimization model is constructed to find the optimal layout of the passive micromixers. Being different from the topology optimization methods with Eulerian description of the convection-diffusion dynamics, this proposed method considers the extreme case, where the mixing is dominated completely by the convection with negligible diffusion. In this method, the mixing dynamics is modeled by the mapping method, a Lagrangian description that can deal with the case with convection-dominance. Several numerical examples have been presented to demonstrate the validity of the proposed method.

Numerical Investigation of DC Dielectrophoretic Deformable Particle⁻Particle Interactions and Assembly.

In a non-uniform electric field, the surface charge of the deformable particle is polarized, resulting in the dielectrophoretic force acting on the surface of the particle, which causes the electrophoresis. Due to dielectrophoretic force, the two deformable particles approach each other, and distort the flow field between them, which cause the hydrodynamic force correspondingly. The dielectrophoresis (DEP) force and the hydrodynamic force together form the net force acting on the particles. In this paper, based on a thin electric double layer (EDL) assumption, we developed a mathematical model under the arbitrary Lagrangian⁻Eulerian (ALE) numerical approach method to simulate the flow field, electric field, and deformable particles simultaneously. Simulation results show that, when two deformable particles' distances are in a certain range, no matter the initial position of the two particles immersed in the fluid field, the particles will eventually form a particle⁻particle chain parallel to the direction of the electric field. In actual experiments, the biological cells used are deformable. Compared with the previous study on the DEP motion of the rigid particles, the research conclusion of this paper provides a more rigorous reference for the design of microfluidics.

Optimal Control-Based Inverse Determination of Electrode Distribution for Electroosmotic Micromixer.

This paper presents an optimal control-based inverse method used to determine the distribution of the electrodes for the electroosmotic micromixers with external driven flow from the inlet. Based on the optimal control method, one Dirichlet boundary control problem is constructed to inversely find the optimal distribution of the electrodes on the sidewalls of electroosmotic micromixers and achieve the acceptable mixing performance. After solving the boundary control problem, results are also provided to demonstrate the effectiveness of the proposed method; the step-shaped distribution of the external electric potential imposed on the sidewalls is obtained, and the electrodes with an interlaced arrangement are inversely derived according to the obtained external electric potential.

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

Euler force actuation mechanism for siphon valving in compact disk-like microfluidic chips.

Based on the Euler force induced by the acceleration of compact disk (CD)-like microfluidic chip, this paper presents a novel actuation mechanism for siphon valving. At the preliminary stage of acceleration, the Euler force in the tangential direction of CD-like chip takes the primary place compared with the centrifugal force to function as the actuation of the flow, which fills the siphon and actuates the siphon valving. The Euler force actuation mechanism is demonstrated by the numerical solution of the phase-field based mathematical model for the flow in siphon valve. In addition, experimental validation is implemented in the polymethylmethacrylate-based CD-like microfluidic chip manufactured using CO2 laser engraving technique. To prove the application of the proposed Euler force actuation mechanism, whole blood separation and plasma extraction has been conducted using the Euler force actuated siphon valving. The newly introduced actuation mechanism overcomes the dependence on hydrophilic capillary filling of siphon by avoiding external manipulation or surface treatments of polymeric material. The sacrifice for highly integrated processing in pneumatic pumping technique is also prevented by excluding the volume-occupied compressed air chamber.

Hydrodynamic particle focusing design using fluid-particle interaction.

For passive sheathless particles focusing in microfluidics, the equilibrium positions of particles are typically controlled by micro channels with a V-shaped obstacle array (VOA). The design of the obstacles is mainly based on the distribution of flow streamlines without considering the existence of particles. We report an experimentally verified particle trajectory simulation using the arbitrary Lagrangian-Eulerian (ALE) fluid-particle interaction method. The particle trajectory which is strongly influenced by the interaction between the particle and channel wall is systematically analyzed. The numerical experiments show that the streamline is a good approximation of particle trajectory only when the particle locates on the center of the channel in depth. As the advantage of fluid-particle interaction method is achieved at a high computational cost and the streamline analysis is complex, a heuristic dimensionless design objective based on the Faxen's law is proposed to optimize the VOA devices. The optimized performance of particle focusing is verified via the experiments and ALE method.

A flexible layout design method for passive micromixers.

This paper discusses a flexible layout design method of passive micromixers based on the topology optimization of fluidic flows. Being different from the trial and error method, this method obtains the detailed layout of a passive micromixer according to the desired mixing performance by solving a topology optimization problem. Therefore, the dependence on the experience of the designer is weaken, when this method is used to design a passive micromixer with acceptable mixing performance. Several design disciplines for the passive micromixers are considered to demonstrate the flexibility of the layout design method for passive micromixers. These design disciplines include the approximation of the real 3D micromixer, the manufacturing feasibility, the spacial periodic design, and effects of the Péclet number and Reynolds number on the designs obtained by this layout design method. The capability of this design method is validated by several comparisons performed between the obtained layouts and the optimized designs in the recently published literatures, where the values of the mixing measurement is improved up to 40.4% for one cycle of the micromixer.