A vectorial model for the nonlinear gradient force exerted on metallic Rayleigh nanoparticles

Optical tweezers have proved to be a powerful tool with a wide range of applications.The gradient force plays a vital role in the stable optical trapping of nano-objects.The scalar method is convenient and effective for analyzing the gradient force in traditional optical trapping.However,when the third-order nonlinear effect of the nano-object is stimulated,the scalar method cannot adequately present the optical response of the metal nanoparticle to the external optical field.Here,we propose a theoretical model to interpret the nonlinear gradient force using the vector method.By combining the optical Kerr effect,the polarizability vector of the metallic nanoparticle is derived.A quantitative analysis is obtained for the gradient force as well as for the optical potential well.The vector method yields better agreement with reported experimental observations.We suggest that this method could lead to a deeper understanding of the physics relevant to nonlinear optical trapping and binding phenomena.

Resonant gradient force on atom interacting with laser field

The gradient force, as a function of position and velocity, is derived for a two-level atom interacting with a standing-wave laser field. Basing on optical Bloch equations, the numerical solutions for the gradient force f⊥,n (n = 0,1, 2,3,4, …) pointing in the direction of the transverse of the laser beam are given. It is shown the higher order gradient force plays important role at strong intensity (G = 64), the contribution of them can not be neglected.

Shape gradient and classical gradient of curvatures:driving forces on micro/nano curved surfaces

Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a gen- eral theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived： （a） Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. （b） On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. （c） Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradi- ents form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. （d） The direction of the driving force induced by the hard curved surface is independent of the hydrophilieity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.

Theoretical study of the trapping efficiency of an optical tweezers array system

Optical tweezers have been a valuable research tool since their invention in the 1980s. One of the most important developments in optical tweezers in recent years is the creation of two-dimensional arrays of optical traps. In this paper, a method based on interference is discussed to form gradient laser fields, which may cause the spatial modulation of particle concentration. The parameters related to the optical tweezers array are discussed in detail and simulated by the Matlab software to show the influence of important parameters on the distribution of particle concentration. The spatial redistribution of particles in a laser interference field can also be predicted according to the theoretical analysis.

Conditions for formation and trapping of the two-ion Coulomb cluster in the dissipative optical superlattice

Conditions have been studied under which a polychromatic optical superlattice can form and trap the Coulomb cluster of two strongly interacting ions. In our previous work （Krasnov I V and Kamenshchikov L P 2014 Opt. Comm. 312 192） this new all-optical method of obtaining and confining the Coulomb clusters was demonstrated by numerical simulations for special values of the optical superlattice parameters and in the case of Yb ions. In the present paper the conditions are explicitly formulated, under which the long-lived two-ion cluster in the superlattice cell is formed. The peculiarity of these conditions is the renormalization of the ion-ion Coulomb interaction. Notably, the renormalized Coulomb force is determined by the effective charge which depends on the light field parameters and can strongly differ from the ＂bare＂ ion charge. This result can be accounted for by the combined manifestation of the quantum fluctuations of optical forces, nonlinear dependence of these forces on the velocity, and non-Maxwellian （Tsallis type） velocity distribution of the ions in the optical superlattice. Explicit analytical formulas are also obtained for the parameters of the optical two-ion cluster.

Optomechanical force gradient sensing with levitated nanosphere pair

Guided by recent progress in ground state cooling and ultraweak force sensing in the optomechanical systems with optically levitated particles,we propose a novel quantum sensing protocol that can detect the gradient of a force field directly with extremely high sensitivity.The system consists of a pair of nanospheres levitated in the high vacuum environment with optical tweezers and an optical resonator.By positioning the two spheres suitably relative to the cavity,only the collective breathing mode of the sphere pair couples to the cavity field.This optomechanical coupling will transfer the information of force difference acting on the two sensors to cavity photons,which can then be detected directly at the output of the cavity.Given the optimal control of various technical noise sources,the sensitivity could reach 10^(-15)N m^(-1)/√HZ with a high spatial resolution of micron scale on a state-of-the-art experimental setup.The potential application of this protocol in searching for short range“new force”is analyzed.Compared with conventional searching protocols with a single levitated sphere,the method proposed here can increase the signal-to-noise ratio by more than one magnitude in a large searching parameter space.

Guided motion of short carbon nanotube driven by non-uniform electric field

The molecular dynamics simulations are performed to show that in aque- ous environments, a short single-walled carbon nanotube （SWCNT） guided by a long SWCNT, either inside or outside the longer tube, is capable of moving along the nanotube axis unidirectionally in an electric field perpendicular to the carbon nanotube （CNT） axis with the linear gradient. The design suggests a new way of molecule transportation or mass delivery. To reveal the mechanism behind this phenomenon, the free energy profiles of the system are calculated by the method of the potential of mean force （PMF）.

Optimized Vertical Layers for the Hybrid Terrain-Following Coordinate Minimizing Numerical Errors in a 2D Rising Bubble Experiment near Steep Terrain

The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smooth slopes of vertical layers(slopeVL)generally overcome this difficulty.Therefore,the HTF coordinate becomes very desirable for atmospheric and oceanic numerical models.However,improper vertical layering in HTF coordinates may also increase the incidence of error.Except for the slopeVL of an HTF coordinate,this study further optimizes the HTF coordinate focusing on the thickness of vertical layers(thickVL).Four HTF coordinates(HTF1–HTF4)with similar slopeVL but different vertical transition methods of thickVL are designed,and the relationship between thickVL and numerical errors in each coordinate is compared in the classic idealized thermal convection[two-dimensional(2D)rising bubble]experiment over steep terrain.The errors of potential temperatureθand vertical velocity w are reduced most,by approximately 70%and 40%,respectively,in the HTF1 coordinate,with a monotonic increase in thickVL according to the increasing height;however,the errors ofθincreased in all the other HTF coordinates,with nonmonotonic thickVLs.Furthermore,analyses of the errors of vertical pressure gradient force(VPGF)show that due to the interpolation errors of thickVL,the inflection points in the vertical transition of thickVL induce the initial VPGF errors;therefore,the HTF1 coordinate with a monotonic increase in thickVL has the smallest errors among all the coordinates.More importantly,the temporal evolution of VPGF errors manifests top-type VPGF errors that propagate upward gradually during the time integration.Only the HTF1 and HTF4 coordinates with a monotonic increase in thickVL near the top of the terrain can suppress this propagation.This optimized HTF coordinate(i.e.,HTF1)can be a reference for designing a vertical thickVL in a numerical model.

A New Approach to Implement Sigma Coordinate in a Numerical Model

This study shows a new way to implement terrain-following s-coordinate in a numerical model,which does not lead to the well-known"pressure gradient force(PGF)"problem.First,the causes of the PGF problemare analyzedwith existing methods that are categorized into two different types based on the causes.Then,the new method that bypasses the PGF problem all together is proposed.By comparing these threemethods and analyzing the expression of the scalar gradient in a curvilinear coordinate system,this study finds out that only when using the covariant scalar equations of s-coordinate will the PGF computational form have one term in each momentum component equation,thereby avoiding the PGF problem completely.A convenient way of implementing the covariant scalar equations of s-coordinate in a numerical atmospheric model is illustrated,which is to set corresponding parameters in the scalar equations of the Cartesian coordinate.Finally,two idealized experimentsmanifest that the PGF calculated with the new method is more accurate than using the classic one.This method can be used for oceanic models as well,and needs to be tested in both the atmospheric and oceanic models.

Migration of Paramagnetic Ions in Glass Melts Under Influence of a Magnetic Field

Magnetic forces are widely used to influence the properties of materials.The main focus of recent investigations concerning oxide melts mainly was on the use of Lorentz forces either to mix glass melts to avoid an improved inhomogeneity or to measure the flow of these melts.In the last years also the use of magnetic gradient forces has become an object of research mainly in electrochemistry.On the basis of preliminary investigations the influence of these forces on paramagnetic ions such as Fe;in oxide melts is investigated to examine the potential of magnetic gradient forces as a tool to create defined gradient materials.

;heoretical analysis for optomechanical all-optical transistor

In this paper, we propose an on-chip all optical transistor driven by optical gradient force. The transistor consists of a single micro-ring resonator, half of which is suspended from the substrate, and a bus waveguide. The free-standing arc is bent by optical gradient force generated when the control light is coupled into the ring. The output power of the probe light is tuned continuously as the transmission spectrum red-shift due to the displacement of the free-standing arc. The transistor shows three working regions known as cutoff region, amplified region and saturate region, and the characteristic curve is tunable by changing the wavelength of the control light. Potential applications of the all optical transistor include waveform regeneration and other optical computing.

Influence of carrier concentration on the resistive switching characteristics of a ZnO-based memristor

Sandwich-style memristor devices were synthesized by electrochemical deposition with a ZnO film serving as the active layer between Al-doped ZnO （AZO） and Au electrodes. The carrier concentration of the ZnO films is controlled by adding HNO3 during the growth process. A resulting increase in carrier concentration from 10^17 to 10^19 cm^-3 was observed, along with a corresponding drop in the on--off ratio from 6,437% to 100%. The resistive switching characteristics completely disappeared when the carrier concentration was above 1029 cm-3, making it unsuitable for a memory device. The decreasing switching ratio is attributed to a reduction in the driving force for oxygen vacancy drift. Systematic analysis of the migration of oxygen vacancies is presented, including the concentration gradient and electrical potential gradient. Such oxygen vacancy migration dynamics provide insight into the mechanisms of the oxygen vacancy drift and provide valuable information for industrial production of memristor devices.