Motion Of Trapped Particles Research Articles

Local angular momentum induced dual orbital effect

Spin angular momentum (SAM) and orbital angular momentum (OAM) are two important fundamental degrees of freedom of light and play crucial roles in various light–matter interactions. SAM usually makes the microparticle rotate around its axis, while OAM causes orbital motion of the microparticles around the beam axis. For an optical field with only SAM, the spin-to-orbit conversion may occur under the tightly focused condition, leading to the orbital motion of probing particles. However, it is invalid for weakly focused conditions. Here, we generated an annular optical field without intrinsic OAM by weakly focusing (i.e., negligible spin-to-orbit conversion) a circularly polarized light with a linearly varying radial phase and then observed a kind of dual orbital motion of asymmetric probing particles (Janus particles) in the focal plane. The two orbital motions have opposite directions on both sides across the strongest ring of the annular optical field. In addition to the SAM, the local angular momentum (AM) density also depends on the radial intensity gradient. The radial intensity gradient has the opposite signs on both sides across the strongest ring of the annular optical field, which results in the opposite orbital motions of trapped particles. The manipulation of the local AM density and the resulting novel dual orbital effect in the absence of intrinsic OAM provide a new scene to understand the physics underlying the light–matter interaction, paving the way to some new applications involving the sorting and delivery of microparticles.

Optical conveyor belt based on a plasmonic metasurface with polarization dependent hot spot arrays.

In this Letter, we propose a novel metasurface conveyor belt with periodic orientated arrays of gold plasmonic elliptical elements (GPEEs), which can be continuously lit in a relay way by switching the polarization of the excitation beam and can be used to trap, transport, and sort particles. The array of the hot field can provide a larger trapping area and better stiffness. With the incident optical intensity of 0.08mW/µm2, the depth of the potential well could be as high as 10KBT. By setting a narrow interval between plasmonic ellipses in principal axes, it can help further enhance their directional resonant coupling and polarization dependence. Furthermore, based on consideration of the Brownian motion of trapped particles in aqueous solution, we analyzed its time response property of particle manipulation with different applied switching frequencies from a statistical point of view. As confirmed by numerical analysis, our design offers a novel scheme of particle sorting using a scalable hot spot array with better performance, which could be used in many on-chip optofluidic applications.

Nonlinear accelerated orbiting motions of optical trapped particles through two-photon absorption.

Vortex beams carrying optical angular momentum (AM) could drive the orbital motion of a small particle around the optical axis. In general, the orbital rotation speed of trapped particles increases linearly with the increasing laser power. Beyond the linear optics regime, in this work, we investigate both the optical force and torque on a two-photon absorbing Rayleigh particle produced by the tightly focused femtosecond-pulsed circularly polarized vortex beam. Different from the trapping dynamics of particles without two-photon absorption (TPA), it is shown that the orbital motion of trapped particles with TPA accelerates nonlinearly as the laser power increases. Moreover, the orbital motion acceleration of trapped particles is proportional to the TPA coefficient. The corresponding underlying mechanism is discussed in detail. Our results may find interesting applications in the characterization of the optical nonlinearity of a single nanoparticle, and AM manipulation and particle transportation in the nonlinear optics regime.

Optically trapped particle dynamic responses under varying frequency sinusoidal stimulus

Optical tweezers have become indispensable and powerful micro-manipulation tools and acute force probes in biomedical fields. Therefore, calibrating the optical trap is essential for precise force measurements in biomolecular interactions. Currently, however, mainstream calibration methods mainly focus on analyzing nanometer level Brownian motions of trapped particles. There is thus an urgent need to investigate trapped particle dynamic processes in slightly large range to address practical situations for the biological application of optical tweezers. This paper proposes a varying frequency sinusoidal excitation method to probe trapped particle responses and develops a mathematical model to extract trap stiffness. Experimental results revealed that the proposed method achieved significantly lower relative error ( < 5%) even when particle size or laser power varied, and that the excitation frequency didn’t have much impact on trap stiffness. Thanks to its simplicity, effectiveness and robustness, our method provides an ideal candidate for further picoNewton force measurement studies for dynamic interactions in biomedical applications.

Specific Features of Charged Particle Confinement in the T-15 Tokamak in the Presence of Magnetic Perturbations

Charged particle motion in the regions of magnetic islands and near-separatrix ergodicity of magnetic field lines in the Т-15 tokamak is studied numerically. The trajectories are calculated by integration of exact three-dimensional equations of motion for trapped and passing charged particles starting at different pitch angles. It is shown that the presence of resonant magnetic perturbations qualitatively affects the trajectories of passing particles. In the region of magnetic islands, the orbits of passing particles acquire an island structure, while in the region of the near-separatrix ergodicity of magnetic field lines, the orbits are stochastized. It is shown that magnetic perturbations insignificantly affect trapped particle motion. Even in the absence of magnetic surfaces, the trajectories of trapped particles are regular and their cross sections have the shape of a standard banana orbit. The possibility of charged particles to pass between regions with different magnetic topologies is analyzed.

Tunable optofluidic sorting and manipulation on micro-ring resonators from a statistics perspective.

Based on the optical trapping force of an evanescent wave at a micro-ring resonator alongside a waveguide, we propose a tunable optofluidic sorting unit for micro-nanoparticles by localized thermal phase tuning. With the tuning of field build-up factor of resonator, the depth of trapping potential well and the size of trapped particle are adjustable. Furthermore, by considering the Brownian motion of trapped particles from a statistics perspective, we verify the critical trapping threshold of a potential well, which is usually assumed to be 1kBT. The threshold depends not only on the optical power and particle size, but also on the length of the coupling region. Compared with a wavelength tuning mechanism, localized thermal tuning enables large-scale integration of many independent tunable resonators. As a demonstration, we propose a set of operations with three resonators for nanoparticle manipulation, including sorting, storing, and mixing. Our proposed function units are of great importance for on-chip large-scale integration of optofluidic systems.

Feedback control in optical tweezers enables thermodynamic experiments for biological molecules

Adding feedback capabilities to standard optical tweezers greatly enhances the control of trapped particle motion at small length and time scales by actively changing the forces induced by a focused laser.

Collisionless distribution function of charged particles ensemble in a tokamak magnetic configuration with magnetic island

The collisionless distribution function of charged particle ensemble in the magnetic field of tokamak with a magnetic island is calculated. The calculation is based on the solution of the kinetic equation with source together with three-dimensional numerical calculations of charged particle trajectories. It is shown that in case of an inhomogeneous source trajectory, motion of trapped particles leads to anisotropization of the initially isotropic distribution of particle ensemble. The absence of contribution from the passing particles decreases the efficiency of spontaneous generation of a non-induction current in the magnetic island in comparison with the bootstrap effect in the system of nested magnetic surfaces.

Trajectory-based unveiling of the angular momentum of photons

The Heisenberg uncertainty principle suggests that it is impossible to determine the trajectory of a quantum particle in the same way as a classical particle. However, we may still yield insight into novel behavior of photons based on the average photon trajectories (APTs). Here we explore the APTs of photons carrying spin angular momentum (SAM) and/or orbital angular momentum (OAM) under the paraxial condition. We define the helicity and differential helicity for unveiling the three-dimensional spiral structures of the APTs of photons. We clarify the novel behaviors of the APTs caused by the SAM and OAM as well as the SAM-OAM coupling. The APT concept is very helpful for profoundly understanding the motion of trapped particles and for elucidating other physical systems. Due to the presence of the helical path caused by the SAM and/or the OAM, the actual traveling distance of the photons might be much longer than the geometric distance.

Derivation of multi-photon anharmonic oscillator model from its classical counterpart

The electromagnetic field coupled to a nonlinear medium of having nonvanishing polarizations and magnetizations could be modeled as a classical anharmonic oscillator with velocity (p)- and position (q)-dependent anharmonicities. The position and velocity dependent anharmonic oscillators are also realized for center of mass motion of trapped particles in magneto optical trap. The Hamiltonian corresponding to the quantum anharmonic oscillator with velocity- and position-dependent anharmonicities is obtained from the knowledge of its classical counterpart. Under rotating wave approximation, the Heisenberg formalism are used to obtain the solution of the quantum oscillator with q-dependent and p-dependent anharmonicities. The analytical solution is used to obtain the dipole moment matrix elements and hence the shifts of the frequency of the oscillator. Interestingly, the shifts of the oscillator due to the q-dependent anharmonicity is opposite to those of the shifts due to the p-dependent anharmonicity. Therefore, the shifts of the frequency assert the presence of particular anharmonicity as well (i.e. p- or q-type).

Characteristics of the orbital rotation in dual-beam fiber-optic trap with transverse offset.

The orbital rotation is an important type of motion of trapped particles apart from translation and spin rotation. It could be realized by introducing a transverse offset to the dual-beam fiber-optic trap. The characteristics (e.g. rotation perimeter and frequency) of the orbital rotation have been analyzed in this article. We demonstrate the influences of offset distance, beam waist separation distance, light power, and radius of the microsphere by both experimental and numerical work. The experiment results, i.e. orbital rotation perimeter and frequency as functions of these parameters, are consistent with the theoretical model in the present work. The orbital rotation amplitude and frequency could be exactly controlled by varying these parameters. This controllable orbital rotation can be easily applied to the area where microfluidic mixing is required.

Dynamic axial control over optically levitating particles in air with an electrically-tunable variable-focus lens.

Efficient delivery of viruses, proteins and biological macromelecules into a micrometer-sized focal spot of an XFEL beam for coherent diffraction imaging inspired new development in touch-free particle injection methods in gaseous and vacuum environments. This paper lays out our ongoing effort in constructing an all-optical particle delivery approach that uses piconewton photophoretic and femtonewton light-pressure forces to control particle delivery into the XFEL beam. We combine a spatial light modulator (SLM) and an electrically tunable lens (ETL) to construct a variable-divergence vortex beam providing dynamic and stable positioning of levitated micrometer-size particles, under normal atmospheric pressure. A sensorless wavefront correction approach is used to reduce optical aberrations to generate a high quality vortex beam for particle manipulation. As a proof of concept, stable manipulation of optically-controlled axial motion of trapped particles is demonstrated with a response time of 100ms. In addition, modulation of trapping intensity provides a measure of the mass of a single, isolated particle. The driving signal of this oscillatory motion can potentially be phase-locked to an external timing signal enabling synchronization of particle delivery into the x-ray focus with XFEL pulse train.

Optically induced rotation of Rayleigh particles by vortex beams with different states of polarization

Optical vortex beams carry optical orbital angular momentum (OAM) and can induce an orbital motion of trapped particles in optical trapping. We show that the state of polarization (SOP) of vortex beams will affect the details of this optically induced orbital motion to some extent. Numerical results demonstrate that focusing the vortex beams with circular, radial or azimuthal polarizations can induce a uniform orbital motion on a trapped Rayleigh particle, while in the focal field of the vortex beam with linear polarization the particle experiences a non-uniform orbital motion. Among the formers, the vortex beam with circular polarization induces a maximum optical torque on the particle. Furthermore, by varying the topological charge of the vortex beams, the vortex beam with circular polarization gives rise to an optimum torque superior to those given by the other three vortex beams. These facts suggest that the circularly polarized vortex beam is more suitable for rotating particles.

Stability of relativistic electron trapping by strong whistler or electromagnetic ion cyclotron waves

In the present paper, we investigate the trapping of relativistic electrons by intense whistler-mode waves or electromagnetic ion cyclotron waves in the Earth's radiation belts. We consider the non-resonant impact of additional, lower amplitude magnetic field fluctuations on the stability of electron trapping. We show that such additional non-resonant fluctuations can break the adiabatic invariant corresponding to trapped electron oscillations in the effective wave potential. This destruction results in a diffusive escape of electrons from the trapped regime of motion and thus can lead to a significant reduction of the efficiency of electron acceleration. We demonstrate that when energetic electrons are trapped by intense parallel or very oblique whistler-mode waves, non-resonant magnetic field fluctuations in the whistler-mode frequency range with moderate amplitudes around 3−15 pT (much less intense than the primary waves) can totally disrupt the trapped motion. However, the trapping of relativistic electrons by electromagnetic ion cyclotron waves is noticeably more stable. We also discuss how the proposed approach can be used to estimate the effects of wave amplitude modulations on the motion of trapped particles.

Polarization evolution characteristics of focused hybridly polarized vector fields

We investigate the focusing property and the polarization evolution characteristics of hybridly polarized vector fields in the focal region. Three types of hybridly polarized vector fields, namely azimuthal-variant hybridly polarized vector field, radial-variant hybridly polarized vector field, and spatial-variant hybridly polarized vector field, are experimentally generated. The intensity distributions and the polarization evolution of these hybridly polarized vector fields focused under low numerical aperture (NA) are experimentally studied and good agreements with the numerical simulations are obtained. The three-dimensional (3D) state of polarization and the field distribution within the focal volume of these hybridly polarized vector fields under high-NA focusing are studied numerically. The optical curl force on Rayleigh particles induced by tightly focused hybridly polarized vector fields, which results in the orbital motion of trapped particles, is analyzed. Simulation results demonstrate that polarization-only modulation provided by the hybridly polarized vector field allows one to control both the intensity distribution and 3D elliptical polarization in the focal region, which may find interesting applications in particle trapping, manipulation, and orientation analysis.

Radially selective inward transport of positrons in a Penning–Malmberg trap

The anharmonic component of the electric field of a Penning–Malmberg trap is exploited to manipulate a subset of the radial (r) distribution of trapped positrons, using a dipole field made to rotate about the long-axis (z) of the trap. This ‘rotating wall’ technique (RW) induces inward transport at frequencies associated with the motion of trapped particles, although similarly it causes heating. The motional frequencies vary spatially within a non-ideal trap, thus resonant interaction with the rotating field may be restricted to a region selected to lie away from the trap centre, thereby forming a pseudo-potential barrier and reducing losses due to both heating and expansion. We demonstrate this effect for improved accumulation of positrons and further outline a technique to achieve strong compression with low RW amplitudes by chirping the drive frequency.

A tunable line optical tweezers instrument with nanometer spatial resolution.

We describe a simple scanning-line optical tweezers instrument for measuring pair interactions between micrometer-sized colloidal particles. Our instrument combines a resonant scanning mirror and an acousto-optic modulator. The resonant scanning mirror creates a time-averaged line trap whose effective one-dimensional intensity profile, and corresponding trapping potential energy landscape can be programmed using the acousto-optic modulator. We demonstrate control over the confining potential by designing and measuring a family of one-dimensional harmonic traps. By adjusting the spring constant, we balance scattering-induced repulsive forces between a pair of trapped particles, creating a flat potential near contact that facilitates interaction measurements. We also develop a simple method for extracting the out-of-plane motion of trapped particles from their relative brightness, allowing us to resolve their relative separation to roughly 1 nm.

Ion motion in the current sheet with sheared magnetic field – Part 2: Non-adiabatic effects

Abstract. We investigate dynamics of charged particles in current sheets with the sheared magnetic field. In our previouspaper (Artemyev et al., 2013) we studied the particle motion in such magnetic field configurations on the basis of the quasi-adiabatic theory and conservation of the quasi-adiabatic invariant. In this paper we concentrate on violation of the adiabaticity due to jumps of this invariant and the corresponding effects of stochastization of a particle motion. We compare effects of geometrical and dynamical jumps, which occur due to the presence of the separatrix in the phase plane of charged particle motion. We show that due to the presence of the magnetic field shear, the average value of dynamical jumps is not equal to zero. This effect results in the decrease of the time interval necessary for stochastization of trapped particle motion. We investigate also the effect of the magnetic field shear on transient trajectories, which cross the current sheet boundaries. Presence of the magnetic field shear leads to the asymmetry of reflection and transition of particles in the current sheet. We discuss the possible influence of single-particle effects revealed in this paper on the current sheet structure and dynamics.

Rotational Resonance of Nonaxisymmetric Magnetic Braking in the KSTAR Tokamak

One of the important rotational resonances in nonaxisymmetric neoclassical transport has been experimentally validated in the KSTAR tokamak by applying highly nonresonant n=1 magnetic perturbations to rapidly rotating plasmas. These so-called bounce-harmonic resonances are expected to occur in the presence of magnetic braking perturbations when the toroidal rotation is fast enough to resonate with periodic parallel motions of trapped particles. The predicted and observed resonant peak along with the toroidal rotation implies that the toroidal rotation in tokamaks can be controlled naturally in favorable conditions to stability, using nonaxisymmetric magnetic perturbations.

A charged-particle manipulator utilizing a co-axial tube electrodynamic trap with an integrated camera

A charged-particle manipulator was designed and fabricated with an integrated imaging camera allowing real-time in-situ monitoring of trapped particle motion even when the trap device is under motion or rotation. The trap device was made of two co-axial electrically conductive tubes with diameters of 5.5 mm and 7 mm for the inner tube and outer tube, respectively; the imaging camera with its optical fiber bundle was integrated within the tubular trap device to realize a single instrument functioning as a manipulator. Motion of suspended microparticles of 3 μm to 50 μm in diameter can be monitored using the integrated camera regardless of the trap device orientations. This manipulator provides capability of controlled manipulation of trapped particles by tuning the operating conditions while monitoring the feedback of real-time particle motion. Imaging of suspended particles was not interrupted while the manipulator was translated and/or rotated. This integrated manipulator can be used for charged particle transport and repositioning.