Rayleigh Particles Research Articles

Manipulation of dielectric Rayleigh particles using highly focused elliptically polarized vector fields.

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in areas where exotic optical fields are desired. In this work, we experimentally demonstrate the versatile generation of linearly polarized vector fields, elliptically polarized vector fields, and circularly polarized vortex beams through introducing attenuators in a common-path interferometer. By means of Richards-Wolf vectorial diffraction method, the characteristics of the highly focused elliptically polarized vector fields are studied. The optical force and torque on a dielectric Rayleigh particle produced by these tightly focused vector fields are calculated and exploited for the stable trapping of dielectric Rayleigh particles. It is shown that the additional degree of freedom provided by the elliptically polarized vector field allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force and torque on a dielectric Rayleigh particle.

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.

Helical tractor beam: analytical solution of Rayleigh particle dynamics

We analyze particle dynamics in an optical force field generated by helical tractor beams obtained by the interference of a cylindrical beam with a topological charge and a co-propagating temporally de-phased plane wave. We show that, for standard experimental conditions, it is possible to obtain analytical solutions for the trajectories of particles in such force field by using of some approximations. These solutions show that, in contrast to other tractor beams described before, the intensity becomes a key parameter for the control of particle trajectories. Therefore, by tuning the intensity value the particle can describe helical trajectories upstream and downstream, a circular trajectory in a fixed plane, or a linear displacement in the propagation direction. The approximated analytical solutions show good agreement to the corresponding numerical solutions of the exact dynamical differential equations.

Radiation forces on a Rayleigh particle by highly focused radially polarized beams modulated by DVL.

The intensity and the radiation forces acting on a Rayleigh particle near the focus of completely coherent radially polarized beams whose phase are modulated by a devil's vortex-lens (DVL) are studied. The influence of the structure of a DVL on the radiation force distribution is analyzed. It is found by numerical simulations that the modulated beams show a clear advantage over the unmodulated highly focused radially polarized beams, as the modulated beam can simultaneously trap and manipulate the multiple Rayleigh particles, while the unmodulated beam can trap only one particle under the same condition.

Time-average forces over Rayleigh particles by superposition of equal-frequency arbitrary-order Bessel beams

We investigate optical forces exerted by suitable superpositions of equal-frequency Bessel beams—frozen waves—over dielectric, magnetodielectric, and negative-index Rayleigh particles. Frozen waves are capable of providing virtually any desired longitudinal intensity pattern by adequately superposing arbitrary-order Bessel beams, serving as potential beams in optical trapping, atom guiding, optical bistouries, and so on. Analytical expressions for gradient and scattering forces experienced by very small particles are deduced, and our numerical examples reveal that both low- and high-index dielectric and magnetodielectric particles can be efficiently trapped and manipulated. Our results indicate that such wave fields could actually provide three-dimensional traps in multiple transverse planes.

AlN/SiO2/Si3N4/Si(100)-Based CMOS Compatible Surface Acoustic Wave Filter With −12.8-dB Minimum Insertion Loss

A CMOS compatible AlN/SiO2/Si3N4/Si(100) surface acoustic wave (SAW) device has been fabricated and will be compared with standard AlN/SiO2-based devices. The presented filter demonstrates high potential for CMOS integrated high-frequency SAW devices. The filter insertion loss could be improved to −12.8 dB. The device exhibits high crosstalk suppression of −50 dB on a standard Si-substrate (10 $\Omega $ cm). X-ray diffraction, (scanning) transmission electron microscopy, and energy dispersive X-ray spectroscopy studies correlate the signal quality with $c$ -axis orientation of aluminum nitride films on interdigitated transducer finger electrodes. Finite-element method simulations are in good agreement with the electric measurements and show typical Rayleigh particle displacement.

PUSH-PULL PHENOMENON OF A DIELECTRIC PARTICLE IN A RECTANGULAR WAVEGUIDE

The electromagnetic force acting on a Rayleigh particle placed in a rectangular waveguide is studied. The particle is excited using the lowest order TE10 mode. It is determined that the particle is laterally trapped at the high intensity region of the electric field and either pushed away from or pulled toward the light source. This push-pull phenomenon depends on whether the frequency of the light wave is above or below the cutoff frequency (i.e., the particle can be pushed or pulled by tuning the frequency). While conventional optical tweezers rely on a balance of scattering and gradient force in the propagation direction, the phenomenon predicted here switches between the two forces near the lowest cutoff in a waveguide.

强聚焦混合偏振矢量光束在瑞利粒子上产生的辐射力

The radiation force of highly focused hybridly polarized beams on a Rayleigh particle was theoretically studied and the expression was derived.The influence of numerical apertures of an objective and radial coefficient on the radiation force distribution and the longitudinal intensity distribution on the focal plane were numerically simulated.The numerical results show that radiation forces by highly focused hybridly polarized vector beams can be used to trap three-dimensional Rayleigh particles,and the trapping property is affected by the numerical aperture and radial coefficient obviously.Copious experimental data indicate that it can be done only when the radial coefficient is greater than 3.

Brownian Motion of a Rayleigh Particle Confined in a Channel: A Generalized Langevin Equation Approach

We study confined Brownian motion by investigating the memory function of a $$d$$ -dimensional hypercube ( $$d\ge 2$$ ), which is subject to a harmonic potential and suspended in an ideal gas confined by two parallel walls. For elastic walls and under the infinite-mass limit, we obtain analytic expressions for the force autocorrelation function and the memory function. The transverse-direction memory function possesses a nonnegative tail decaying like $$t^{-(d-1)}$$ , from which anomalous diffusion is expected for $$d=2$$ . For $$d=3$$ , the position-dependent friction coefficient becomes larger than the unconfined case and the increment is inversely proportional to the square of the distance from the wall. We also perform molecular dynamics simulations with thermal walls and/or a finite-mass hypercube. We observe faster decay due to the thermal wall ( $$t^{-3}$$ for $$d=2$$ and $$t^{-5}$$ for $$d=3$$ under the fully thermalizing wall) and convergence behaviors of the finite-mass memory function, which are different from the unconfined case.

Highly Focused Conical Optical Field for Pico-Newton Scale Force Sensing

We propose to use a highly focused conical optical field generated by cone-frustum-shaped annular core fiber (ACF) tip for Pico-Newton scale force sensing. And we theoretically calculate the wave propagation in the ACF tip and its surrounding medium based on angular spectrum representation. The propagation properties and focusing effect of the highly focused conical optical field are also discussed and demonstrated experimentally. The ACF tip provides very strong focusing effect for the guided mode in the ACF. We show that there are stable three-dimensional trap-points for Rayleigh particles in the main lobe and every ring of the focused field with Bessel-like profile. And the transverse trapping forces are much greater (almost 30 times) than their corresponding longitudinal radiation forces so that a particle trapped by highly focused conical beam is only sensitive for disturbing force in longitudinal direction. Force sensitivities in longitudinal direction and the detection range are also discussed.

Tight focusing of a radially polarized Laguerre–Bessel–Gaussian beam and its application to manipulation of two types of particles

Abstract The intensity distributions near the focus for radially polarized Laguerre–Bessel–Gaussian beams by a high numerical aperture objective in the immersion liquid are computed based on the vector diffraction theory. We compare the focusing properties of the radially polarized Laguerre–Bessel–Gaussian beams with those of Laguerre–Gaussian and Bessel–Gaussian modes. Furthermore, the effects of the optimally designed concentric three-zone phase filters on the intensity profiles in the focal region are examined. We further analyze the radiation forces on Rayleigh particles produced by the highly focused radially polarized Laguerre–Bessel–Gaussian beams using the specially engineered three-zone phase filters.

Pulling extremely anisotropic lossy particles using light without intensity gradient

We study the effect of pulling optical force acting on a nonmagnetic anisotropic bead in electromagnetic fields without intensity gradient. Extreme anisotropy can be realized by a hyperbolic metamaterial made of metal-dielectric multilayers. We find that a passive anisotropic Rayleigh particle cannot be pulled by the electromagnetic beam without intensity gradient and the nonparaxial incident beams can exert backward negative force acting on anisotropic dipole spheres. We investigate the validity of the dipole approximation and establish the conditions for pulling hyperbolic-metamaterial particles. It is important to note that the loss in hyperbolic metamaterial does not suppress the effect of pulling force. We notice that the nonradial components of the permittivity tensor strongly affect the optical force and propose the way of material engineering to ensure the optical pulling.

Radiation forces on Rayleigh particles using a focused anomalous vortex beam under paraxial approximation

The radiation forces of focused anomalous vortex beams acting upon a Rayleigh dielectric sphere are studied theoretically and numerically, based on the Rayleigh scattering theory, within the framework of paraxial approximation. It is shown that a focused anomalous vortex beam with a suitable mode order and topological charge can be used to trap and manipulate a dielectric sphere whose refractive index is smaller or bigger than the ambient one at the focal point. The influences of the topological charges and the beam orders on the radiation force are also discussed. Furthermore, the stability conditions for effective trapping the Rayleigh particles are analyzed.

Energy-redistribution signatures in transmission microscopy of Rayleigh and Mie particles.

We describe the transmission characteristics for the interaction of an arbitrary beam with (possibly multilayered) spherical particles of arbitrary size and electric permeability. Within the generalized Lorenz-Mie theory, expressions that generalize the total cross sections to their fractional counterparts are presented, which allow for an analytic quantification of transmission signals, both on-axis and off-axis. For Gaussian (Davis) beams, the relative angular domain of collection as compared to the beam's angle of divergence determines sensitively the shape and magnitude of the interference signal. Depending on the particle's position within the beam, the transmission signatures related to a pure energy redistribution as well as to accompanying absorption are discussed for Rayleigh particles in terms of their complex-valued polarizability. Implications for positioning, temperature control, spectroscopy, and optimized extinction measurements are discussed.

Beam configuration proposal to verify that scattering forces come from the orbital part of the Poynting vector.

In this Letter, the optical forces on an electric dipole generated by a beam made up of two circularly polarized Hermite-Gaussian modes have been analyzed. When the intensity of the two modes is not the same, the mechanical action of the scattering force is completely different from the behavior of the Poynting vector. The dynamics of resonant metallic nanoparticles under this field have been calculated by means of Langevin molecular dynamic simulations. This configuration could be useful to experimentally verify how radiation pressure on a Rayleigh particle is due to the transfer of linear momentum coming solely from the orbital part of the Poynting vector.

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.

Communication: A scaling approach to anomalous diffusion

The paper presents a rigorous derivation of the velocity autocorrelation function for an anomalously diffusing slow solute particle in a bath of fast solvent molecules. The result is obtained within the framework of the generalized Langevin equation and uses only scaling arguments and identities which are based on asymptotic analysis. It agrees with the velocity autocorrelation function of an anomalously diffusing Rayleigh particle whose dynamics is described by a fractional Ornstein-Uhlenbeck process in velocity space. A simple semi-analytical example illustrates under which conditions the latter model is appropriate.

Optical trapping Rayleigh particles by using focused multi-Gaussian Schell-model beams

We numerically investigate the radiation forces of multi-Gaussian Schell-model (MGSM) beams, in which the degree of coherence is modeled by the multi-Gaussian function, exerted on the Rayleigh dielectric sphere. By simulation of the forces calculation it is found that the steepness of the edge of the intensity profile (i.e., the summation index M) and the initial coherence width of the MGSM beams play important roles in the trapping range and stability. We can increase the trapping range at the focal plane by increasing the value of M or decreasing the initial coherence of the MGSM beams. It is also found that the trapping stability becomes lower due to the increase of the value of M or the decrease of coherence. Furthermore, the trapping stability under different conditions is explicitly analyzed. The results presented here are helpful for some possible applications.

Improving the trapping capability using radially polarized narrow-width annular beam

A novel optical-trap method for improving the trapping capability using a radially polarized narrow-width annular beam (NWAB) has been proposed. In this paper, we theoretically study the tight focusing properties of a radially polarized NWAB, formed by subtly blocking the central portion of a radially polarized Bessel–Gaussian beam (the original doughnut beam), through a high-numerical aperture objective. It is shown that a sub-wavelength focal spot () with a quite long depth of focus (about ) can be formed in the vicinity of the focus. Furthermore, the optical trapping forces acting on a metallic Rayleigh particle are calculated for the case where a radially polarized annular beam is applied. Numerical results show that the radially polarized NWAB can largely enhance the transverse trap stiffness and broaden the longitudinal trap range compared with the usage of the original doughnut beam. The influence of the annular factor δ on the focusing properties and the trap stiffness is investigated in detail.

Radiation forces on a Rayleigh particle by a highly focused elliptically polarized beam

The radiation force of highly focused elliptically polarized beams on a Rayleigh particle is theoretically studied. The numerical results show that elliptically polarized beams can be used to trap particles. The influence of the beam widths, phase retardations of the incident beam, and numerical apertures of an objective lens on the radiation force distribution has been studied. Studies in transverse scattering forces reveal that torques can be produced by elliptically polarized beams carrying spin angular momentum, and that the torque, in the focal plane, produced by elliptically polarized beams can be regarded as the superposition of those by right-hand circularly and left-hand circularly polarized beams with different ratios between them.