Optical trapping force and torque on spheroidal Rayleigh particles with arbitrary spatial orientations

Optically levitated micro gyroscopes with an MHz rotational vaterite rotor

The field of levitated optomechanics has experienced significant advancements in manipulating the translational and rotational dynamics of optically levitated particles and exploring their sensing applications. The concept of using optically levitated particles as gyroscopes to measure angular motion has long been explored but has not yet been proven either theoretically or experimentally. In this study, we present the first rotor gyroscope based on optically levitated high-speed rotating particles. The gyroscope is composed of a micrometer-size ellipsoidal vaterite particle that is driven to rotate at MHz frequencies in a vacuum environment. When an external angular velocity is input, the optical axis deviates from its initial position, resulting in changes in the frequency and amplitude of the rotational signal. By analyzing these changes, the angular velocity of the input can be accurately detected, making it the smallest rotor gyroscope in the world. The angular rate bias instability of the gyroscope is measured to be 0.08°/s and can be further improved to as low as 10-9°/h theoretically by cooling the motion and increasing the angular moment of the levitated particle. Our work opens a new application paradigm for levitated optomechanical systems and may pave the way for the development of quantum rotor gyroscopes.

Optical Force Effects of Rayleigh Particles by Cylindrical Vector Beams

High-order cylindrical vector beams possess flexible spatial polarization and exhibit new effects and phenomena that can expand the functionality and enhance the capability of optical systems. However, building a general analytical model for highly focused beams with different polarization orders remains a challenge. Here, we elaborately develop the vector theory of high-order cylindrical vector beams in a high numerical aperture focusing system and achieve the vectorial diffraction integrals for describing the tight focusing field with the space-variant distribution of polarization orders within the framework of Richards-Wolf diffraction theory. The analytical formulae include the exact three Cartesian components of electric and magnetic distributions in the tightly focused region. Additionally, utilizing the analytical formulae, we can achieve the gradient force, scattering force, and curl-spin force exerted on Rayleigh particles trapped by high-order cylindrical vector beams. These results are crucial for improving the design and engineering of the tightly focused field by modulating the polarization orders of high-order cylindrical vector beams, particularly for applications such as optical tweezers and optical manipulation. This theoretical analysis also extends to the calculation of complicated optical vortex vector fields and the design of diffractive optical elements with high diffraction efficiency and resolution.

Polarization characteristics and transverse spin of Mie scattering

Complicated polarization states in the near field of Mie scattering have aroused wide interest due to their broad potential applications. In this work, we investigated polarization properties, including polarization dimension, degree of nonregularity, and transverse electric-field spin, of scattering of a partially polarized plane wave by a dielectric nanosphere based on the rigorous Mie scattering theory. It is shown that with the decrease of the correlation coefficient, the polarization dimension and degree of nonregularity generally increase. In the limit of unpolarized incident light, a nearly-perfect nonregular polarization state (PN = 0.928) appears in the near field and the spin is transverse to the radial direction everywhere. The rich structure contained by the partially polarized scattered light offers an approach to manipulating the interaction between light and nanoparticles, which may lead to novel designs of nanoantenna, optical trap and sensing.

Hot Brownian Motion of Thermoresponsive Microgels in Optical Tweezers Shows Discontinuous Volume Phase Transition and Bistability

Microgels are soft microparticles that often exhibit thermoresponsiveness and feature a transformation at a critical temperature, referred to as the volume phase transition temperature. Whether this transformation occurs as a smooth or as a discontinuous one is still a matter of debate. This question can be addressed by studying individual microgels trapped in optical tweezers. For this aim, composite particles are obtained by decorating  Poly-N-isopropylacrylamide (pNIPAM) microgels with iron oxide nanocubes. These composites become self-heating when illuminated by the infrared trapping laser, performing hot Brownian motion within the trap. Above a certain laser power, a single decorated microgel features a volume phase transition that is discontinuous, while the usual continuous sigmoidal-like dependence is recovered after averaging over different microgels. The collective sigmoidal behavior enables the application of a power-to-temperature calibration and provides the effective drag coefficient of the self-heating microgels, thus establishing these composite particles as potential micro-thermometers and micro-heaters. Moreover, the self-heating microgels also exhibit an unexpected and intriguing bistability behavior above the critical temperature, probably due to partial collapses of the microgel. These results set the stage for further studies and the development of applications based on the hot Brownian motion of soft particles.

Gradient torque and its effect on rotational dynamics of optically trapped non-spherical particles in the elliptic Gaussian beam

Rotational motion of the optically trapped particle is a topic of enduring interest, while the changes of angular velocity in one rotation period remain largely unexplored. Here, we proposed the optical gradient torque in the elliptic Gaussian beam, and the instantaneous angular velocities of alignment and fluctuant rotation of the trapped non-spherical particles are investigated for the first time. The fluctuant rotations of optically trapped particles are observed, and the angular velocity fluctuated twice per rotation period, which can be used to determine the shape of trapped particles. Meanwhile, a compact optical wrench is invented based on the alignment, and its torque is adjustable and is larger than the torque of a linearly polarized wrench with the same power. These results provide a foundation for precisely modelling the rotational dynamics of optically trapped particles, and the presented wrench is expected to be a simple and practical micro-manipulating tool.

Understanding of transverse spin angular momentum in tightly focused linearly polarized vortex beams

Spin angular momentum (SAM) is widely used in spin-dependent unidirectional optical interfaces, optical manipulation, integrated optical signal processing, laser structuring and other fields, but its physical mechanism has not been fully understood so far. In this work, we investigate the three-dimensional (3D) SAM in tightly focused x-polarized first-order vortex beams from the perspectives of light field itself, phase distribution, and focusing propagation. It is shown that the distribution of three orthogonal components of SAM at the focal plane has pseudo two-fold rotational symmetry, because the cycloidal rotation of the electric field of the tightly focused vortex beam is opposite. The 3D SAM distribution in the focal region is visualized by mapping the 3D distribution of state of polarization (SoP). In addition, a principle experimental method for identifying the transverse SAM by using the direction of particle's rotation axis in optical tweezers is proposed.

Optical Force on a Metal Nanorod Exerted by a Photonic Jet

In this article, we study the optical force exerted on nanorods. In recent years, the capture of micro-nanoparticles has been a frontier topic in optics. A Photonic Jet (PJ) is an emerging subwavelength beam with excellent application prospects. This paper studies the optical force exerted by photonic jets generated by a plane wave illuminating a Generalized Luneburg Lens (GLLs) on nanorods. In the framework of the dipole approximation, the optical force on the nanorods is studied. The electric field of the photonic jet is calculated by the open-source software package DDSCAT developed based on the Discrete Dipole Approximation (DDA). In this paper, the effects of the nanorods' orientation and dielectric constant on the transverse force Fx and longitudinal force Fy are analyzed. Numerical results show that the maximum value of the positive force and the negative force are equal and appear alternately at the position of the photonic jet. Therefore, to capture anisotropic nanoscale-geometries (nanorods), it is necessary to adjust the position of GLLs continuously. It is worth emphasizing that manipulations with nanorods will make it possible to create new materials at the nanoscale.

Optical tweezers for trapping in a microfluidic environment

Optical tweezers use the force from a light beam to implement a precise gripping tool. Based purely on an optical principle, it works without any bodily contact with the object. In this paper we describe an optical tweezers that targets an application within the framework of nuclear magnetic resonance (NMR) spectroscopy of small objects, which are embedded inside a microfluidic channel that will be integrated in a micro-NMR detector. In the project's final stages, the whole system will be installed within the wide bore of a superconducting magnet. The aim is to precisely maintain the position of the object to be measured, without the use of susceptibility disturbing materials or geometries. In this contribution we focus on the design and construction of the tweezers. For the optical force simulation of the system we used a geometrical optics approach, which we combined with a ray fan description of the output beam of an optical system. By embedding both techniques within an iterative design process, we were able to design efficient optical tweezers that met the numerous constraints. Based on details of the constraints and requirements given by the application, different system concepts were derived and studied. Next, a highly adapted and efficient optical trapping system was designed and manufactured. After the components were characterized using vertical scanning interferometry, the system was assembled to achieve a monolithic optical component. The proper function of the optical tweezers was successfully tested by optical trapping of fused silica particles.

Influence of permittivity on gradient force exerted on Mie spheres

In optical trapping, whether a particle could be stably trapped into the focus region greatly depends on the strength of the gradient force. Individual theoretical study on gradient force exerted on a Mie particle is rare because the mathematical separation of the gradient force and the scattering force in the Mie regime is difficult. Based on the recent forces separation work by Du et al. [Sci. Rep.7, 18042 (2017)SRCEC32045-232210.1038/s41598-017-17874-1], we investigate the influence of permittivity (an important macroscopic physical quantity) on the gradient force exerted on a Mie particle by cooperating numerical calculation using fast Fourier transform and analytical analysis using multipole expansion. It is revealed that gradient forces exerted on small spheres are mainly determined by the electric dipole moment except for certain permittivity with which the real part of polarizability of the electric dipole approaches zero, and gradient forces exerted on larger spheres are complex because of the superposition of the multipole moments. The classification of permittivity corresponding to different varying tendencies of gradient forces exerted on small spheres or larger Mie particles are illustrated. Absorption of particles favors the trapping of small spheres by gradient force, while it is bad for the trapping of larger particles. Moreover, the absolute values of the maximal gradient forces exerted on larger Mie particles decline greatly versus the varied imaginary part of permittivity. This work provides elaborate investigation on the different varying tendencies of gradient forces versus permittivity, which favors more accurate and free optical trapping.

Negative optical radiation force and spin torques on subwavelength prolate and oblate spheroids in fractional Bessel-Gauss pincers light-sheets

Fractional Bessel-Gauss light-sheets [J. Opt.19, 055602 (2017)JOOPDB0150-536X10.1088/2040-8986/aa649a], which correspond to finite optical "slices" in 2D and possess asymmetric slit openings and bending characteristics, are examined from the standpoint of optical radiation force and spin torque theories for a subwavelength spheroid with arbitrary orientation in space. The vector angular spectrum decomposition method in addition to the Lorenz gauge condition and Maxwell's equations are used to determine the Cartesian components of the incident radiated electric field of the Bessel-Gauss light-sheets. In the framework of the dipole approximation, the numerical results for the Cartesian components of the optical radiation force and spin torque vectors show that negative forces (oriented in the opposite direction of wave motion) and spin torques arise depending on the beam parameters, the orientation of the subwavelength spheroid in 3D space, and its aspect ratio (i.e., prolate versus oblate). The spin torque sign reversal reveals that counter-clockwise or clockwise rotations around the center of mass of the spheroid can occur. The results find important applications in the application of auto-focusing light-sheets in particle manipulation, rotation, and optical sorting devices.

Optical Torques on Upconverting Particles for Intracellular Microrheometry

Precise knowledge and control over the orientation of individual upconverting particles is extremely important for full exploiting their capabilities as multifunctional bioprobes for interdisciplinary applications. In this work, we report on how time-resolved, single particle polarized spectroscopy can be used to determine the orientation dynamics of a single upconverting particle when entering into an optical trap. Experimental results have unequivocally evidenced the existence of a unique stable configuration. Numerical simulations and simple numerical calculations have demonstrated that the dipole magnetic interactions between the upconverting particle and trapping radiation are the main mechanisms responsible of the optical torques that drive the upconverting particle to its stable orientation. Finally, how a proper analysis of the rotation dynamics of a single upconverting particle within an optical trap can provide valuable information about the properties of the medium in which it is suspended is demonstrated. A proof of concept is given in which the laser driven intracellular rotation of upconverting particles is used to successfully determine the intracellular dynamic viscosity by a passive and an active method.