Photophoretic Force Research Articles

A study of the coupled dynamics of asymmetric absorbing clusters in a photophoretic trap

Abstract We report a study on the dynamics of absorbing asymmetric carbon clusters trapped by a loosely focused Gaussian beam using photophoretic force. At high laser powers, all the trapped clusters display rotation coupled with oscillation along the axial direction, with a majority spinning about a body fixed axis, while the rest display dual spin as well as orbital motion about a fixed point in space. The spinning and orbiting frequency is inversely proportional to the amplitude of the axial oscillation - with one growing at the expense of the other. Further, the frequencies of these rotations are not proportional to the laser power, but to the trap stiffnesses inferred from the corresponding natural frequencies. The clusters also stop rotating below a certain laser power, and execute random thermal fluctuations. Our work suggests that the dynamics of clusters trapped with photophoretic force are largely dependent on the cluster size and morphology, which could, in principle, be tuned to obtain various motional responses, and help in the design of rotating micromachines in air.

Sedimentation and photophoretic levitation of aerosol clusters in the free molecular regime

Sedimentation of fractal aerosol clusters in rarefied gas medium in the dark and under external illumination similar to sunlight is studied in a numerical experiment taking into account orientation effects, depending on fractal dimension varying within a broad range. The calculation of forces and their moments, including friction forces and photophoretic forces, was carried out on the basis of approximation of free molecular gas kinetic regime and previously developed Monte-Carlo algorithms. Calculation involved 10000 clusters, each of them containing 160 primary spherical particles and efficiently absorbing sunlight and IR radiation, similarly to the particles of soot aggregates.The velocity of multi-particle cluster settling in the absence of illumination, when particle temperatures are equal to the temperature of the gaseous environment, is a distinct function of fractal dimension and is rather close to the velocity of settling of single spherical particles. The settling velocity approximation depending on fractal dimension has been obtained.Illumination brings dramatic changes into sedimentation pattern. The range of cluster sedimentation rate variations broadens substantially, which is a manifestation of gravito-photophoretic effect, so that some clusters even start to levitate. The proportion of levitating clusters is essentially dependent on fractal dimension. For soot-like clusters under irradiation similar to sunlight and pressure equal to atmospheric at the altitude of 30 km, the proportion of levitating aggregates is approximately 7%, which is in good agreement with the experimental data. In the dark and under irradiation, the aggregates rotate, and their trajectories are shaped as spirals.In the context of photophoretic phenomena, a result of principle has been obtained: under irradiation with sunlight, gravito-photophoretic levitation of aerosol soot-like aggregates composed of identical primary particles is possible at a pressure corresponding to the stratospheric altitudes. This result points to the possibility of substantial influence of gravito-photophoretic effect on transport and localization of soot aerosol in the Earth’s stratosphere and mesosphere.

Measurement of the optical stiffness of photophoretic force tweezers in air

We report on a method of measuring the stiffness in photophoretic force tweezers in air by using an experimental configuration with two counter-propagating hollow beams. By setting the optical traps of both beams in the same focal plane of the camera, we are able to record the flight procedure of a trapped particle into the other trap after the initial trapping beam is switched off. Then, the stiffness of optical trap can be obtained by fitting the relationship of particle position vs time during the flight procedure. It is found that the measurement is tolerant to the distance between the traps and laser power variation. In addition, the measured stiffness is demonstrated applicable in determining the size of aerosol particles. The reliable method provided in this work is not only useful in studying the physical behavior of signal particle under atmosphere condition but also meaningful in the applications of aerosol studies, such as in situ aerosol characterization and the local surrounding environment sensing.

Modeling the photophoretic force on a perforated membrane

Modeling the photophoretic force on a perforated membrane

Optimization Of Photophoretic Forces In Coated-Hollow Microspheres

Photophoresis, a thermal phenomenon, generates non-contact forces on microparticles in a fluid when exposed to a light beam, such as a laser. These forces depend on the geometrical, thermal, and optical properties of the particles, and aligning these properties in inhomogeneous particles can enhance photophoretic forces. The use of coated-hollow microspheres offers a promising approach to this challenge. This work presents a photophoresis model for a threelayered microsphere in the slip-flow regime, applying Navier-Stokes equations with corrected boundary conditions. We used numerical approaches to compute the heat source function using Lorenz-Mie theory and validated the results against previous works. Applied to a copper-coated glass bubble, the model analyzed the photophoretic force as a function of coating thickness, considering several shell thicknesses. Results show that nanometric scale coatings enhance the force up to a maximum, after which the high thermal conductivity of copper reduces it. For coatings above 100 nm, the force becomes insensitive to shell thickness, demonstrating copper’s dominance in optical and thermal phenomena. The study suggests depositing excess coating for higher photophoretic forces, providing a framework for optimizing microparticle design for photophoretic applications. Future work includes further validation through numerical models and experiments and finding analytical solutions for integrals associated with terms in the boundary coefficients using Lorenz-Mie Theory, which holds great promise for advancing our understanding of photophoresis.

Analysis Of The Asymmetry Factor In Photophoresis Problems With Uniform Polychromatic Fields And Spherical Absorbers

Photophoresis with plane waves and spherical absorbers is traditionally investigated by considering monochromatic radiation. The asymmetry factor, which is proportional to the photophoretic force, can be expressed in using the Mie theory in terms of an infinite sum of terms depending on the wavelength of the impinging light. Here, we analyze an extension of the photophoresis problem for a polychromatic uniform optical field. Such an analysis demands the introduction of a spectrum which describes the weight of each plane wave for the total, polychromatic field. We expect that this work can find applications or pave the way for more advanced investigations in diverse areas of physics and engineering such as optical levitation, optical trap displays and spectroscopy.

Features of the photophoretic motion of an evaporating droplet in a viscous non-isothermal binary gas medium

A theoretical description of the photophoretic motion in a viscous nonisothermal binary gas mixture of a large evaporating spherical droplet with significant relative temperature differences in its vicinity is carried out in the quasi-stationary approximation for small Reynolds and Pecle numbers. When describing the properties of a gaseous medium, a power-law type of dependence of the coefficients of molecular transport (viscosity, diffusion and thermal conductivity) and density on temperature was taken into account. Numerical estimates have shown the nonlinear nature of the dependence of the photophoretic force and velocity on the average temperature of the droplet surface.

Improvement of the reproducibility in LIBS single levitated aerosol particle analysis based on particle size-selectivity of photophoretic optical trap

To improve the reproducibility of single particle analysis with LIBS, we study the particle size selectivity of photophoretic optical trap. Firstly, the photophoretic force is theoretically simulated and size selectivity in a Gaussian trapping beam is analyzed. Then, the particle size is statistically examined under different power of the trapping Gaussian beam. The results indicate the larger particles are selected by the trap with higher laser power, which is in good agreement with the theoretical expectation. In addition, comparing the particle size distribution of hollow beam trapping with that of Gaussian beam, we found the particle size distribution in hollow beam trapping is broader, which is due to the larger freedom of radiating area on the particle in the hollow beam. Finally, the reproducibility of single particle LIBS is testified. The results show better reproducibility can be achieved with Gaussian beam as a narrower range in particle size is obtained by the trap. This work suggest optical trap can provide a useful tool to control the freedom of particle size and therefore improve the reproducibility of single particle analysis.

Laser-induced crystallization of fluoranthene in both vapor and solution media

Organic single crystals are attracting enormous attention and playing an indispensable role in the realization of high-performance electronic devices. In this paper, we reported an in situ growth method for two-dimensional branch-like and hexagonal shapes of fluoranthene crystals under the photophoretic and dielectrophoretic forces generated by the photothermal and photovoltaic effects in both vapor- and liquid- environments. The crystals grown via this method are characterized by real-time controllability and large size. At the same time, the crystal morphology can also be modified through non-contact illumination. This growth method may serve the future demand for crystal growth in different phases.

Minimizing the Ground Effect for Photophoretically Levitating Disks

Photophoretic levitation is a propulsion mechanism by which lightweight objects can be lifted and controlled through their interactions with light. Since photophoretic forces on macroscopic objects are usually maximized at low pressures, they may be tested in a vacuum chamber in close proximity to the chamber floor and walls. We report experimental evidence that the terrain under levitating microflyers, including the chamber floor or the launchpad from which the microflyer lifts off, can greatly increase the photophoretic lift forces relative to their free-space (midair) values. To characterize this so-called ``ground effect'' during vacuum-chamber tests, we introduce a miniature launchpad composed of three J-shaped (candy-cane-like) wires that minimize the microflyer's extraneous interactions with the underlying surfaces. We compare our J-shaped-wire launchpad with previously used wire-mesh launchpads for simple levitating Mylar-based disks with diameters of 2, 4, and 8 cm. Importantly, we discover that wire-mesh launchpads increase the photophoretic lift force by up to sixfold. A significant ground effect is also associated with the bottom of the vacuum chamber, particularly when the distance to the bottom surface is less than the diameter of the levitating disk. We provide guidelines to minimize the ground effect in vacuum-chamber experiments, which are necessary to test photophoretic microflyers intended for high-altitude exploration and surveillance on Earth or on Mars.

Optical Bottle Shaping Using Axicons with Amplitude or Phase Apodization

We investigate the formation of single and multiple optical bottle beams on the optical axis using a diffractive axicon with amplitude or phase apodization. The proposed approach allows one to control the location and the contrast of the boundaries of the generated dark intensity regions on the optical axis. Experimental results obtained using a spatial light modulator are in good agreement with numerically obtained ones. We successfully used the designed and experimentally formed set of three optical bottle beams for trapping light-absorbing agglomerations of carbon nanoparticles in air under the action of photophoretic forces. This confirms the efficiency of the proposed approach for optical manipulation applications.

Measurement of scattering intensity distribution of single microparticles/nanoclusters based on laser levitation

The scattering measurement of particulates in gaseous medium is helpful in understanding light transmission, laser detection, combustion radiation and atmospheric environment. In order to explore the scattering characteristics of micron-/nano-sized particles, this paper proposes a method of accurately measuring the scattering intensity distribution of a single micron-sized particles/nanoclusters by combining laser levitation and scattering measurement. An experimental apparatus is first built based on the counter-propagated bi-Bessel beams levitation system and scattering test system. The microparticles/nanoclusters of various matters and sizes are then levitated and their stabilities are evaluated. Finally, the scattering intensity distribution of levitated particles within 2π scattering angle is accurately measured with an angular resolution of 9.2″. The forces acting on particles under laser irradiation and the scattering intensity distribution of different particle parameters are simulated and calculated, and compared with experimental results. The influence of noise on the uncertainty of the scattering measurement system is analyzed in depth, including background light, laser beam, and reflected light from the walls. The results show that the signal-to-noise ratio of scattering measurement for metallic magnesium and aluminum, whether single particles or clusters, are both greater than 20 dB and their maximum values are both 94.6 dB in a range of 2π angle. For graphite nanoclusters, the signal-to-noise ratio in the backscattering direction is relatively poor. The influence of levitation instability on the scattering measurement results is estimated in detail, verifying that the influence of levitation instability in the test system on the scattering measurement is ignorable. Metallic magnesium, aluminum, and graphite particles can be stably levitated by the counter-propagated bi-Bessel beams, with a relative instability of less than 0.15. During the levitation, the photophoretic force plays a dominant role. The scattering intensity distribution of a single micron-sized particles and nanoclusters both conform to the scattering characteristics of Mie particles. Microparticles with large refractive index imaginary parts have stronger forward scattering characteristics. The larger the particle size parameter, the stronger the forward scattering effect becomes. The accurate measurement of the scattering intensity distribution of a single microparticles confirms the versatility and reliability of the levitation scattering test system, providing a new research method for in-depth understanding of the scattering characteristics of substances.

Two-dimensional complex (dusty) plasma with active Janus particles

A two-dimensional complex plasma containing active Janus particles was experimentally studied. A single layer of micrometer-sized plastic microspheres was suspended in the plasma sheath of a radio frequency discharge in argon at low pressure. The particle sample used was a mixture of regular particles and Janus particles, which were coated on one side with a thin layer of platinum. Unlike a suspension consisting of regular particles only, the suspension with the inclusion of Janus particles did not form an ordered lattice in the experimental conditions used. Instead, the particles moved around with high kinetic energy in a disordered suspension. Unexpectedly, the mean kinetic energy of the particles declined as the illumination laser power was increased. This is explained by the competition of two driving forces: the photophoretic force and the oppositely directed ion drag force. The mean-squared displacement of the particles scaled as tα with α = 2 at small times t indicating ballistic motion and α=0.56 ± 0.27 at longer times due to the combined effect of the Janus particle propensity to move in circular trajectories and external confinement.

Multi-plane photophoretic trapping of airborne particles with a multi-linear optical trap

We investigate the possibility of multi-plane photophoretic trapping of airborne light-absorbing particles using a multi-linear optical trap created with a cylindrical lens. The diffraction of a Gaussian beam on the edge of the lens leads to the generation of a set light lines with decreasing intensities in a transverse plane. Each of the shaped light lines can be used for trapping of different particles because of the photophoretic forces acting on the trapped particles depend on the light intensity. We show that larger particles cannot be trapped by light lines with decreased intensity, while smaller particles can. In addition, initial laser power attenuation leads to intensity fading of the generated non-main light lines and considerable decreasing in trapping robustness which causes to the escape of the smaller particles trapped in these light lines. All these results were experimentally confirmed and can be used for implementation of passive sorting of particles based on their physical properties.

Photophoresis of spherical particles in slip-flow regime

Photophoresis is a particle-light-induced phenomenon with several applications, such as spectroscopy, three-dimensional displays, and nanomanufacturing, to name a few. This work synthesizes, criticizes, and compares the main hydrodynamic and gas-kinetic models developed to quantify photophoretic forces in the slip-flow regime for uniform light beams, contrasting their predictions with experimental data available in the literature. The results comparing the different models evidence the simplicity and accuracy of Loesche and Husmann's model, which is then confronted with the experimental data available in the literature. However, considering the noticeable effect of high irradiance levels on photophoretic forces, namely, when temperature variations significantly change the thermofluid properties of the gaseous layer around the particle, more experiments are recommended to validate theoretical models. Finally, considering the photophoretic models that depend on two asymmetry factors, J0 and J1, a physical interpretation of their meaning is provided, especially for the oscillations in the latter argued as the result of Mie resonance effects.

Longitudinal and transverse photophoretic force on a homogeneous sphere exerted by a Bessel beam with selective polarizations.

Predicting the photophoretic force exerted on an optical absorptive particle in a gaseous medium is a challenging problem because the problems of electromagnetic scattering, heat transfer, and gaseous molecule dynamics are involved and coupled with each other. Based on the calculation of the source function distribution inside a homogeneous sphere excited by a Bessel beam using the generalized Lorenz-Mie theory, analytical expressions of the asymmetry vector, which is the key quantity in the calculation of photophoretic force, are given using the adjoint boundary value method. Numerical simulations are performed to analyze the influences of polarization, the half-cone angle, and the beam order of the incident beam, particle size, and absorptivity of the particle on the asymmetry vector for both on-axis and off-axis illuminations. Longitudinal and transverse photophoretic forces on a homogeneous sphere are displayed for the slip-flow regime of gaseous media. The results offer important insights into the working mechanism underpinning the development of heat-mediated optical manipulation techniques and the measurement of the refractive index of particles.

Trapping multiple absorbing particles in air using an optical fiber by photophoretic forces

We demonstrate photophoretic force-based optical trapping of multiple absorbing particles in air by loosely focusing a Gaussian beam emanating from a single mode fiber using convex lenses of different focal lengths, and investigate the dependence of the number of trapped particles and their sizes on the focal length. We observe the formation of particle chains at a particular focal length, and measure the axial dynamic range of optical trapping for each lens system. We then develop a numerical simulation to explain this observed dynamic range by estimating the temperature distribution across a particle surface, and determining the axial photophoretic force. Our simulation results are in reasonable agreement with experimental results. Interestingly, we also observe that the average size of trapped particles reduces as we increase the lens focal lengths. This is somewhat intriguing as each lens produces the same intensity profile, albeit at different axial distances. However, the axial intensity gradient reduces as the lens focal length is increased, which suggests that such gradients may somehow be involved in the mechanism of photophoretic confinement.

Three-dimensional optical manipulation of trapped light-absorbing particles based on a hollow beam

We report a method for optical trapping and three-dimensional manipulation of light-absorbing particles in air based on a hollow beam. The particles can be stably trapped for hours in the focused hollow beam with either horizontal or vertical trapping configuration. Particle revolution in the lateral plane (x-y plane) is achieved by employing a wedge prism to deviate and rotate the optical traps. And the particle movement along the laser propagating direction (z-direction) is realized by changing the size of the hollow trapping beam. The mechanism of particle trapping and manipulation in air is analyzed based on the characteristics of photophoretic force. As high trapping power is avoided, this method is meaningful for the particles of low damage threshold and provides a useful tool for in situ analysis of the single aerosol particle in a non-destructive and non-contact manner.

Towards photophoresis with the generalized Lorenz-Mie theory

Based on the adjoint boundary value problem proposed decades ago by Zulehner and Rohatschek [1], analytic and closed-form expressions for the photophoretic forces exerted by arbitrary-shaped beams on homogeneous and low-loss spherical particles is derived in both the free molecular and slip flow regimes. To do so, the asymmetry vector for arbitrary refractive index particles is explicitly calculated by expanding the internal electromagnetic fields with the aid of the generalized Lorenz-Mie theory (GLMT). The approach here proposed is, to the best of the authors’ knowledge, the first systematic attempt to incorporate the GLMT stricto sensu into the field of photophoresis and might as well be extended, e.g. to spheroids and find important applications, among others, in optical trapping and manipulation of microparticles, in geoengineering, particle levitation, optical trap displays and so on.

Optical Funnel to Guide and Focus Virus Particles for X-Ray Diffractive Imaging

Photophoretic forces are induced when light causes a net momentum exchange between a particle and a surrounding gas. Such forces have been shown to be a robust means for trapping and guiding particles in air over long distances. Here, we apply the concept of an optical funnel for the delivery of bioparticles to the focus of an x-ray free-electron laser (XFEL) for femtosecond x-ray diffractive imaging. We provide the experimental demonstration of transversely compressing a high-speed beam of aerosolized viruses via photophoretic forces in a low-pressure gas environment. Relative temperature gradients induced on the viruses by the laser are estimated via particle-velocimetry measurements. The results demonstrate the potential for an optical funnel to improve particle-delivery efficiency in XFEL imaging and spectroscopy.