Investigation on the laser trapping mechanism of light-absorbing particles in air

Bo He, Xuemei Cheng, Yongjie Zhan, Qian Zhang, Haowei Chen, Zhaoyu Ren, Chen Niu, Jingjing Yao, Tengfei Jiao and Jintao Bai

We report on the micron-sized light-absorbing particle trapping in two configurations (horizontal and vertical), in order to elucidate the laser trapping mechanism based on the photophoretic force. Two types of carbon particles (irregular graphite particles and carbon microspheres) were tested in both Gaussian and hollow beam traps. By comparing the trapping efficiency and stability under various circumstances, we confirmed that there are two types of photophoretic forces: $F_{\Delta \alpha}$ and $F_{\Delta T}$ forces on the laser irradiating particle. Furthermore, the forces and moments exerting the particles in various traps were analyzed, which explained the experimental phenomena very well. It was found that the $F_{\Delta \alpha}$ force due to the thermal accommodation difference among the irregular particles helps the irregular particles to be balanced more easily and of higher trapping efficiency and stability. This work provides important references for people to choose a suitable trapping scheme according to the particles, which would be of significance in the applications of single-particle analysis.

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Disappearance and reappearance of an optical trap for silver nanoparticles under femtosecond pulsed excitation: A theoretical investigation

Anita Devi, Shruthi S Nair and Arijit K. De

Recently, the role of ultrafast pulsed excitation in laser trapping of dielectric nanoparticles has been explored and it was observed that the optical Kerr effect (OKE) plays an important role in determining the stability of the trap. Here, we theoretically investigate the trapping behaviour of metallic (silver) nanoparticles and study the effect of OKE (up to sixth order) under high repetition rate femtosecond pulsed excitation. We observe that the trapping potential is first stabilized, then destabilized and again stabilized with an increase in laser power. This work shows how one can fine-tune the stability of an optical trap for metallic nanoparticles through OKE.

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Zero-point electromagnetic stress tensor for studying Casimir forces on colloidal particles in media

Friedrich Anton Burger, Johannes Fiedler and Stefan Yoshi Buhmann

We address the question of the correct electromagnetic stress tensor in media and its consequences for the Casimir force. The latter being due to the zero-point momentum of the electromagnetic field, competing approaches based on the Abraham or Maxwell stress tensor lead to different predictions. We consider the test scenario of two colloidal spherical particles submerged in a dielectric medium and use three criteria to distinguish the two approaches: we show that the Abraham stress tensor, and not the Maxwell stress tensor, leads to a Casimir force that is form-equivalent to Casimir-Polder and van der Waals forces, obeys duality as a fundamental symmetry and is consistent with microscopic many-body calculations. On this basis, we derive general formulas for the dispersion forces on one and between two colloidal particles in arbitrary liquid-media environments in terms of their dipole polarisabilities, allowing for more elaborate theoretical descriptions and bridging the gap between microscopic and macroscopic accounts.

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2-D evanescent trapping of colloids in the vicinity of a micrometer waveguide

O. Emile, J. Emile and H. Tabuteau

We report on the trapping of micrometer colloids using the evanescent wave from a multimode cylindrical optical waveguide. We show that the particle trapping is a two-step process. With a low-power visible laser injected in the device, particles are first captured at a radial distance twice greater than the diameter of the waveguide and then drawn near to it. In a second time particles turn around the waveguide and get trapped in a direction corresponding to the TM polarization of the laser. Such a device could be easily implemented in microfluidic systems in order to coat surfaces or to control particles deposition and assembly. Conversely, it could find applications in the filtration process to aggregate and remove colloidal pollutants.

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Nonequilibrium dissipation in living oocytes

É. Fodor, W. W. Ahmed, M. Almonacid, M. Bussonnier, N. S. Gov, M.-H. Verlhac, T. Betz, P. Visco and F. van Wijland

Living organisms are inherently out-of-equilibrium systems. We employ recent developments in stochastic energetics and rely on a minimal microscopic model to predict the amount of mechanical energy dissipated by such dynamics. Our model includes complex rheological effects and nonequilibrium stochastic forces. By performing active microrheology and tracking micron-sized vesicles in the cytoplasm of living oocytes, we provide unprecedented measurements of the spectrum of dissipated energy. We show that our model is fully consistent with the experimental data, and we use it to offer predictions for the injection and dissipation energy scales involved in active fluctuations.

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Tunable Fano resonant optical forces exerted on a graphene-coated dielectric particle by a Gaussian evanescent wave

Yang Yang, Xiaofu Zhang, Anping Huang and Zhisong Xiao

In this paper, we investigate the optical forces exerted on a graphene-coated dielectric particle by the Gaussian beam transmitted through the prism setup systematically. It is shown that the optical force spectra exhibit significant Fano resonance under the excitation of a Gaussian evanescent wave. The magnitude and morphology of Fano resonance can be modulated effectively by the graphene coating. Also, the modification on the threshold of the Fermi energy of graphene could help to regulate the trapping behavior efficiently. The proposed work may provide a new avenue in the specific optical tweezers and nano-optics.

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Probing the Casimir force with optical tweezers

D. S. Ether jr., L. B. Pires, S. Umrath, D. Martinez, Y. Ayala, B. Pontes, G. R. de S. Araújo, S. Frases, G.-L. Ingold, F. S. S. Rosa

We propose to use optical tweezers to probe the Casimir interaction between microspheres inside a liquid medium for geometric aspect ratios far beyond the validity of the widely employed proximity force approximation. This setup has the potential for revealing unprecedented features associated to the non-trivial role of the spherical curvatures. For a proof of concept, we measure femtonewton double-layer forces between polystyrene microspheres at distances above 400 nm by employing very soft optical tweezers, with stiffness of the order of fractions of a fN/nm. As a future application, we propose to tune the Casimir interaction between a metallic and a polystyrene microsphere in saline solution from attraction to repulsion by varying the salt concentration. With those materials, the screened Casimir interaction may have a larger magnitude than the unscreened one. This line of investigation has the potential for bringing together different fields including classical and quantum optics, statistical physics and colloid science, while paving the way for novel quantitative applications of optical tweezers in cell and molecular biology.

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Activity-driven fluctuations in living cells

É. Fodor, M. Guo, N. S. Gov, P. Visco, D. A. Weitz and F. van Wijland

We propose a model for the dynamics of a probe embedded in a living cell, where both thermal fluctuations and nonequilibrium activity coexist. The model is based on a confining harmonic potential describing the elastic cytoskeletal matrix, which undergoes random active hops as a result of the nonequilibrium rearrangements within the cell. We describe the probe's statistics and we bring forth quantities affected by the nonequilibrium activity. We find an excellent agreement between the predictions of our model and experimental results for tracers inside living cells. Finally, we exploit our model to arrive at quantitative predictions for the parameters characterizing nonequilibrium activity, such as the typical time scale of the activity and the amplitude of the active fluctuations.

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Probing linear and nonlinear microrheology of viscoelastic fluids

J. R. Gomez-Solano and C. Bechinger

Bulk rheological properties of viscoelastic fluids have been extensively studied in macroscopic shearing geometries. However, little is known when an active microscopic probe is used to locally perturb them far from the linear-response regime. Using a colloidal particle dragged periodically by scanning optical tweezers through a viscoelastic fluid, we investigate both, its linear and nonlinear microrheological response. With increasing particle velocity, we observe a transition from constant viscosity to a thinning regime, where the drag force on the probe becomes a nonlinear function of the particle velocity. We demonstrate that this transition is only determined by the ratio of the fluid's equilibrium relaxation time and the period of the driving.

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Energy flow between two hydrodynamically coupled particles kept at different effective temperatures

A. Bérut, A. Petrosyan and S. Ciliberto

We measure the energy exchanged between two hydrodynamically coupled micron-sized Brownian particles trapped in water by two optical tweezers. The system is driven out of equilibrium by random-forcing the position of one of the two particles. The forced particle behaves as it has an "effective temperature" higher than that of the other bead. This driving modifies the equilibrium variances and cross-correlation functions of the bead positions: we measure an energy flow between the particles and an instantaneous cross-correlation, proportional to the effective temperature difference between the two particles. A model of the interaction which is based on classical hydrodynamic coupling tensors is proposed. The theoretical and experimental results are in excellent agreement.

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Probing active forces via a fluctuation-dissipation relation: Application to living cells

P. Bohec, F. Gallet, C. Maes, S. Safaverdi, P. Visco and F. van Wijland
We derive a new fluctuation-dissipation relation for non-equilibrium systems with long-term memory. We show how this relation allows one to access new experimental information regarding active forces in living cells that cannot otherwise be accessed. For a silica bead attached to the wall of a living cell, we identify a crossover time between thermally controlled fluctuations and those produced by the active forces. We show that the probe position is eventually slaved to the underlying random drive produced by the so-called active forces.
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Radiation pressure makes ellipsoidal particles tumble

B. M. Mihiretie, P. Snabre, J. C. Loudet and B. Pouligny

We report on optical levitation of dielectric particles, of prolate ellipsoidal shape, a few tens of micrometers in length, in a low-aperture laser beam. Ellipsoids of moderate aspect ratio (k < 3) are observed to be trapped on the axis of the laser beam, similarly to simple spheres. Conversely, elongated particles (k > 3) cannot be kept immobile, and rather undergo sustained oscillating motions, comprising both lateral and angular excursions around the beam axis; hence the name "tumble". The observed tumbling motion, a straightforward manifestation of the non-conservative character of radiation pressure forces, is explained through a 2-dimensional ray optics model of the interaction of light with an ellipsoid.

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Force sensing with a shaped dielectric micro-tool

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles and D. M. Carberry

We analyse the thermal motion of a holographically trapped non-spherical force probe, capable of interrogating arbitrary samples with nanometer resolution. High speed video stereo-microscopy is used to track the translational and rotational coordinates of the micro-tool in three dimensions, and the complete 6 × 6 stiffness matrix for the system is determined using equipartition theorem. The Brownian motion of the extended structure is described in terms of a continuous distribution ofthermal ellipsoids. A centre of optical stress, at which rotational and translational motion is uncoupled, is observed and controlled. Once calibrated, the micro-tool is deployed in two modes of operation: as a force sensor with <150 femto-Newton sensitivity, and in a novel form of photonic force microscopy.

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Fluctuations, linear response and heat flux of an aging system

J. R. Gomez-Solano, A. Petrosyan and S. Ciliberto

We measure the fluctuations of the position of a Brownian particle confined by an optical trap in an aging gelatin droplet after a fast quench. Its linear response to an external perturbation is also measured. We compute the spontaneous heat flux from the particle to the bath due to the non-equilibrium formation of the gel. We show that the mean heat flux is quantitatively related to the violation of the equilibrium fluctuation-dissipation theorem as a measure of the broken detailed balance during the aging process.

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Pattern formation in colloidal explosions

A. V. Straube, A. A. Louis, J. Baumgartl, C. Bechinger and R. P. A. Dullens

We study the non-equilibrium pattern formation that emerges when magnetically repelling colloids, trapped by optical tweezers, are abruptly released, forming colloidal explosions. For multiple colloids in a single trap we observe a pattern of expanding concentric rings. For colloids individually trapped in a line, we observe explosions with a zigzag pattern that persists even when magnetic interactions are much weaker than those that break the linear symmetry in equilibrium. Theory and computer simulations quantitatively describe these phenomena both in and out of equilibrium. An analysis of the mode spectrum allows us to accurately quantify the non-harmonic nature of the optical traps. Colloidal explosions provide a new way to generate well-characterized non-equilibrium behaviour in colloidal systems.

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Irreversibility-to-reversibility crossover in transient response of an optically trapped particle

Manas Khan and A. K. Sood

We study the transient response of a colloidal bead which is released from different heights and allowed to relax in the potential well of an optical trap. Depending on the initial potential energy, the system's time evolution shows dramatically different behaviors. Starting from the short-time reversible to long-time irreversible transition, a stationary reversible state with zero net dissipation can be achieved as the release point energy is decreased. If the system starts with even lower energy, it progressively extracts useful work from thermal noise and exhibits an anomalous irreversibility. In addition, we have verified the Transient Fluctuation Theorem and the Integrated Transient Fluctuation Theorem even for the non-ergodic descriptions of our system.

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Negative light pressure force between two metal bodies separated by a subwavelength slit

V. Nesterov, L. Frumin and E. Podivilov

An explicit analytical expression of a light-induced attractive force between two macroscopic metal bodies or films separated by a subwavelength slit has been derived. The analytical expression obtained agrees well with the numerical calculations for the main TM mode. This force, which acts as a force with negative light pressure, arises by the interaction of plasmon-polaritons excited at the surface of metal when light propagates through the subwavelength slit. Estimations of this light-induced attractive force show that the force is sufficient to enable measurements and practical applications.

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Optical forces, trapping and strain on extended dielectric objects

M. Sonnleitner, M. Ritsch-Marte and H. Ritsch

We show that the optical properties of an extended dielectric object are reliably reproduced by a large number of thin slices forming a linear array of beam splitters. In the infinite slice number limit this self-consistent approach allows to calculate light forces within a medium directly from the Maxwell stress tensor for any dielectric with prescribed refractive index distribution. For the generic example of a thick slab in counterpropagating fields the effective force and internal strain distribution strongly depend on the object's thickness and the injected field amplitudes. The corresponding trapping dynamics may even change from high-field-seeking to low-field-seeking behaviour while internal forces lead to pressure gradients and thus imply stretching or compression of an elastic object. Our results bear important consequences for a wide scope of applications, ranging from cavity optomechanics with membranes, size selective optical trapping and stretching of biological objects, light-induced pressure gradients in gases, to implementing light control in microfluidic devices.

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Microrheology and the fluctuation theorem in dense colloids

L. G. Wilson, A. W. Harrison, W. C. K. Poon and A. M. Puertas

We present experiments and computer simulations of a "tracer" (or "probe") particle trapped with optical tweezers and dragged at constant speed through a bath of effectively hard colloids with approximately the same size as the probe. The results are analyzed taking the single-particle case and assuming effective parameters for the bath. The effective microscopic friction coefficient and effective temperature of the tracer are obtained. At high probe velocities, the experimental microviscosity compares well with the viscosity from bulk rheology, whereas a correction due to hydrodynamic interactions (absent in the simulations) is necessary to collapse the simulation data. Surprisingly, agreement is found without any need of hydrodynamic corrections at small probe velocities. The dynamics of the tracer inside the trap shows, both in the simulations and experiments, a fast relaxation due to solvent friction and a slow one caused by the collisions with other particles. The latter is less effective in dissipating the energy introduced by the moving trap and causes increasing fluctuations in the tracer motion, reflected as higher effective temperature.

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Out-of-equilibrium microrheology using optical tweezers to probe directional viscoelastic properties under shear

Manas Khan and A. K. Sood

Many wormlike micellar systems exhibit appreciable shear thinning due to shear-induced alignment. As the micelles get aligned introducing directionality in the system, the viscoelastic properties are no longer expected to be isotropic. An optical-tweezers–based active microrheology technique enables us to probe the out-of-equilibrium rheological properties of a wormlike micellar system simultaneously along two orthogonal directions —parallel to the applied shear, as well as perpendicular to it. While the displacements of a trapped bead in response to active drag force carry signature of conventional shear thinning, its spontaneous position fluctuations along the perpendicular direction manifest an orthogonal shear thickening, an effect hitherto unobserved.

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