FORMA (force reconstruction via maximum-likelihood-estimator analysis) addresses the need of measuring the force fields acting on microscopic particles. Compared to alternative established methods, FORMA is faster, simpler, more accurate, and more precise. Furthermore, FORMA can also measure non-conservative and out-of-equilibrium force fields. Here, after a brief introduction to FORMA, I will present its use, advantages and limitations. I will conclude with some recent work where we exploit Bayesian inference to expand the scope of application of FORMA.
The methods used to measure force fields have not changed in the last 30 years; their disadvantages have limited the possibility of measuring nanoscopic forces in many potential applications, such as experiments with non-conservative force fields and out-of-equilibrium conditions. We propose a new powerful, simpler, robust, and faster algorithm to measure force fields, Force Reconstruction via Maximum-likelihood-estimator Analysis(FORMA). FORMA has allowed us to retrieve the conservative and non-conservative components
of a force field acting on a Brownian particle from the analysis of its displacements, proving to have essential advantages over established techniques.
A beam of light may possess both spin and orbital angular momentum. In non-paraxial conditions part of the spin converts into orbital angular momentum through the spin-orbit angular momentum conversion phenomenon. This effect has important consequences at the nanoscale, particularly in nano-manipulation and nano-photonics. In this work, we thoroughly analyze the rotation of microscopic beads subjected to a tightly focused Laguerre-Gaussian beam. Particularly, we observe the rotation of particles along circular trajectories that will depend strongly on the combination of topological charges and the state of polarization. Based on Richard and Wolf theory for non-paraxial beam focusing, we found a very good agreement between the experimental results and the theoretical model based on calculation of the optical forces using the generalized Lorenz-Mie theory.
The accurate measurement of microscopic force fields is crucial in many branches of science and technology, from biophotonics and mechanobiology to microscopy and optomechanics. These forces are often probed by analysing their influence on the motion of Brownian particles. Here we introduce a powerful algorithm for microscopic force reconstruction via maximum-likelihood-estimator analysis (FORMA) to retrieve the force field acting on a Brownian particle from the analysis of its displacements . FORMA estimates accurately the conservative and non-conservative components of the force field with important advantages over established techniques, being parameter-free, requiring ten-fold less data and executing orders-of-magnitude faster. We demonstrate FORMA performance using optical tweezers, showing how, outperforming other available techniques, it can identify and characterise stable and unstable equilibrium points in generic force fields. Thanks to its high performance, FORMA can accelerate the development of microscopic and nanoscopic force transducers for physics, biology and engineering.
 García, Laura Pérez, Jaime Donlucas Pérez, Giorgio Volpe, Alejandro V. Arzola, and Giovanni Volpe. "High-performance reconstruction of microscopic force fields from Brownian trajectories." Nature Communications 9, no. 1 (2018): 5166. https://doi.org/10.1038/s41467-018-07437-x
It is well known that speckle fields exhibit a multitude of vortex-type phase dislocations with unitary topological charge and opposite helicities, such that the average angular momentum is null. We tackle this problem the other way around: What is the minimum vortex number embedded in a carrier beam to produce a disordered pattern and what are the necessary conditions in terms of their initial distribution and topological charges? When studying this problem, we found interesting dynamical behavior of vortices in propagation through a focal region where they are forced to interact, depending on the initial conditions, that in some cases resemble the behavior of a system of particles with an effective repulsive interaction.
We present a few of our recent theoretical and experimental results related to the behavior of micron-scale particles placed into nonlinear optical potentials. The two-dimensional optical ratchet can rectify motion of Brownian particles in any direction in the plane and unstable cubic optical potential results in noise-induced particle motion. Action of optical spin-force was demonstrated in a novel geometry where it is responsible for particle orbiting.
We report on the nonlinear effects of light propagation through a fluorescent nanocolloid, where self-collimated beams are formed. The medium is constituted by a bidisperse suspension of fluorescent and nonfluorescent nanospheres of similar diameters (60nm and 62nm, respectively) in distilled water. A CW laser beam (532 nm wavelength) was focused into the nano-suspension. The threshold power and focusing conditions to create a self-collimated beam are analyzed as a function of the incident power, and a hysteresis effect is observed for the size of the output beam when the power is increasing and decreasing. We also discuss other effects associated to the presence of the fluorescent nanospheres.
Larger golden nanoparticles grow into several preferred forms. Some of those may be easily approximated by ellipsoids. In this paper we examine the rotational dynamics of spheroidal particles in an optical trap comprising counter-propagating Gaussian beams of opposing helicity. Isolated spheroids undergo continuous rotation with frequencies determined by their size and aspect ratio. We study the rotational frequencies and stability of these golden nano-particles theoretically by the means of T-Matrix.
A Bessel beam generated with an axicon lens is focused by a low numerical aperture objective lens to create an optical levitation trap. This configuration allows a full three dimensional trapping of solid glass spheres of few microns in diameter immerse in water. We establish a comparison with an optical levitation trap generated with a Gaussian beam under the same focusing conditions. In both cases the particles are lifted up in an axial position above the focal region that depends on the incident power. The spatial stability is investigated in both cases as a function of axial position, which in turn depends on the input optical power.
A spatial light modulator (SLM) is a versatile device capable of real-time generation of diffractive phase gratings. Employing the SLM in an optical setup opens the possibility of dynamic modification of properties of the incident laser beam, such as its splitting into an arbitrary number of diffracted beams, changing its convergence or its modification into non-traditional laser beam profiles. Advanced feedback procedures enable resolving complex phase masks correcting aberrations inherent to the whole optical system, such as imprecisions of manufacturing process, inhomogeneity of refractive index of materials used or misalignment of optical elements. In this work, generation of Bessel beams (BB) using the SLM is presented. The BB quality is very sensitive to the optical aberrations of the system, especially when higher topological charge is applied to create so-called optical vortices. Therefore, the method compensating those aberrations is applied and the corrected beam is inspected by a CCD camera and optical micro-manipulations of micro-particles. Our experimental results demonstrate successful trapping, rotation and translation of micrometer-sized particles purely by optical forces.
We study theoretically the angular momentum transfer between strongly focused laser vortex beam and a dielectric oblate spheroidal particle (OSP). We find sets of geometrical parameters of the particle and the beam for which the particle is stably trapped on the beam axis in a uniform rotating state, thereby serving as a possible test probe of the global beam angular momentum as well as its spin and orbital parts.
We investigated the behavior of an oblate spheroidal polystyrene microparticle trapped in a focused vortex beam when the beam vorticity and polarization were modified. We demonstrated that such particles can be trapped in three dimensions, spin in a circularly polarized beam and an optical vortex beam around the axis parallel to the beam propagation. We compared the immediate frequencies and showed that contribution from the circularly polarized beam is one order of magnitude weaker comparing to the beam angular orbital momentum. Using a phase-only spatial light modulator we generated several vortex beam traps with well-defined parameters. Measuring the rotations of trapped spheroids we observed hydrodynamic phase and frequency locking for certain sets of beam parameters.
While the behavior of spherical particles confined in light beams is well-studied, the dynamics of confined nonspherical particles may be qualitatively different, but remain largely unexplored. We studied the rotation of microscopic dielectric discs induced by the incident angular momentum of an elliptically polarized Laguerre-
Gaussian beam. These flat particles are confined in three dimensions by the beam and are oriented naturally with its long axis along the direction of the propagation of the beam. Due to the rotationally asymmetric shape of the particles, we were able to induce a constant rotation of the particles and control it by changing the vorticity
and ellipticity of the beam. We also showed a strong dependence on the induced rotation respect to size of the particles. These results provide a new approach to generate or study flows in the microscopic realm as an alternative to the former techniques based on birefringent, absorbent or chiral particles.
Recently, we presented an experimental realization of a deterministic optical rocking ratchet [Arzola, A. V., et al. Phys
Rev. Lett. 106: 168104 (2011)]. We obtained a systematic motion of microparticles and demonstrated that it is possible
to control their average velocity and their direction of motion in real time by properly tuning experimental parameters.
We have extended our study in order to establish the conditions for observing the crucial effect of current reversals in
deterministic conditions, phenomenon predicted more than a decade ago, but experimentally demonstrated for the first
time in our system.
We present a theoretical model and the experimental demonstration of the rocking ratchet effect in the deterministic
regime using an optical trapping device. Our system consists of a dielectric spherical particle in a 1D optical potential
created by means of an interference pattern of asymmetric fringes. In order to achieve the asymmetry of the fringes, three
light beams are interfered by pairs by controlling their relative polarization states, intensities and phases. A periodic
time-dependent external force of zero average is introduced by moving the sample with respect to the optical pattern, for
which the translation stage is driven sideways. The drag force acting on the particle due to this relative motion has the
effect of tilting the optical potential periodically in opposite directions, providing the "rocking" mechanism. We show
that an inversion of the asymmetry in the effective optical potential occurs as the size of the particle is varied, and
therefore, we can observe opposite motion of different particles within the same optical pattern. The dynamics of the
system is studied in terms of the different control parameters, such as the size of the particles, the period and asymmetry
of the fringes, the amplitude and frequency of the rocking mechanism, and the power level in the sample.
We demonstrate optical manipulation and sorting of micrometer-sized dielectric particles using one-dimensional
periodic interference pattern created by interference of two beams in a sample space. These beams are generated
by a combined phase grating applied on the spatial light modulator which allows to set dynamically the position
and spatial period of the interference pattern. If a microparticle of fixed size is placed into such pattern, the
optical forces acting upon it vary according to the spatial period of this optical lattice. We show how to use this
property for sorting of mixtures of particles by moving either the interference pattern or the sample chamber.
The mechanism is examined both theoretically and experimentally.
We propose a technique for the characterization of a 1D-periodic optical potential by studying the dynamics of
non-brownian microscopic particles immerse in water (negligible thermal noise). It has been demonstrated that
in the Mie regime, a periodic light pattern applied to a particle acts as an effective potential that depends on
the size of the particle respect to the period of the optical landscape [I. Ricardez-Vargas, et.al. Appl. Phys.
Lett. 88, 121116 (2006)]. We verify this fact by studying the dynamics of a particle moving within the pattern
due to the effect of a known constant external force. The periodic light pattern is generated with interference
techniques whereas the external force is applied by means of a controlled inclination of the sample cell. We fit
the experimental results for the ensemble average of particle position against time with a theoretical model of
the physical situation. In this way we obtain a curve for the optical force as a function of particle's position for
Optical vortices became a hot topic since almost two decades ago, when it was recognized that Laguerre-Gaussian laser
modes carry orbital angular momentum [Allen et al. Phys Rev A 45, 8185 (1992)] related with a screw phase dislocation,
and different from the spin angular momentum associated to circular polarization. In 1995, this dynamical quantity was
transferred to matter in an optical micromanipulation system for the first time [H. He, et al., Phys. Rev. Lett. 75, 826
(1995)], and since then, a number of studies on angular momentum of light have unveiled different interesting aspects on
the subject. However, there are still open questions, which have arisen together with the generation of novel light beams,
such as vector vortices, for instance. In contrast with scalar vortices, with usual polarization states (linear, circular,
elliptical), the orientation and magnitude of the electric field of vector vortices (solutions of the vector wave equation) is
a function of space and time. In this work, we present an experimental study of the local angular momentum density of a
Bessel vector vortex of first order by means of an optical trap. For this purpose, we used different probe particles in order
to sense the local contribution to the optical angular momentum in each region of the beam. But optical fields are not the
only wave fields that may exhibit phase dislocations or singularities. There are close analogies between light and sound
fields that can be exploited in order to get a better understanding of common phenomena and study new aspects in both
branches of physics. Here we also present the first experimental demonstration and theoretical analysis of acoustical
vortices in free field, with similar properties to those of the optical vortices, including the angular momentum that can be
transferred to matter. The corresponding analogies and differences with the optical case turn out to be very enlightening
for the understanding of the phenomenon of angular momentum in wave fields.