FORMA (force reconstruction via maximum-likelihood-estimator analysis) addresses the need to measure 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 the most recent work where we exploit Bayesian inference to expand FORMA's scope of application.
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.
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 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.
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 [1]. 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.
[1] 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
Engineering the wavefront of light in random media allows the control of wave propagation in space and time by exploiting the spatial and spectral degrees of freedom introduced by multiple scattering (M. Mounaix et al, Phys. Rev. Lett. 116, 253901 (2016)). To apply this far-field control strategy and focus electromagnetic energy at the nanoscale, it is necessary to introduce scatterers that feature strongly enhanced and confined optical fields such as plasmonic nanoantennas. In particular, semi-continuous gold films close to the percolation threshold feature high local field enhancements (S. Gresillon et al, Phys. Rev. Lett. 82, 4520 (1999)) but also propagating surface plasmon waves that can be controlled using a spatial light modulator (P. Bondareff et al, ACS Photonics 2, 1658 (2015)). In this presentation, we demonstrate how controlling the phase of an incoming pulsed laser on a chosen 10 µm x 10 µm area of a random plasmonic metasurface allows us to optimize the two-photon luminescence (TPL) of gold at a given position of the sample. The optimized TPL intensities, that are associated with strong local field enhancements, are increased by a factor of 50 for semi-continuous films that are close to percolation compared to samples far from it, demonstrating that the morphology and randomness of the plasmonic film play an essential role in the control of nonlinear luminescence. Furthermore, we show that TPL intensities can be enhanced at any position of a percolated film, opening exciting perspectives for the wavefront engineering of local field enhancements in random plasmonic metasurfaces.
Particles undergoing a stochastic motion within a disordered medium is a ubiquitous physical and biological phenomenon. Examples can be given from organelles as molecular machines of cells performing physical tasks in a populated cytoplasm to human mobility in patchy environment at larger scales. Our recent results showed that it is possible to use the disordered landscape generated by speckle light fields to perform advanced manipulation tasks at the microscale. Here, we use speckle light fields to study the anomalous diffusion of micron size silica particles (5 μm) in the presence of active microswimmers. The microswimmers we used in the experiments are motile bacteria, Escherichia coli (E.coli). They constitute an active background constantly agitating passive silica particles within complex optical potentials. The speckle fields are generated by mode mixing inside a multimode optical fiber where a small amount of incident laser power (maximum power = 12 μW/μm2) is needed to obtain an effective random landscape pattern for the purpose of optical manipulation. We experimentally show how complex potentials contribute to the anomalous diffusion of silica particles undergoing collisions with swimming bacteria. We observed an enhanced diffusion of particles interacting with the active bath of E.coli inside speckle light fields: this effect can be tuned and controlled by varying the intensity and the statistical properties of the speckle pattern. Potentially, these results could be of interest for many technological applications, such as the manipulation of microparticles inside optically disordered media of biological interests.
Optical forces can affect the motion of a Brownian particle. For example, optical tweezers use optical forces to trap a particle at a desirable position. Unlike passive Brownian particles, active Brownian particles, also known as microswimmers, propel themselves with directed motion and thus drive themselves out of equilibrium. Understanding their motion in a confined potential can provide insight into out-of-equilibrium phenomena associated with biological examples such as bacteria, as well as with artificial microswimmers. We discuss how to mathematically model their motion in an optical potential using a set of stochastic differential equations and how to numerically simulate it using the corresponding set of finite difference equations.
Optical tweezers have been widely used in physics, chemistry and biology to manipulate and trap microscopic and nanoscopic objects. Current optical trapping techniques rely on carefully engineered setups to manipulate nanoscopic and microscopic objects at the focus of a laser beam. Since the quality of the trapping is strongly dependent on the focus quality, these systems have to be very carefully aligned and optimized, thus limiting their practical applicability in complex environments. One major challenge for current optical manipulation techniques is the light scattering occurring in optically complex media, such as biological tissues, turbid liquids and rough surfaces, which give rise to apparently random light fields known as speckles. Here, we discuss an experimental implementation to perform optical manipulation based on speckles. In particular, we show how to take advantage of the statistical properties of speckle patterns in order to realize a setup based on a multimode optical fiber to perform basic optical manipulation tasks such as trapping, guiding and sorting. We anticipate that the simplicity of these “speckle optical tweezers” will greatly broaden the perspectives of optical manipulation for real-life applications.
Some randomness is present in most phenomena, ranging from biomolecules and nanodevices to financial markets and human organizations. However, it is not easy to gain an intuitive understanding of such stochastic phenomena, because their modeling requires advanced mathematical tools, such as sigma algebras, the Itô formula and martingales. Here, we discuss a simple finite difference algorithm that can be used to gain understanding of such complex physical phenomena. In particular, we simulate the motion of an optically trapped particle that is typically used as a model system in statistical physics and has a wide range of applications in physics and biophysics, for example, to measure nanoscopic forces and torques.
A project to introduce secondary school students to statistical physics and biophotonics by means of an optical tweezers is presented. Interestingly, the project is completely experimental and no advanced calculus or physics knowledge is necessary. The project starts from the construction of the optical tweezers itself and therefore is also useful to introduce basic concepts of optics.
Optical forces can affect the motion of a Brownian particle. For example, optical tweezers use optical forces to trap a
particle at a desirable position. Using more complex force fields it is possible to generate more complex configurations.
For example, by using two optical traps placed next to each other, it is possible to obtain a bistable potential where a
particle can jump between the two potentials with a characteristic time scale. In this proceeding, we discuss a simple
finite difference algorithm that can be used to simulate the motion of a Brownian particle in a one-dimensional field of optical forces.
Photonics is an upcoming field that offers immense possibilities in frontier science, technology, and industry. The topic needs to be introduced among the young students to motivate their interest and passion for light. However, the potential of optics and photonics as a very exciting part of science is not always fully explored in high school education. With the motivation to contribute an initiative along these lines, a two-hour program was developed and successfully implemented at ICFO-The institute of photonics sciences. Further recent efforts were directed towards the improvement of this program which resulted in the advanced version. This improved version focuses on explaining the ray and wave nature of light, as well as the demonstration of the conservation of energy in relation to optics. The event was organized and the demonstrations were carried out by ICFO PhD students enrolled in the ICFO Optical Society of America (OSA) and SPIE student chapters.
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