Calculation Of Optical Forces Research Articles

Capture Dynamics of Dielectric Microparticles in Hollow-Core-Fiber-Based Optical Traps

Optical traps formed in hollow-core fibers (HCFs) can overcome several limitations of conventional free-space optical tweezers. One of the key issues is to load particles from free space into the hollow core with high efficiency, in which process the capture dynamics of the particles in front of the HCF endface plays an important role. In this work, a comprehensive model of the trapping and capture process of the dielectric particles in front of HCF is established by taking into account the features of the fiber modes and the motional parameters of the particles. Stable capture positions are predicted based on analytical calculations of optical forces, and the dependencies of the equilibrium axial trapping position on the beam numerical aperture, the fiber core and particle diameters are provided. In addition, the trajectories and the capture dynamics of the particles are studied by solving the equation of motion for the particles under the impact of optical forces, predicting feasible parameter ranges of the initial amplitude and direction of particle launch velocity for achieving successful particle capture in front of HCF. The results can provide guidance for further improving the particle-loading efficiencies of the HCF-based optical traps, which may find applications of flying particle sensors and long-range particle binding in HCFs.

Mid-Infrared Optical Force Chromatography of Microspheres Containing Siloxane Bonds.

Recent interest in particle sorting using optical forces has grown due to its ability to separate micro- and nanomaterials based on their optical properties. Here, we present a mid-infrared optical force manipulation technique that enables precise sorting of microspheres based on their molecular vibrational properties using a mid-infrared quantum cascade laser. Utilizing the optical pushing force driven by a 9.3 μm mid-infrared evanescent field generated on a prism through total internal reflection, a variety of microspheres, including those composed of Si-O-Si bonds, can be separated in accordance with their absorbance values at 9.3 μm. The experimental results are in good agreement with the optical force calculations using finite-difference time-domain simulation. Thus, each microsphere's displacement and velocity can be predicted from the absorbance value; conversely, the optical properties (e.g., absorbance and complex refractive index in the mid-infrared region) of individual microspheres can be estimated by monitoring their velocity.

Rigorous full-wave calculation of optical forces on microparticles immersed in vector Pearcey beams.

We present the electromagnetic fields of vector Pearcey beams by employing the vector angular spectrum representation. The beams maintain the inherent properties of autofocusing performance and inversion effect. Based on the generalized Lorenz-Mie theory and Maxwell stress tensor approach, we derive the partial-wave expansion coefficients of arbitrary beams with different polarization and the rigorous solution to evaluate the optical forces. Furthermore, we investigate the optical forces experienced by a microsphere placed in vector Pearcey beams. We study the effects on the longitudinal optical force arising from the particle size, permittivity and permeability. This exotic curved trajectory transport of particles by vector Pearcey beams may find applications in the case where the transport path is partly blocked.

Investigation of Dust Grains by Optical Tweezers for Space Applications

Cosmic dust plays a dominant role in the universe, especially in the formation of stars and planetary systems. Furthermore, the surface of cosmic dust grains is the benchwork where molecular hydrogen and simple organic compounds are formed. We manipulate individual dust particles in a water solution by contactless and noninvasive techniques such as standard optical and Raman tweezers, to characterize their response to mechanical effects of light (optical forces and torques) and to determine their mineral compositions. Moreover, we show accurate optical force calculations in the T-matrix formalism highlighting the key role of composition and complex morphology in the optical trapping of cosmic dust particles. This opens perspectives for future applications of optical tweezers in curation facilities for sample-return missions or in extraterrestrial environments.

Faster and More Accurate Geometrical-Optics Optical Force Calculation Using Neural Networks.

Optical forces are often calculated by discretizing the trapping light beam into a set of rays and using geometrical optics to compute the exchange of momentum. However, the number of rays sets a trade-off between calculation speed and accuracy. Here, we show that using neural networks permits overcoming this limitation, obtaining not only faster but also more accurate simulations. We demonstrate this using an optically trapped spherical particle for which we obtain an analytical solution to use as ground truth. Then, we take advantage of the acceleration provided by neural networks to study the dynamics of ellipsoidal particles in a double trap, which would be computationally impossible otherwise.

Multipolar expansions for scattering and optical force calculations beyond the long wavelength approximation

We review three different approaches for the calculation of electromagnetic multipoles, namely, the Cartesian primitive multipoles, the Cartesian irreducible multipoles, and the spherical multipoles. We identify the latter as the best suited to describe the scattering of electromagnetic radiation, as exemplified for an amorphous silicon sphere. These multipoles are then used to calculate the optical force acting on semiconductor, dielectric or metallic particles in a wide wavelength range, from the dipolar regime down to the Mie regime.

Optical force calculation in the ray-optics regime for beams with arbitrary complex amplitude profiles

In this paper, we propose an augmented ray-optics model for computation of the optical force on spherical microscopic particles due to a beam with an arbitrary complex amplitude profile. The force calculation is based on simple analytical expressions derived considering relevant beam and lens parameters. The proposed model can provide the net optical force for a beam whose intensity or amplitude as well as phase profile in the entrance pupil of the lens can be arbitrary. Accuracy of the augmented model is demonstrated by comparing numerically with the existing model and with the experimental observations considering a focused vortex beam.

FDTD simulation of optical force under non-ideal conditions

In this paper, the optical forces of particles in optical tweezers under non-ideal conditions are investigated. The calculation of optical forces are carried out by combining three dimensional finite-difference time-domain (FDTD) method and Maxwell stress Tensor (MST). Numerical results show the changes of trapping stiffness and equilibrium position induced by several common seen non-ideal conditions in experiment. This study is expected to estimate the error of optical force in real situation and that is of great use to further optimize the performance of optical tweezers.

Numerical analysis on the optical force calculation in the Rayleigh scattering regime

The radiation force calculated in the Rayleigh regime is investigated by comparison with the generalized Lorenz Mie Theory (GLMT). The basic concepts behind the Rayleigh regime and GLMT are introduced, and a numerical simulation is conducted to analyze the difference between these two methods. Several physical parameters are considered to evaluate their effect on the calculation accuracy of the Rayleigh regime, including the particle size, optical wavelength, and beam waist. The numerical results show that the valid region of the Rayleigh regime depends primarily on the ratio of the wavelength and particle size, whereas the Gaussian beam size has a lesser impact on the calculation results for both methods. Our study provides critical conditions under which the Rayleigh regime is applicable. The calculation accuracy of the Rayleigh regime is also theoretically analyzed.

Calculation of optical forces for arbitrary light beams using the Fourier ray method.

The ray-optics (RO) model is a reasonable method to calculate optical force in geometrical optics regime. However, the RO model fails to calculate the optical force produced by diffractive optical field and other arbitrary structured light beams. We propose the Fourier ray (FR) method to calculate the optical force for arbitrary incident beams. Combining the Fourier optics and the geometrical optics, the FRs are defined as rays that inlay on the plane waves weighted by the Fourier angular spectrum of the incident beam. According to traditional RO model and FR method, we can analyze optical forces on a microsphere immersed in various beams. To validate the FR method, forces of the fundamental Gaussian beam and Airy beam are respectively calculated and compared with traditional method. In addition, optical forces in three arbitrary structured light beams are demonstrated as well. Our simulations show that the FR method is able to evaluate the optical forces generated by diffractive optical field and complex structured light beams, and give a solid prediction of their trapping performances. In RO regime, the Fourier ray method is a universal method to predict the interaction between bead and complex optical field.

Optical forces from near-field directionalities in planar structures

Matter manipulation with optical forces has become commonplace in a wide range of research fields and is epitomized by the optical trap. Calculations of optical forces on small illuminated particles typically neglect multiple scattering on nearby structures. However, this scattering can result in large recoil forces, particularly when the scattering includes directional near-field excitations. Near-field recoil forces have been studied in the case of electric, magnetic and circularly polarized dipoles, but they exist for any type of directional near-field excitation. We use the force angular spectrum as a concise and intuitive analytical expression for the force on any dipole near planar surfaces, which allows us to clearly distinguish the effect due to the dipole, and due to the surface. We relate this directly to the coupling efficiency of surface or guided modes via Fermi's golden rule. To exemplify this, a near-field force transverse to the illumination is computationally calculated for a Huygens dipole near a metallic waveguide. We believe this formalism will prove insightful for various nanomanipulation systems within areas such as nanofluidics, sensing, biotechnology and nano-assembly of nanostructures.

Optical forces in the T-matrix formalism

Optical tweezers are a crucial tool for the manipulation and characterisation, without mechanical contact, of micro- and nanoparticles, ranging from biological components, such as biomolecules, viruses, bacteria, and cells, to nanotubes, nanowires, layered materials, plasmonic nanoparticles, and their composites. Despite the many interdisciplinary applications, only recently it has been possible to develop an accurate theoretical modelling for the mesoscale size range. This goes beyond the strong approximations typically used for the calculation of optical forces on particles much smaller (dipole approximation) or much larger (ray optics) than the wavelength of the trapping light. Among the different methods used to calculate optical forces on model particles, the ones based on the transition matrix (T-matrix) are currently among the most accurate and efficient, particularly when applied to non-spherical particles, both isolated and interacting, or in composite structures. Here, we first give an overview of the theoretical background on optical forces, optomechanics, and T-matrix methods. Then, we focus on calculations of optical trapping on model polystyrene nanowires with the aim to investigate their scaling with nanowire length at the mesoscale. We compare the force constant dependence with approximations at small or large length with respect to the trapping wavelength and with calculations on spheres, pointing out the role of shape.

Chiral optical tweezers for optically active particles in the T-matrix formalism

Modeling optical tweezers in the T-matrix formalism has been of key importance for accurate and efficient calculations of optical forces and their comparison with experiments. Here we extend this formalism to the modeling of chiral optomechanics and optical tweezers where chiral light is used for optical manipulation and trapping of optically active particles. We first use the Bohren decomposition to deal with the light scattering of chiral light on optically active particles. Thus, we show analytically that all the observables (cross sections, asymmetry parameters) are split into a helicity dependent and independent part and study a practical example of a complex resin particle with inner copper-coated stainless steel helices. Then, we apply this chiral T-matrix framework to optical tweezers where a tightly focused chiral field is used to trap an optically active spherical particle, calculate the chiral behaviour of optical trapping stiffnesses and their size scaling, and extend calculations to chiral nanowires and clusters of astrophysical interest. Such general light scattering framework opens perspectives for modeling optical forces on biological materials where optically active amino acids and carbohydrates are present.

Approximate and explicit expression of optical forces and pull-in instability of a silicon nano-optomechanical device

Nano-optomechanical systems actuated by optical forces enable many interesting scientific and technological applications. They are vulnerable to the effects of surface stress and Casimir forces. Therefore, calculation of optical forces is essential for the reliability applications of these advanced devices. In this paper, an approximate and explicit expression is developed for the evaluation of the optical force existing between a waveguide and a substrate through the effective refractive index. The influences of surface stress and Casimir forces on the pull-in instability of a silicon nano-optomechanical device actuated by optical forces are investigated. It is found that if neglecting the effect of surface stress, the maximum size, which indicates the device can be safely fabricated, will be over-predicted. The surface stress reduces the critical optical power and its effect is more significant for a slender waveguide.

Rigorous full-wave calculation of optical forces on dielectric and metallic microparticles immersed in a vector Airy beam.

Based on the generalized Lorenz-Mie theory and the Maxwell stress tensor approach we present the first rigorous full-wave solution of the optical forces acting on spherical microparticles immersed in a two-dimensional vector Airy beam beyond the paraxial approximation. The critical aspect lies in evaluating efficiently and accurately the partial wave expansion coefficients of the incident Airy beam, which are achieved by using the vector angular spectrum representation for a variety of polarizations. The optical field distributions are then simulated to show the self-accelerating and self-healing effects of the Airy beam. The dielectric and gold microparticles are shown to be trapped within the main lobe or the nearby side-lobes mostly by the transverse gradient optical force while driven forward along the parabolic trajectory of the Airy beam by the longitudinal scattering force. It is thus demonstrated theoretically that the vector Airy beam has the capability of precisely transporting both dielectric and metallic microparticles along the prespecified curved paths.

Analytical calculations of optical trapping forces for drag calibration: Effects of mismatch between beam focus and particle center

We present analytical calculations of optical forces for drag calibrations via the geometrical optics approximation (GOA) for the case in which a single laser beam is strongly focused on a polystyrene microsphere dispersed in an aqueous phase. When the beam focus is mismatched with the particle center owing to the presence of vertical forces, such as gravity, buoyancy, and the radiation force caused by the laser beam, the trapped particle would be displaced in a radial direction when the lateral drag force is applied. Based on the analytical calculations of optical trapping forces and the force balance upon dragging, we found that the critical laser power at which the beam focus matches the particle center exhibits a power-law relationship with the particle radius a according to the empirical expression log(Pcrit (mW)) = 2.899 log(2a (µm)) - 2.316. We also found an empirical expression for the mechanical equilibrium position of the vertical displacement Δzeq0(Δy=0) as functions of the laser power P and the particle radius, \(\Delta z_{eq}^0 = \frac{{\left[ {{F_{gb}}\left( {pN} \right) - 0.068P\left( {mW} \right)} \right]\left[ {2.7a\left( {\mu m} \right) - 0.252} \right]}}{{P\left( {mW} \right)}}\), where Fgb is the sum of the gravitational and buoyant forces.

Optical tweezers affected by monochromatic aberrations

The performance of optical tweezers in the presence of monochromatic aberrations is investigated theoretically and experimentally. For the calculation of optical forces we use a ray-optics-based force simulation, which is embedded in a ray tracing routine. By considering optical path differences caused by monochromatic aberrations, we are able to simulate their effect on the trapping forces. Optical trapping experiments considering the influence of aberrations were performed with an optical tweezers system, specially adapted to trap particles in gaseous surrounding. The conformity of these measurements with the theoretical predictions verifies the correct performance of the optical force simulation routine. Based on the reliable simulation tool, further theoretical studies are performed on how optical aberrations affect the function and performance of optical tweezers.

A Comprehensive Review of Optical Stretcher for Cell Mechanical Characterization at Single-Cell Level.

This paper presents a comprehensive review of the development of the optical stretcher, a powerful optofluidic device for single cell mechanical study by using optical force induced cell stretching. The different techniques and the different materials for the fabrication of the optical stretcher are first summarized. A short description of the optical-stretching mechanism is then given, highlighting the optical force calculation and the cell optical deformability characterization. Subsequently, the implementations of the optical stretcher in various cell-mechanics studies are shown on different types of cells. Afterwards, two new advancements on optical stretcher applications are also introduced: the active cell sorting based on cell mechanical characterization and the temperature effect on cell stretching measurement from laser-induced heating. Two examples of new functionalities developed with the optical stretcher are also included. Finally, the current major limitation and the future development possibilities are discussed.

Computational toolbox for optical tweezers in geometrical optics

Optical tweezers have found widespread application in many fields, from physics to biology. Here, we explain in detail how optical forces and torques can be described within the geometrical optics approximation, and we show that this approximation provides reliable results in agreement with experiments for particles whose characteristic dimensions are larger than the wavelength of the trapping light. Furthermore, we provide an object-oriented software package implemented in MATLAB for the calculation of optical forces and torques in the geometrical optics regime: Optical Tweezers in Geometrical Optics (OTGO). We provide all source codes for OTGO as well as documentation and code examples—e.g., standard optical tweezers, optical tweezers with elongated particles, the windmill effect, and Kramers transitions between two optical traps—necessary to enable users to effectively employ it in their research.

Forces due to pulsed beams in optical tweezers: linear effects.

We present a method for the precise calculation of optical forces due to a tightly-focused pulsed laser beam using generalized Lorenz-Mie theory or the T-matrix method. This method can be used to obtain the fields as a function of position and time, allowing the approximate calculation of weak non-linear effects, and provides a reference calculation for validation of calculations including non-linear effects. We calculate forces for femtosecond pulses of various widths, and compare with forces due to a continuous wave (CW) beam. The forces are similar enough so that the continuous beam case provides a useful approximation for the pulsed case, with trap parameters such as the radial spring constant usually differing by less than 1% for pulses of 100 fs or longer. For large high-index (e.g., polystyrene, with n = 1.59) particles, the difference can be as large as 3% for 100 fs pulses, and up to 8% for 25 fs pulses. A weighted average of CW forces for individual spectral components of the pulsed beam provides a simple improved approximation, which we use to illustrate the physical principles responsible for the differences between pulsed and CW beams.