Understanding Optical Trapping Phenomena: a Simulation for Undergraduates

Optical trapping is an attractive and multidisciplinary topic that has become the center of attention to a large number of researchers. Moreover, it is a suitable subject for advanced students that requires a knowledge of a wide range of topics. As a result, it has been incorporated into some syllabuses of both undergraduate and graduate programs. In this paper, basic concepts in laser trapping theory are reviewed. To provide a better understanding of the underlying concepts for students, a Java application for simulating the behavior of a dielectric particle trapped in a highly focused beam has been developed. The program illustrates a wide range of theoretical results and features, such as the calculation of the force exerted by a beam in the Mie and Rayleigh regimes or the calibration of the trap stiffness. Some examples that are ready to be used in the classroom or in the computer lab are also supplied.

Optical trapping: a review of essential concepts

Optical tweezers are an innovative technique for the non-contact, all-optical manipulation of small material samples, which has extraordinarily expanded and evolved since its inception in the mid-80s of the last century. Nowadays, the potential of optical tweezers has been clearly proven and a wide range of applications both from the physical and biological sciences have solidly emerged, turning the early ideas and techniques into a powerful paradigm for experimentation in the micro- and nanoworld. This review aims at highlighting the fundamental concepts that are essential for a thorough understanding of optical trapping, making emphasis on both its manipulation and measurement capabilities, as well as on the vast array of important biological applications appeared in the last years.

Optical trapping and manipulation of neutral particles using lasers

The techniques of optical trapping and manipulation of neutral particles by lasers provide unique means to control the dynamics of small particles. These new experimental methods have played a revolutionary role in areas of the physical and biological sciences. This paper reviews the early developments in the field leading to the demonstration of cooling and trapping of neutral atoms in atomic physics and to the first use of optical tweezers traps in biology. Some further major achievements of these rapidly developing methods also are considered.

Calculation of optical trapping landscapes

Manipulation of micrometer sized particles with optical tweezers can be precisely modeled with electrodynamic theory using Mie's solution for spherical particles or the T-matrix method for more complex objects. We model optical tweezers for a wide range of parameters including size, relative refractive index and objective numerical aperture. We present the resulting landscapes of the trap stiffness and maximum applicable trapping force in the parameter space. These landscapes give a detailed insight into the requirements and possibilities of optical trapping and provide detailed information on trapping of nanometer sized particles or trapping of high index particles like diamond.

Computational modeling of optical trapping of vaterite microspheres

The ability to grow microscopic spherical birefringent crystals of vaterite, a calcium carbonate mineral, has allowed the development of an optical microrheometer based on optical tweezers. However, since these crystals are birefringent, and worse, are expected to have non-uniform birefringence, computational modeling of the microrheometer is a highly challenging task. Modeling the microrheometer - and optical tweezers in general - typically requires large numbers of repeated calculations for the same trapped particle. This places strong demands on the efficiency of computational methods used. While our usual method of choice for computational modelling of optical tweezers - the T-matrix method - meets this requirement of efficiency, it is restricted to homogeneous isotropic particles. General methods that can model complex structures such as the vaterite particles, such as finite-difference time-domain (FDTD) or finite-difference frequency-domain (FDFD) methods, are inefficient. Therefore, we have developed a hybrid FDFD/T-matrix method that combines the generality of volume-discretisation methods such as FDFD with the efficiency of the T-matrix method. We have used this hybrid method to calculate optical forces and torques on model vaterite spheres in optical traps. We present and compare the results of computational modelling and experimental measurements.

Optical trapping of a cube

The successful development and optimisation of optically-driven micromachines will be greatly enhanced by the ability to computationally model the optical forces and torques applied to such devices. In principle, this can be done by calculating the light-scattering properties of such devices. However, while fast methods exist for scattering calculations for spheres and axisymmetric particles, optically-driven micromachines will almost always be more geometrically complex. Fortunately, such micromachines will typically possess a high degree of symmetry, typically discrete rotational symmetry. Many current designs for optically-driven micromachines are also mirror-symmetric about a plane. We show how such symmetries can be used to reduce the computational time required by orders of magnitude. Similar improvements are also possible for other highly-symmetric objects such as crystals. We demonstrate the efficacy of such methods by modelling the optical trapping of a cube, and show that even simple shapes can function as optically-driven micromachines.

Optical trapping with superfocused high-M2 laser diode beam

Many applications of high-power laser diodes demand tight focusing. This is often not possible due to the multimode nature of semiconductor laser radiation possessing beam propagation parameter M2 values in double-digits. We propose a method of 'interference' superfocusing of high-M2 diode laser beams with a technique developed for the generation of Bessel beams based on the employment of an axicon fabricated on the tip of a 100 μm diameter optical fiber with highprecision direct laser writing. Using axicons with apex angle 140º and rounded tip area as small as 10 μm diameter, we demonstrate 2-4 μm diameter focused laser 'needle' beams with approximately 20 μm propagation length generated from multimode diode laser with beam propagation parameter M2=18 and emission wavelength of 960 nm. This is a few-fold reduction compared to the minimal focal spot size of 11 μm that could be achieved if focused by an 'ideal' lens of unity numerical aperture. The same technique using a 160º axicon allowed us to demonstrate few-μm-wide laser 'needle' beams with nearly 100 μm propagation length with which to demonstrate optical trapping of 5-6 μm rat blood red cells in a water-heparin solution. Our results indicate the good potential of superfocused diode laser beams for applications relating to optical trapping and manipulation of microscopic objects including living biological objects with aspirations towards subsequent novel lab-on-chip configurations.

Optical trapping with Bessel beams generated from semiconductor lasers

In this paper, we study generation of Bessel beams from semiconductor lasers with high beam propagation parameter M2 and their utilization for optical trapping and manipulation of microscopic particles including living cells. The demonstrated optical tweezing with diodegenerated Bessel beams paves the way to replace their vibronic-generated counterparts for a range of applications towards novel lab-on-a-chip configurations.

Optical trapping with Bessel beams generated from semiconductor lasers

In this paper, we demonstrate, for the first time to the best of our knowledge, utilization of Bessel beams generated from a semiconductor laser for optical trapping and manipulation of microscopic particles including living cells. © 2014 OSA.

Growth of crystals in optical tweezers

We report here on the use of optical tweezers in the growth and manipulation of protein and inorganic crystals. Sodium chloride and hen egg-white lysozyme crystals were grown in a batch process, and then seeds from the solution were introduced into the optical tweezers. The regular and controllable shape and the known optical birefringence in these structures allowed a detailed study of the orientation effects in the beam due to both polarization and gradient forces. Additionally, we determined that the laser tweezers could be used to suspend a crystal for three-dimensional growth under varying conditions. Studies included increasing the protein concentration, thermal cycling, and a diffusion-induced increase in precipitant concentration. Preliminary studies on the use of the tweezers to create a localized seed for growth from polyethylene oxide solutions are also reported.

Linear and nonlinear microrheology of dense colloidal suspensions

The length and time scales accessible to optical tweezers make them an ideal tool for the examination of colloidal systems. Embedded high-refractive-index tracer particles in an index-matched hard sphere suspension provide 'handles' within the system to investigate the mechanical behaviour. Passive observations of the motion of a single probe particle give information about the linear response behaviour of the system, which can be linked to the macroscopic frequency-dependent viscous and elastic moduli of the suspension. Separate 'dragging' experiments allow observation of a sample's nonlinear response to an applied stress on a particle-by particle basis. Optical force measurements have given new data about the dynamics of phase transitions and particle interactions; an example in this study is the transition from liquid-like to solid-like behaviour, and the emergence of a yield stress and other effects attributable to nearest-neighbour caging effects. The forces needed to break such cages and the frequency of these cage breaking events are investigated in detail for systems close to the glass transition.

The load dependence of kinesin’s mechanical cycle

Kinesin is a dimeric motor protein that transports organelles in a stepwise manner toward the plus-end of microtubules by converting the energy of ATP hydrolysis into mechanical work. External forces can influence the behavior of kinesin, and force-velocity curves have shown that the motor will slow down and eventually stall under opposing loads of ≈5 pN. Using an in vitro motility assay in conjunction with a high-resolution optical trapping microscope, we have examined the behavior of individual kinesin molecules under two previously unexplored loading regimes: super-stall loads (>5 pN) and forward (plus-end directed) loads. Whereas some theories of kinesin function predict a reversal of directionality under high loads, we found that kinesin does not walk backwards under loads of up to 13 pN, probably because of an irreversible transition in the mechanical cycle. We also found that this cycle can be significantly accelerated by forward loads under a wide range of ATP concentrations. Finally, we noted an increase in kinesin’s rate of dissociation from the microtubule with increasing load, which is consistent with a load dependent partitioning between two recently described kinetic pathways: a coordinated-head pathway (which leads to stepping) and an independent-head pathway (which is static).

Movements of truncated kinesin fragments with a short or an artificial flexible neck

To investigate the role of the neck domain of kinesin, we used optical trapping nanometry to perform high-resolution measurements of the movements and forces produced by recombinant kinesin fragments in which the neck domains were shortened or replaced by an artificial random coil. Truncated kinesin fragments (K351) that contain a motor domain consisting of ≈340 aa and a short neck domain consisting of ≈11 aa showed fast movement (800 nm/s) and 8-nm steps. Such behavior was similar to that of recombinant fragments containing the full-length neck domain (K411) and to that of native kinesin. Kinesin fragments lacking the short neck domain (K340), however, showed very slow movement (<50 nm/s), as previously reported. Joining an artificial 11-aa sequence that was expected to form a flexible random chain to the motor domain (K340–chain) produced normal fast (≈700 nm/s) and stepwise movement. The results suggest that the neck domain does not act as a rigid lever arm to magnify the structural change at the catalytic domain as has been believed for myosin, but it does act as a flexible joint to guarantee the mobility of the motor domain.

Manipulating the genetic identity and biochemical surface properties of individual cells with electric-field-induced fusion

A method for cell–cell and cell–liposome fusion at the single-cell level is described. Individual cells or liposomes were first selected and manipulated either by optical trapping or by adhesion to a micromanipulator-controlled ultramicroelectrode. Spatially selective fusion of the cell–cell or cell–liposome pair was achieved by the application of a highly focused electric field through a pair of 5-μm o.d. carbon-fiber ultramicroelectrodes. The ability to fuse together single cells opens new possibilities in the manipulation of the genetic and cellular makeup of individual cells in a controlled manner. In the study of cellular networks, for example, the alteration of the biochemical identity of a selected cell can have a profound effect on the behavior of the entire network. Fusion of a single liposome with a target cell allows the introduction of the liposomal content into the cell interior as well as the addition of lipids and membrane proteins onto the cell surface. This cell–liposome fusion represents an approach to the manipulation of the cytoplasmic contents and surface properties of single cells. As an example, we have introduced a membrane protein (γ-glutamyltransferase) reconstituted in liposomes into the cell plasma membrane.