Optical tweezers - Knowledge

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cluster of microparticles provides a new force equilibrium on the cluster as a whole. As such we can say that the cluster of microparticles are somewhat bound together by light. One of the first experimental evidence of optical binding was reported by Michael M. Burns, Jean-Marc Fournier, and Jene A. Golovchenko, though it was originally predicted by T. Thirunamachandran. One of the many recent studies on optical binding has shown that for a system of chiral nanoparticles, the magnitude of the binding forces are dependent on the polarisation of the laser beam and the handedness of interacting particles themselves, with potential applications in areas such as enantiomeric separation and optical nanomanipulation.

4583:-like facet, the nearly gaussian beam carried by a single mode standard fiber will be focused at some distance from the fiber tip. The effective Numerical Aperture of such assembly is usually not enough to allow for a full 3D optical trap but only for a 2D trap (optical trapping and manipulation of objects will be possible only when, e.g., they are in contact with a surface ). A true 3D optical trapping based on a single fiber, with a trapping point which is not in nearly contact with the fiber tip, has been realized based on a not-standard annular-core fiber arrangement and a total-internal-reflection geometry. 1090: 287: 20: 4559:-driven mirrors, a single laser beam can be shared among hundreds of optical tweezers in the focal plane, or else spread into an extended one-dimensional trap. Specially designed diffractive optical elements can divide a single input beam into hundreds of continuously illuminated traps in arbitrary three-dimensional configurations. The trap-forming hologram also can specify the mode structure of each trap individually, thereby creating arrays of optical vortices, optical tweezers, and holographic line traps, for example. When implemented with a 4614:, 5451 (2000), who made use of this technique to stretch microparticles. By manipulating the input power into the two ends of the fiber, there will be an increase of an "optical stretching" that can be used to measure viscoelastic properties of cells, with sensitivity sufficient to distinguish between different individual cytoskeletal phenotypes. i.e. human erythrocytes and mouse fibroblasts. A recent test has seen great success in differentiating cancerous cells from non-cancerous ones from the two opposed, non-focused laser beams. 4631:

were able to orient various human cell types (individual cells and clusters) on a microscope. The main advantage of the so-called "optical cell rotator" technology over standard optical tweezers is the decoupling of trapping from imaging optics. This, its modular design, and the high compatibility of divergent laser traps with biological material indicates the great potential of this new generation of laser traps in medical research and life science. Recently, the optical cell rotator technology was implemented on the basis of

4412: 742: 4395:. Typically, particles (including biological objects such as cells, bacteria, DNA/RNA) drift towards the cold - resulting in particle repulsion using optical tweezers. Overcoming this limitation, different techniques such as beam shaping and solution modification with electrolytes and surfactants were used to successfully trap the objects. Laser cooling was also achieved with Ytterbium-doped yttrium lithium fluoride crystals to generate cold spots using lasers to achieve trapping with reduced 421: 2399:

proportional to the gradient along the intensity of the beam. In other words, the gradient force described here tends to attract the particle to the region of highest intensity. In reality, the scattering force of the light works against the gradient force in the axial direction of the trap, resulting in an equilibrium position that is displaced slightly downstream of the intensity maximum. Under the Rayleigh approximation, we can also write the scattering force as

433: 4719:). The resulting evanescent field has a directional sense and will propel microparticles along its propagating path. This work was first pioneered by S. Kawata and T. Sugiura, in 1992, who showed that the field can be coupled to the particles in proximity on the order of 100 nanometers. This direct coupling of the field is treated as a type of photon tunnelling across the gap from prism to microparticles. The result is a directional optical propelling force. 9125: 4736:

study by Statsenko et al. described optical force enhancement by molecular vibrational resonance by exciting the stretching mode of Si-O-Si bond at 9.3 μm. It is shown that silica microspheres containing significant Si-O-Si bond move up to ten times faster than polystyrene microspheres due to molecular vibrational resonance. Moreover, this same group also investigated the possibility of optical force chromatography based on molecular vibrational resonance.

4623: 4647:. In this method, a suspension of biologic cells is sorted into two or more containers, based upon specific fluorescent characteristics of each cell during an assisted flow. By using an electrical charge that the cell is "trapped" in, the cells are then sorted based on the fluorescence intensity measurements. The sorting process is undertaken by an electrostatic deflection system that diverts cells into containers based upon their charge. 4474:

translational freedom. This can be done by translating the first of the two lenses labelled as "Beam Steering" in the figure. For example, translation of that lens in the lateral plane will result in a laterally deflected beam from what is drawn in the figure. If the distance between the beam steering lenses and the objective is chosen properly, this will correspond to a similar deflection before entering the objective and a resulting

1085:{\displaystyle {\begin{aligned}\mathbf {F} &=q\left(\mathbf {E} (\mathbf {x} _{1})-\mathbf {E} (\mathbf {x} _{2})+{\frac {d(\mathbf {x} _{1}-\mathbf {x} _{2})}{dt}}\times \mathbf {B} \right)\\&=q\left(\mathbf {E} (\mathbf {x} _{1})+\left((\mathbf {x} _{1}-\mathbf {x} _{2})\cdot \nabla \right)\mathbf {E} -\mathbf {E} (\mathbf {x} _{1})+{\frac {d(\mathbf {x} _{1}-\mathbf {x} _{2})}{dt}}\times \mathbf {B} \right).\\\end{aligned}}} 2675: 191:. In an interview, Steven Chu described how Ashkin had first envisioned optical tweezing as a method for trapping atoms. Ashkin was able to trap larger particles (10 to 10,000 nanometers in diameter) but it fell to Chu to extend these techniques to the trapping of neutral atoms (0.1 nanometers in diameter) using resonant laser light and a magnetic gradient trap (cf. 3793: 4740:

the first time measured using a photonic force microscope, the total force magnitude being found 40 times stronger compared to a normal evanescent wave. By patterning the surface with gold microscopic islands it is possible to have selective and parallel trapping in these islands. The forces of the latter optical tweezers lie in the femtonewton range.

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light far exceeds the particle dimensions, the particles can be treated as electric dipoles in an electric field. For optical trapping of dielectric objects of dimensions within an order of magnitude of the trapping beam wavelength, the only accurate models involve the treatment of either time dependent or time harmonic

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on chromosome structure and dynamics. In 2003 the techniques of optical tweezers were applied in the field of cell sorting; by creating a large optical intensity pattern over the sample area, cells can be sorted by their intrinsic optical characteristics. Optical tweezers have also been used to probe the

168:. Years later, Ashkin and colleagues reported the first observation of what is now commonly referred to as an optical tweezer: a tightly focused beam of light capable of holding microscopic particles stable in three dimensions. In 2018, Ashkin was awarded the Nobel Prize in Physics for this development. 472:

If the particle is located at the center of the beam, then individual rays of light are refracting through the particle symmetrically, resulting in no net lateral force. The net force in this case is along the axial direction of the trap, which cancels out the scattering force of the laser light. The

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The manipulation/tweezing process is done by the variations between the electric field actuated by the light pattern. The particles will be either attracted or repelled from the actuated point due to its induced electrical dipole. Particles suspended in a liquid will be susceptible to the electrical

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in the sample plane. The position of the beam waist, that is the focus of the optical trap, can be adjusted by an axial displacement of the initial lens. Such an axial displacement causes the beam to diverge or converge slightly, the result of which is an axially displaced position of the beam waist

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mode) profile intensity. In this case, if the particle is displaced from the center of the beam, as in the right part of the figure, the particle has a net force returning it to the center of the trap because more intense beams impart a larger momentum change towards the center of the trap than less

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In addition to keeping the bead in the center of the laser, a focused laser also keeps the bead in a fixed axial position: The momentum change of the focused rays causes a force towards the laser focus, both when the bead is in front (left image) or behind (right image) the laser focus. So, the bead

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This allows applications such as measuring: protein/DNA localization binding, protein folding, condensation, motor protein force generation, visualization of cytoskeletal filaments and motor dynamics, microtubule dynamics, manipulating liquid droplet (rheology) or fusion. These setups are difficult

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In recent studies, the evanescent field generated by mid-infrared laser has been used to sort particles by molecular vibrational resonance selectively. Mid-infrared light is commonly used to identify molecular structures of materials because the vibrational modes exist in the mid-infrared region. A

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In the last two decades, optical forces are combined with thermophoretic forces to enable trapping at reduced laser powers, thus resulting in minimized photon damage. By introducing light-absorbing elements (either particles or substrates), microscale temperature gradients are created, resulting in

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Since the scattering is isotropic, the net momentum is transferred in the forward direction. On the quantum level, we picture the gradient force as forward Rayleigh scattering in which identical photons are created and annihilated concurrently, while in the scattering (radiation) force the incident

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When the bead is displaced from the beam center (right image), the larger momentum change of the more intense rays cause a net force to be applied back toward the center of the laser. When the bead is laterally centered on the beam (left image), the resulting lateral force is zero. But an unfocused

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For quantitative scientific measurements, most optical traps are operated in such a way that the dielectric particle rarely moves far from the trap center. The reason for this is that the force applied to the particle is linear with respect to its displacement from the center of the trap as long as

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Optical tweezers have proven useful in other areas of biology as well. They are used in synthetic biology to construct tissue-like networks of artificial cells, and to fuse synthetic membranes together to initiate biochemical reactions. They are also widely employed in genetic studies and research

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Another approach that has been recently proposed makes use of surface plasmons, which is an enhanced evanescent wave localized at a metal/dielectric interface. The enhanced force field experienced by colloidal particles exposed to surface plasmons at a flat metal/dielectric interface has been for

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from the optical lattice point. By shifting the arrangement of the optical lattice point, there is a preferred optical path where the optical forces are dominant and biased. With the aid of the flow of the cells, there is a resultant force that is directed along that preferred optical path. Hence,

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Optical traps are very sensitive instruments and are capable of the manipulation and detection of sub-nanometer displacements for sub-micron dielectric particles. For this reason, they are often used to manipulate and study single molecules by interacting with a bead that has been attached to that

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While earlier version of fiber-based laser traps exclusively used single mode beams, M. Kreysing and colleagues recently showed that the careful excitation of further optical modes in a short piece of optical fiber allows the realization of non-trivial trapping geometries. By this the researchers

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When a cluster of microparticles are trapped within a monochromatic laser beam, the organization of the microparticles within the optical trapping is heavily dependent on the redistributing of the optical trapping forces amongst the microparticles. This redistribution of light forces amongst the

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In the optically actuated sorting process, the cells are flowed through into an optical landscape i.e. 2D or 3D optical lattices. Without any induced electrical charge, the cells would sort based on their intrinsic refractive index properties and can be re-configurability for dynamic sorting. An

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On the other hand, if the ends of the fiber are not moulded, the laser exiting the fiber will be diverging and thus a stable optical trap can only be realised by balancing the gradient and the scattering force from two opposing ends of the fiber. The gradient force will trap the particles in the

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Proper explanation of optical trapping behavior depends upon the size of the trapped particle relative to the wavelength of light used to trap it. In cases where the dimensions of the particle are much greater than the wavelength, a simple ray optics treatment is sufficient. If the wavelength of

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Wu transformed the optical energy from low powered light emitting diodes (LED) into electrical energy via a photoconductive surface. The idea is to allow the LED to switch on and off the photoconductive material via its fine projection. As the optical pattern can be easily transformable through

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is the relative refractive index between the particle and the medium. The square of the magnitude of the electric field is equal to the intensity of the beam as a function of position. Therefore, the result indicates that the force on the dielectric particle, when treated as a point dipole, is

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One clear advantage is that the electrical conductivity is different between different kinds of cells. Living cells have a lower conductive medium while the dead ones have minimum or no conductive medium. The system may be able to manipulate roughly 10,000 cells or particles at the same time.

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A typical setup uses one laser to create one or two traps. Commonly, two traps are generated by splitting the laser beam into two orthogonally polarized beams. Optical tweezing operations with more than two traps can be realized either by time-sharing a single laser beam among several optical

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of the objective will result in a tighter, diffraction-limited spot. While lateral translation of the trap relative to the sample can be accomplished by translation of the microscope slide, most tweezer setups have additional optics designed to translate the beam to give an extra degree of

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used a spatial light modulator to project an intensity pattern to enable the optical sorting process. K. Xiao and D. G. Grier applied holographic video microscopy to demonstrate that this technique can sort colloidal spheres with part-per-thousand resolution for size and refractive index.

4563:, such holographic optical traps also can move objects in three dimensions. Advanced forms of holographic optical traps with arbitrary spatial profiles, where smoothness of the intensity and the phase are controlled, find applications in many areas of science, from micromanipulation to 3561: 2301: 290:

Dielectric objects are attracted to the center of the beam, slightly above the beam waist, as described in the text. The force applied on the object depends linearly on its displacement from the trap center just as with a simple spring system. It is a restoring force and thus equal to

369:: photons that are absorbed or scattered by the tiny dielectric particle impart momentum to the dielectric particle. This is known as the scattering force and results in the particle being displaced slightly downstream from the exact position of the beam waist, as seen in the figure. 364:

varies rapidly in space. Dielectric particles are attracted along the gradient to the region of strongest electric field, which is the center of the beam. The laser light also tends to apply a force on particles in the beam along the direction of beam propagation. This is due to

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to build and traditionally are found in non correlated 'academic' setups. In the recent years even home builders (both biophysics and general biologists) are converting to the alternative and are acquiring total correlated solution with easy data acquisition and data analysis.

1971:, which describes the power per unit area passing through a surface. Since the power of the laser is constant when sampling over frequencies much longer than the frequency of the laser's light ~10 Hz, the derivative of this term averages to zero and the force can be written as 6207:

Bluvstein, Dolev; Evered, Simon J.; Geim, Alexandra A.; Li, Sophie H.; Zhou, Hengyun; Manovitz, Tom; Ebadi, Sepehr; Cain, Madelyn; Kalinowski, Marcin; Hangleiter, Dominik; Ataides, J. Pablo Bonilla; Maskara, Nishad; Cong, Iris; Gao, Xun; Rodriguez, Pedro Sales (2023-12-06).

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that creates well-defined optical potential wells (replacing the waveguide). This means that particles are propelled by the evanescent field while being trapped by the linear bright fringes. At the moment, there are scientists working on focused evanescent fields as well.

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Competition of the forces in the sorting environment need fine tuning to succeed in high efficient optical sorting. The need is mainly with regards to the balance of the forces; drag force due to fluid flow and optical gradient force due to arrangement of intensity spot.

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First, the vector equality will be inserted for the first term in the force equation above. Maxwell's equation will be substituted in for the second term in the vector equality. Then the two terms which contain time derivatives can be combined into a single term.

1960: 4825:. Such instruments are particularly useful when it comes to studying single or small numbers of biological molecules that have been fluorescently labelled, or in applications in which fluorescence is used to track and visualize objects that are to be trapped. 7549:

Bowman, D.; Harte, T. L.; Chardonnet, V.; Groot, C. De; Denny, S. J.; Goc, G. Le; Anderson, M.; Ireland, P.; Cassettari, D. (1169). "High-fidelity phase and amplitude control of phase-only computer generated holograms using conjugate gradient minimisation".

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This approach has been extended for simultaneous sensing and imaging of dynamic protein complexes using long and strong tethers generated by a highly efficient multi-step enzymatic approach and applied to investigations of disaggregation machines in action.

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optical force comes from the scattering force of the two counter propagating beams emerging from the two fibers. The equilibrium z-position of such a trapped bead is where the two scattering forces equal each other. This work was pioneered by A. Constable

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While alternatives are available, perhaps the simplest method for position detection involves imaging the trapping laser exiting the sample chamber onto a quadrant photodiode. Lateral deflections of the beam are measured similarly to how it is done using

1198: 4708:. This "leaking" of light fades off at an exponential rate. The evanescent field has found a number of applications in nanometer resolution imaging (microscopy); optical micromanipulation (optical tweezers) are becoming ever more relevant in research. 4234: 2670:{\displaystyle \mathbf {F} _{\text{scat}}(\mathbf {r} )={\frac {k^{4}\alpha ^{2}}{6\pi cn_{0}^{3}\epsilon _{0}^{2}}}I(\mathbf {r} ){\hat {z}}={\frac {8\pi n_{0}k^{4}a^{6}}{3c}}\left({\frac {m^{2}-1}{m^{2}+2}}\right)^{2}I(\mathbf {r} ){\hat {z}}.} 2691:

A useful way to study the interaction of an atom in a Gaussian beam is to look at the harmonic potential approximation of the intensity profile the atom experiences. In the case of the two-level atom, the potential experienced is related to its

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In cases where the diameter of a trapped particle is significantly greater than the wavelength of light, the trapping phenomenon can be explained using ray optics. As shown in the figure, individual rays of light emitted from the laser will be

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Lin, Linhan; Wang, Mingsong; Peng, Xiaolei; Lissek, Emanuel N.; Mao, Zhangming; Scarabelli, Leonardo; Adkins, Emily; Coskun, Sahin; Unalan, Husnu Emrah; Korgel, Brian A.; Liz-Marzán, Luis M.; Florin, Ernst-Ludwig; Zheng, Yuebing (April 2018).

3135: 1433: 4317: 4120: 1596: 260:. A bio-molecular assay in which clusters of ligand coated nano-particles are both optically trapped and optically detected after target molecule induced clustering was proposed in 2011 and experimentally demonstrated in 2013. 6133:

Scholl, Pascal; Schuler, Michael; Williams, Hannah J.; Eberharter, Alexander A.; Barredo, Daniel; Schymik, Kai-Niklas; Lienhard, Vincent; Henry, Louis-Paul; Lang, Thomas C.; Lahaye, Thierry; Läuchli, Andreas M. (2021-07-08).

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A photograph of a nanoparticle (diameter 103 nm) trapped by an optical tweezer. The nanoparticle can be seen as the tiny bright spot in the middle. For additional control two copper electrodes are placed above and below the

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For a shiny object, such as a metallic micro-sphere, stable optical levitation has not been achieved. Optical levitation of a macroscopic object is also theoretically possible, and can be enhanced with nano-structuring.

4789:"The system was able to move live E. coli bacteria and 20-micrometre-wide particles, using an optical power output of less than 10 microwatts. This is one-hundred-thousandth of the power needed for optical tweezers". 3788:{\displaystyle {\frac {1}{2!}}{\frac {\partial ^{2}U}{\partial z^{2}}}{\Biggr |}_{r,z=0}z^{2}={\frac {\alpha }{2\epsilon _{0}c}}{\frac {2P_{0}\lambda ^{2}}{\pi ^{3}w_{0}^{6}}}z^{2}={\frac {1}{2}}m\omega _{z}^{2}z^{2}} 3551: 3226: 7762:

Jochen Guck; Stefan Schinkinger; Bryan Lincoln; Falk Wottawah; Susanne Ebert; Maren Romeyke; Dominik Lenz; Harold M. Erickson; Revathi Ananthakrishnan; Daniel Mitchell; Josef Käs; Sydney Ulvick; Curt Bilby (2005).

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A recent updated version of the evanescent field optical tweezers makes use of extended optical landscape patterns to simultaneously guide a large number of particles into a preferred direction without using a

4015:{\displaystyle {\frac {1}{2!}}{\frac {\partial ^{2}U}{\partial r^{2}}}{\Biggr |}_{r,z=0}r^{2}={\frac {\alpha }{2\epsilon _{0}c}}{\frac {4P_{0}}{\pi w_{0}^{4}}}r^{2}={\frac {1}{2}}m\omega _{r}^{2}r^{2}} 508: 3290: 4529:

Optical tweezers based on Laguerre-Gaussian beams have the unique capability of trapping particles that are optically reflective and absorptive. Laguerre-Gaussian beams also possess a well-defined

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photons travel in the same direction and ‘scatter’ isotropically. By conservation of momentum, the particle must accumulate the photons' original momenta, causing a forward force in the latter.

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Ebadi, Sepehr; Wang, Tout T.; Levine, Harry; Keesling, Alexander; Semeghini, Giulia; Omran, Ahmed; Bluvstein, Dolev; Samajdar, Rhine; Pichler, Hannes; Ho, Wen Wei; Choi, Soonwon (2021-07-08).

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atoms in vacuum, mainly for applications in quantum science. Some achievements in this area include trapping of a single atom in 2001, trapping of 2D arrays of atoms in 2002, trapping of

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Interview conducted for internal newsletter at Bell Labs. Contains confirmation of Ashkin as the inventor of optical trapping and provides information on the 1997 Nobel Prize in Physics.

659: 4796:. The strategy is to use light to create a temperature gradient and exploit the thermophoretic migration of matter for optical trapping. The team further integrated thermophoresis with 1369:{\displaystyle {\begin{aligned}\mathbf {F} &=\left(\mathbf {p} \cdot \nabla \right)\mathbf {E} +{\frac {d\mathbf {p} }{dt}}\times \mathbf {B} \\&=\alpha \left,\\\end{aligned}}} 333: 5154:

Rørvig-Lund, Andreas; Bahadori, Azra; Semsey, Szabolcs; Bendix, Poul Martin; Oddershede, Lene B. (2015-05-29). "Vesicle Fusion Triggered by Optically Heated Gold Nanoparticles".

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Both zero and higher order Bessel Beams also possess a unique tweezing ability. They can trap and rotate multiple particles that are millimeters apart and even around obstacles.

4454:. Perhaps the most important consideration in optical tweezer design is the choice of the objective. A stable trap requires that the gradient force, which is dependent upon the 4340:

of a focused laser beam of enough intensity counters the downward force of gravity while also preventing lateral (side to side) and vertical instabilities to allow for a stable

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Liberale C, Minzioni P, Bragheri F, De Angelis F, Di Fabrizio E, Cristiani I (2007). "Miniaturized all-fibre probe for three-dimensional optical trapping and manipulation".

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Visualization of the sample plane is usually accomplished through illumination via a separate light source coupled into the optical path in the opposite direction using

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Smalley, D. E.; Nygaard, E.; Squire, K.; Van Wagoner, J.; Rasmussen, J.; Gneiting, S.; Qaderi, K.; Goodsell, J.; Rogers, W.; Lindsey, M.; Costner, K. (January 2018).

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Noom, Maarten C; van den Broek, Bram; van Mameren, Joost; Wuite, Gijs J L (11 November 2007). "Visualizing single DNA-bound proteins using DNA as a scanning probe".

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there is a relationship of the flow rate with the optical gradient force. By adjusting the two forces, one will be able to obtain a good optical sorting efficiency.

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The main mechanism for sorting is the arrangement of the optical lattice points. As the cell flow through the optical lattice, there are forces due to the particles

1534:{\displaystyle \left(\mathbf {E} \cdot \nabla \right)\mathbf {E} =\nabla \left({\frac {1}{2}}E^{2}\right)-\mathbf {E} \times \left(\nabla \times \mathbf {E} \right)} 2348: 2847: 3462: 3436: 7326: 4249: 271:

entangled pairs in 2010, trapping precisely assembled 2-dimensional arrays of atoms in 2016 and 3-dimensional arrays in 2018. These techniques have been used in

4399:. The sample temperature has also been reduced to achieve optical trapping for a significantly increased selection of particles using optothermal tweezers for 3410: 3390: 2321: 1144: 4035: 6896:

Kollipara, Pavana Siddhartha; Li, Xiuying; Li, Jingang; Chen, Zhihan; Ding, Hongru; Kim, Youngsun; Huang, Suichu; Qin, Zhenpeng; Zheng, Yuebing (2023-08-23).

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Guccione, G.; M. Hosseini; S. Adlong; M. T. Johnsson; J. Hope; B. C. Buchler; P. K. Lam (July 2013). "Scattering-Free Optical Levitation of a Cavity Mirror".

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Researchers have worked to convert optical tweezers from large, complex instruments to smaller, simpler ones, for use by those with smaller research budgets.

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intense beams, which impart a smaller momentum change away from the trap center. The net momentum change, or force, returns the particle to the trap center.

4446:(1064 nm wavelength) is a common choice of laser for working with biological specimens. This is because such specimens (being mostly water) have a low 164:

The detection of optical scattering and the gradient forces on micron sized particles was first reported in 1970 by Arthur Ashkin, a scientist working at

4748: 2126:{\displaystyle \mathbf {F} ={\frac {1}{2}}\alpha \nabla E^{2}={\frac {2\pi n_{1}a^{3}}{c}}\left({\frac {m^{2}-1}{m^{2}+2}}\right)\nabla I(\mathbf {r} ),} 4027:

This means that when solving for the harmonic frequencies (or trap frequencies when considering optical traps for atoms), the frequencies are given as:

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cancellation of this axial gradient force with the scattering force is what causes the bead to be stably trapped slightly downstream of the beam waist.

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To approximate this Gaussian potential in both the radial and axial directions of the beam, the intensity profile must be expanded to second order in

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Righini M, Volpe G, Girard C, Petrov D, Quidant R (2008). "Surface Plasmon Optical Tweezers: Tunable Optical Manipulation in the Femtonewton Range".

6661: 5498: 5615:"Micro-optical Realization of Arrays of Selectively Addressable Dipole Traps: A Scalable Configuration for Quantum Computation with Atomic Qubits" 8742:

Avellaneda MJ, Franke KB, Sunderlikova V, Bukau B, Mogk A, Tans SJ (2020). "Processive extrusion of polypeptide loops by a Hsp100 disaggregase".

5938: 6418: 3467: 2693: 2296:{\displaystyle \mathbf {p} =\alpha \mathbf {E} (\mathbf {r} ,t)=4\pi n_{1}^{2}\epsilon _{0}a^{3}(m^{2}-1)/(m^{2}+2)\mathbf {E} (\mathbf {r} ,t)} 449:

as it enters and exits the dielectric bead. As a result, the ray will exit in a direction different from which it originated. Since light has a

3147: 7445:"Rapid phase calibration of a spatial light modulator using novel phase masks and optimization of its efficiency using an iterative algorithm" 4575:

The standard fiber optical trap relies on the same principle as the optical trapping, but with the Gaussian laser beam delivered through an

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The standard tweezers works with the trapping laser propagated in the direction of gravity and the inverted tweezers works against gravity.

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level; optical trap force-spectroscopy has since led to greater understanding of the stochastic nature of these force-generating molecules.

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The force on the dipole can be calculated by substituting two terms for the electric field in the equation above, one for each charge. The

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Other than 'standard' fluorescence optical tweezers are now being built with multiple color Confocal, Widefield, STED, FRET, TIRF or IRM.

4486:. This light is incident on a CCD camera and can be viewed on an external monitor or used for tracking the trapped particle position via 8062: 5089:

Bolognesi, Guido; Friddin, Mark S.; Salehi-Reyhani, Ali; Barlow, Nathan E.; Brooks, Nicholas J.; Ces, Oscar; Elani, Yuval (2018-05-14).

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Ashkin A, Dziedzic JM, Bjorkholm JE, Chu S (1986). "Observation of a single-beam gradient force optical trap for dielectric particles".

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and Joseph M. Dziedzic demonstrated the first application of the technology to the biological sciences, using it to trap an individual

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Li, Jingang; Chen, Zhihan; Liu, Yaoran; Kollipara, Pavana Siddhartha; Feng, Yichao; Zhang, Zhenglong; Zheng, Yuebing (2021-06-25).

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The second term in the last equality is the time derivative of a quantity that is related through a multiplicative constant to the

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Ladavac, K.; Kasza, K.; Grier, D. (2004). "Sorting mesoscopic objects with periodic potential landscapes: Optical fractionation".

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Xiao, Ke; Grier, David G. (2010). "Multidimensional Optical Fractionation of Colloidal Particles with Holographic Verification".

6035: 609:{\displaystyle \mathbf {F_{1}} =q\left(\mathbf {E} (\mathbf {x} _{1})+{\frac {d\mathbf {x_{1}} }{dt}}\times \mathbf {B} \right).} 232:

are ubiquitous in biology, and are responsible for locomotion and mechanical action within the cell. Optical traps allowed these

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The Optical Cell Rotator is a fiber based laser trap that can hold and precisely orient living cells for tomographic microscopy.

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at this wavelength. A low absorption is advisable so as to minimise damage to the biological material, sometimes referred to as

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In cases where the diameter of a trapped particle is significantly smaller than the wavelength of light, the conditions for

4727:. It is termed as Lensless Optical Trapping ("LOT"). The orderly movement of the particles is aided by the introduction of 2797:{\displaystyle \mathbf {\Delta E} _{\text{AC Stark}}={\frac {3\pi c^{2}\Gamma }{2\omega _{0}^{3}\delta }}\mathbf {I(r,z)} } 5766:

Isenhower, L.; Urban, E.; Zhang, X. L.; Gill, A. T.; Henage, T.; Johnson, T. A.; Walker, T. G.; Saffman, M. (2010-01-08).

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Lin S.; K. B. Crozier (2013). "Trapping-Assisted Sensing of Particles and Proteins Using On-Chip Optical Microcavities".

4644: 8599: 4688:) for an optical sorting machine. This new technology could rival the conventional fluorescence-activated cell sorting. 690: 7296: 7185:"Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity" 4760: 2138:

where in the second part we have included the induced dipole moment (in MKS units) of a spherical dielectric particle:

1955:{\displaystyle {\begin{aligned}\mathbf {F} &=\alpha \left\\&=\alpha \left\\&=\alpha \left.\\\end{aligned}}} 4458:

of the objective, be greater than the scattering force. Suitable objectives typically have an NA between 1.2 and 1.4.

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In order to levitate the particle in air, the downward force of gravity must be countered by the forces stemming from

1384: 9159: 4793: 4530: 4241:

so that the relative trap frequencies for the radial and axial directions as a function of only beam waist scale as:

275:

to obtain programmable arrays of 196 and 256 atoms in 2021 and represent a promising platform for quantum computing.

7881:

Kreysing, M.; Ott, D.; Schmidberger, M. J.; Otto, O.; Schürmann, M.; Martín-Badosa, E.; Whyte, G.; Guck, J. (2014).

8824: 7883:"Dynamic operation of optical fibres beyond the single-mode regime facilitates the orientation of biological cells" 4800:

to develop opto-refrigerative tweezers to avoid thermal damages for noninvasive optical trapping and manipulation.

213: 7339:

Ladavac K, Grier DG (2004). "Microoptomechanical pump assembled and driven by holographic optical vortex arrays".

8555:

Thirunamachandran, T. (1980-06-10). "Intermolecular interactions in the presence of an intense radiation field".

7765:"Optical Deformability as an Inherent Cell Marker for Testing Malignant Transformation and Metastatic Competence" 6255:"Optical trapping, manipulation, and sorting of cells and colloids in microfluidic systems with diode laser bars" 5962:

Barredo, Daniel; Lienhard, Vincent; de Léséleuc, Sylvain; Lahaye, Thierry; Browaeys, Antoine (5 September 2018).

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Kawata, S; Sugiura, T (1992). "Movement of micrometer-sized particles in the evanescent field of a laser beam".

4533:

that can rotate particles. This is accomplished without external mechanical or electrical steering of the beam.

8994: 8693:"Simultaneous sensing and imaging of individual biomolecular complexes enabled by modular DNA–protein coupling" 4506:. However a number of other beam types have been used to trap particles, including high order laser beams i.e. 4368: 5693:

Wilk, T.; Gaëtan, A.; Evellin, C.; Wolters, J.; Miroshnychenko, Y.; Grangier, P.; Browaeys, A. (2010-01-08).

1422: 6604: 4382:

Materials that have been successfully levitated include Black liquor, aluminum oxide, tungsten, and nickel.

8642:

High-Resolution "Fleezers": Dual-Trap Optical Tweezers Combined with Single-Molecule Fluorescence Detection

5864:

Barredo, Daniel; de Léséleuc, Sylvain; Lienhard, Vincent; Lahaye, Thierry; Browaeys, Antoine (2016-11-25).

294: 6948: 389:

the displacement is small. In this way, an optical trap can be compared to a simple spring, which follows

9184: 9050: 6466:

Harada Y, Asakura T (1996). "Radiation Forces on a dielectric sphere in the Rayleigh Scattering Regime".

5451:"Optical detection of target molecule induced aggregation of nanoparticles by means of high-Q resonators" 4351:

spheres, oil or water droplets, are used in this type of experiment. The laser radiation can be fixed in

4229:{\displaystyle \omega _{z}={\sqrt {\frac {2\alpha P_{0}\lambda ^{2}}{m\pi ^{3}\epsilon _{0}cw_{0}^{6}}}}} 268: 9164: 8854: 4711:

In optical tweezers, a continuous evanescent field can be created when light is propagating through an

4555:

tweezers, or by diffractively splitting the beam into multiple traps. With acousto-optic deflectors or

1418: 454: 81:

between particle and surrounding medium. Levitation is possible if the force of the light counters the

8171:

Darmawan, Yoshua Albert; Goto, Takuma; Yanagishima, Taiki; Fuji, Takao; Kudo, Tetsuhiro (2023-08-17).

5839: 1100: 9179: 7824:

Moritz Kreysing; Tobias Kießling; Anatol Fritsch; Christian Dietrich; Jochen Guck; Josef Käs (2008).

7061: 4767:

optical projection, this method allows a high flexibility of switching different optical landscapes.

4716: 4705: 4347:

Micrometer sized (from several to 50 micrometers in diameter) transparent dielectric spheres such as

8109: 7444: 4953: 4763:

Professor of electrical engineering and computer sciences invented the new optoelectronic tweezers.

4635:, allowing to dynamically reconfigure the optical trap during operation and adapt it to the sample. 4419:

The most basic optical tweezer setup will likely include the following components: a laser (usually

7111: 2353: 366: 6947:

D. J. Stevenson; T. K. Lake; B. Agate; V. Gárcés-Chávez; K. Dholakia; F. Gunn-Moore (2006-10-16).

5215:"Genetic Material Manipulation and Modification by Optical Trapping and Nanosurgery-A Perspective" 4792:

Another notably new type of optical tweezers is optothermal tweezers invented by Yuebing Zheng at

1171: 1149: 664: 148:(to study the interaction of single particles with light). The development of optical tweezing by 4822: 4560: 4542:

can be driven by these unique optical beams due to their intrinsic rotating mechanism due to the

4515: 4463: 3130:{\displaystyle I(r,z)=I_{0}\left({\frac {w_{0}}{w(z)}}\right)^{2}e^{-{\frac {2r^{2}}{w^{2}(z)}}}} 2852: 8049: 2902: 9024: 8844: 8104: 7184: 4948: 4860: 4447: 4428: 1381:

where in the second equality, it has been assumed that the dielectric particle is linear (i.e.

184: 153: 7823: 7234: 5613:

Dumke, R.; Volk, M.; Müther, T.; Buchkremer, F. B. J; Birkl, G.; Ertmer, W. (August 8, 2002).

348:

particles, and even individual atoms, by exerting extremely small forces via a highly focused

9189: 9169: 8912: 8066: 7672:"Manipulation and arrangement of biological and dielectric particles by a lensed fiber probe" 6655: 5492: 5038: 4507: 2961: 2928: 2879: 2812: 493: 453:

associated with it, this change in direction indicates that its momentum has changed. Due to

36: 8141: 5041:(2004), Institute of International Studies, UC Berkeley. Last accessed on September 2, 2006. 9019: 8902: 8890: 8817: 8751: 8614: 8564: 8521: 8464: 8407: 8288: 8227: 8096: 8008: 7947: 7894: 7837: 7776: 7736: 7683: 7642: 7569: 7513: 7466: 7358: 7259: 7199: 7133: 7017: 6960: 6688: 6619: 6605:"Self-stabilizing photonic levitation and propulsion of nanostructured macroscopic objects" 6561: 6514: 6475: 6440: 6323: 6266: 6157: 6083: 5985: 5887: 5789: 5716: 5667: 5560: 5462: 5339: 5163: 5102: 5051:

Ashkin A, Dziedzic JM (1987). "Optical trapping and manipulation of viruses and bacteria".

4996: 4940: 4903: 4855: 4680:

Scientists at the University of St. Andrews have received considerable funding from the UK

4312:{\displaystyle {\frac {\omega _{r}}{\omega _{z}}}={\sqrt {2}}{\frac {w_{0}\pi }{\lambda }}} 2326: 622: 203: 192: 145: 7124:

Swartzlander, G. A.; Gahagan, K. T. (1996-06-01). "Optical vortex trapping of particles".

6312:"Differential detection of dual traps improves the spatial resolution of optical tweezers" 5767: 5694: 5547:

Schlosser, Nicolas; Reymond, Georges; Protsenko, Igor; Grangier, Philippe (28 June 2001).

2832: 8: 9174: 9149: 9070: 8989: 8929: 8849: 5614: 4115:{\displaystyle \omega _{r}={\sqrt {\frac {4\alpha P_{0}}{\pi \epsilon _{0}cmw_{0}^{4}}}}} 3441: 3415: 485: 188: 8755: 8618: 8568: 8525: 8468: 8411: 8292: 8231: 8100: 8012: 7951: 7898: 7841: 7780: 7740: 7687: 7646: 7573: 7517: 7502:"Freestyle 3D laser traps: tools for studying light-driven particle dynamics and beyond" 7470: 7362: 7263: 7203: 7137: 7081: 7021: 6964: 6932: 6692: 6623: 6565: 6518: 6479: 6444: 6327: 6270: 6161: 6087: 5989: 5891: 5793: 5720: 5671: 5564: 5466: 5343: 5167: 5106: 5000: 4944: 4907: 2896:

is the detuning or difference between the laser frequency and the transition frequency.

180: 9154: 8775: 8719: 8692: 8668: 8485: 8452: 8451:

Jingang Li; Z. Chen; Y. Liu; P. S. Kollipara; Y. Feng; Z. Zhang; Yuebing Zheng (2021).

8428: 8395: 8312: 8261: 8172: 8032: 7998: 7971: 7915: 7882: 7863: 7797: 7761: 7709: 7632: 7601: 7559: 7482: 7456: 7425: 7382: 7348: 7275: 7249: 7165: 7093: 7038: 7005: 6981: 6873: 6824: 6766: 6733: 6643: 6585: 6551: 6395: 6370: 6346: 6311: 6292: 6217: 6189: 6147: 6115: 6073: 6017: 5975: 5919: 5877: 5821: 5779: 5748: 5706: 5626: 5592: 5426: 5401: 5363: 5300: 5273: 5254: 5241: 5214: 5195: 5131: 5090: 4455: 4424: 4423:), a beam expander, some optics used to steer the beam location in the sample plane, a 4337: 3395: 3375: 2306: 1591:{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}} 1129: 734:

Taking into account that the two charges have opposite signs, the force takes the form

440:

will stay slightly behind the focus, where this force compensates the scattering force.

397: 353: 225: 67: 19: 8509: 8356: 5865: 286: 9090: 8964: 8939: 8779: 8767: 8724: 8673: 8653: 8580: 8537: 8490: 8433: 8304: 8253: 8200: 8192: 8173:"Mid-Infrared Optical Force Chromatography of Microspheres Containing Siloxane Bonds" 8157: 8140:

Statsenko, Anna; Darmawan, Yoshua Albert; Fuji, Takao; Kudo, Tetsuhiro (2022-11-15).

8122: 8024: 7963: 7920: 7855: 7810: 7802: 7701: 7655: 7620: 7593: 7585: 7531: 7486: 7417: 7374: 7215: 7157: 7149: 7085: 7043: 6986: 6919: 6897: 6878: 6860: 6840: 6811: 6791: 6771: 6753: 6714: 6706: 6647: 6635: 6577: 6487: 6400: 6351: 6284: 6235: 6209: 6193: 6181: 6173: 6119: 6107: 6099: 6009: 6001: 5911: 5903: 5813: 5805: 5740: 5732: 5584: 5576: 5529: 5480: 5431: 5402:"Single-molecule studies of high-mobility group B architectural DNA bending proteins" 5355: 5305: 5258: 5246: 5199: 5187: 5179: 5136: 5118: 5068: 4966: 4772: 4712: 409: 272: 8316: 8265: 8218:

Volpe G, Quidant R, Badenes G, Petrov D (2006). "Surface Plasmon Radiation Forces".

8036: 7975: 7867: 7713: 7605: 7386: 6589: 6135: 6061: 6021: 5923: 5752: 9100: 9065: 9045: 9014: 8759: 8714: 8704: 8663: 8645: 8622: 8572: 8529: 8480: 8472: 8423: 8415: 8381: 8300: 8296: 8243: 8235: 8184: 8153: 8114: 8020: 8016: 7955: 7910: 7902: 7845: 7792: 7784: 7744: 7691: 7650: 7577: 7521: 7474: 7429: 7409: 7366: 7279: 7267: 7207: 7169: 7141: 7097: 7077: 7033: 7025: 6976: 6968: 6927: 6909: 6868: 6852: 6819: 6803: 6761: 6745: 6696: 6627: 6573: 6569: 6522: 6483: 6448: 6390: 6382: 6341: 6331: 6296: 6274: 6227: 6165: 6091: 5993: 5963: 5895: 5825: 5801: 5797: 5728: 5724: 5675: 5636: 5596: 5568: 5521: 5470: 5421: 5413: 5367: 5347: 5327: 5295: 5285: 5236: 5226: 5171: 5126: 5110: 5060: 5004: 4958: 4911: 4865: 4588: 496:. The force applied on a single charge in an electromagnetic field is known as the 229: 208: 78: 8239: 7478: 7183:

He, H.; Friese, M. E. J.; Heckenberg, N. R.; Rubinsztein-Dunlop, H. (1995-07-31).

5866:"An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays" 5640: 4435:) to measure beam displacements and a microscope illumination source coupled to a 4411: 9128: 9009: 8999: 8810: 7300: 6946: 5388: 5381: 5175: 4697: 4632: 4564: 4499: 4483: 4360: 1968: 237: 129: 8649: 8533: 8188: 7788: 6749: 5212: 4987:

Matthews J.N.A. (2009). "Commercial optical traps emerge from biophysics labs".

4643:

One of the more common cell-sorting systems makes use of flow cytometry through

9105: 9095: 9055: 9004: 8922: 8875: 8859: 8626: 7959: 7621:"Fast universal two-qubit gate for neutral fermionic atoms in optical tweezers" 7211: 6914: 6527: 6502: 6231: 6169: 6095: 5114: 4916: 4891: 4870: 4744: 4543: 4487: 4396: 4392: 4372: 390: 361: 141: 113: 8797: 8763: 8709: 8576: 8419: 6807: 6631: 5997: 5417: 5231: 4782:

See comments by Professor Kishan Dholakia on this new technique, K. Dholakia,

4651:

optical lattice can be created using diffractive optics and optical elements.

9143: 9060: 9040: 8981: 8907: 8584: 8196: 7748: 7589: 7535: 7153: 6923: 6864: 6815: 6757: 6710: 6639: 6239: 6177: 6103: 6005: 5907: 5809: 5736: 5580: 5290: 5183: 5122: 4797: 4728: 4701: 4580: 4576: 4539: 4400: 684: 683:

is the distance between the two charges. For a point dipole, the distance is

497: 461: 264: 257: 249: 217: 199: 176: 149: 133: 74: 7526: 7501: 7325:

McGloin D, Garces-Chavez V, Paterson L, Carruthers T, Melvil H, Dholakia K,

7293: 6336: 5899: 5064: 4367:

focused to a spot size of several tens of micrometers. Phenomena related to

2899:

The intensity of a gaussian beam profile is characterized by the wavelength

9080: 8949: 8944: 8885: 8771: 8728: 8677: 8541: 8494: 8476: 8437: 8308: 8257: 8204: 8142:"Midinfrared Optical Manipulation Based on Molecular Vibrational Resonance" 8126: 8028: 7967: 7924: 7859: 7806: 7705: 7696: 7671: 7597: 7421: 7378: 7370: 7219: 7161: 7065: 7047: 6990: 6882: 6856: 6775: 6718: 6581: 6404: 6355: 6288: 6279: 6254: 6185: 6111: 6013: 5915: 5817: 5744: 5588: 5548: 5533: 5484: 5435: 5359: 5309: 5250: 5191: 5140: 4970: 4818: 4567:. Ultracold atoms could also be used for realization of quantum computers. 4556: 4443: 4431:

to create the trap in the sample plane, a position detector (e.g. quadrant

4420: 4348: 245: 221: 48: 8507: 7089: 6541: 6452: 6431:

Gordon, J. P. (1973). "Radiation Forces and Momenta in Dielectric Media".

6136:"Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms" 5072: 3546:{\displaystyle {\frac {1}{2}}m(\omega _{z}^{2}z^{2}+\omega _{r}^{2}r^{2})} 9110: 8971: 8954: 8934: 8118: 7850: 7825: 7581: 7353: 7145: 6972: 5679: 5655: 5631: 5475: 5450: 5091:"Sculpting and fusing biomimetic vesicle networks using optical tweezers" 4962: 4850: 4523: 3221:{\displaystyle w(z)=w_{0}{\sqrt {1+\left({\frac {z}{z_{R}}}\right)^{2}}}} 457:, there should be an equal and opposite momentum change on the particle. 420: 253: 7254: 6701: 6676: 5351: 344:

Optical tweezers are capable of manipulating nanometer and micron-sized

8959: 8248: 7906: 7235:"Optical alignment and spinning of laser-trapped microscopic particles" 6062:"Quantum phases of matter on a 256-atom programmable quantum simulator" 4663: 4622: 4436: 4432: 4352: 446: 432: 357: 345: 233: 172: 121: 90: 86: 8450: 7413: 7029: 6386: 6036:"Highly programmable quantum simulator operates with up to 256 qubits" 5964:"Synthetic three-dimensional atomic structures assembled atom by atom" 5525: 5008: 4415:

A generic optical tweezer diagram with only the most basic components.

9075: 8917: 8897: 8880: 5695:"Entanglement of Two Individual Neutral Atoms Using Rydberg Blockade" 5572: 5549:"Sub-poissonian loading of single atoms in a microscopic dipole trap" 4817:

In order to simultaneously manipulate and image samples that exhibit

4724: 4356: 165: 7233:

Friese, M. E. J.; Heckenberg, N. R.; Rubinsztein-Dunlop, H. (1998).

7182: 5088: 8691:

Avellaneda MJ, Koers EJ, Minde DP, Sunderlikova V, Tans SJ (2020).

7637: 7564: 7461: 6222: 6152: 6078: 5980: 5882: 5330:, Dholakia K (2003). "Microfluidic sorting in an optical lattice". 4470: 4333: 450: 378: 137: 109: 105: 52: 43:

beam to hold and move microscopic and sub-microscopic objects like

8644:. Methods in Molecular Biology. Vol. 1486. pp. 183–256. 8003: 7726: 7271: 7232: 6556: 6503:"Manipulating particles with light: radiation and gradient forces" 5784: 5711: 4832: 8741: 8640:

Whitley, Kevin D.; Comstock, Matthew J.; Chemla, Yann R. (2017).

7399: 5546: 382: 212:

bacterium. Throughout the 1990s and afterwards, researchers like

101: 82: 8690: 5961: 5863: 6949:"Optically guided neuronal growth at near infrared wavelengths" 6674: 6210:"Logical quantum processor based on reconfigurable atom arrays" 6132: 5153: 4330: 489: 56: 7442: 4892:"Acceleration and Trapping of Particles by Radiation Pressure" 236:

to observe the forces and dynamics of nanoscale motors at the

8833: 6309: 5768:"Demonstration of a Neutral Atom Controlled-NOT Quantum Gate" 5213:

Blázquez-Castro A.; Fernández-Piqueras J.; Santos J. (2020).

4685: 356:. Near the narrowest point of the focused beam, known as the 349: 117: 71: 40: 8393: 5939:"Atomic Eiffel tower looms over quantum computing landscape" 5274:"Laser Scissors and Tweezers to Study Chromosomes: A Review" 352:

beam. The beam is typically focused by sending it through a

8170: 7880: 4666:

that is competing directly with the optical gradient force

4364: 44: 7548: 5039:"Conversations with History: An Interview with Steven Chu" 4930: 4747:

and molecules near the surface of an optical waveguide or

8802: 8217: 8139: 5612: 5448: 5325: 488:

are satisfied and the particle can be treated as a point

374: 228:

to characterize molecular-scale biological motors. These

179:

and trapping neutral atoms. This research earned Chu the

125: 8278: 6732:

Chen, Zhihan; Li, Jingang; Zheng, Yuebing (2022-02-09).

6419:"Novel micromanipulation techniques in optical tweezers" 6252: 5692: 4355:

such as that of an argon ion laser or that of a tunable

428:

laser still causes a force pointing away from the laser.

385:

that interact with it are commonly studied in this way.

8508:

Burns M.M.; Golovchenko J-M.; Golovchenko J.A. (1989).

7114:(August 22, 2006). Last accessed on September 12, 2006. 6253:

Applegate, Jr. R. W.; Vestad, Tor; et al. (2004).

6059: 5765: 3553:. These expansions are evaluated assuming fixed power. 3285:{\displaystyle z_{R}={\frac {\pi w_{0}^{2}}{\lambda }}} 396:

Further information on the light scattering force:

8063:"Evanescent Field Polarization and Intensity Profiles" 7070:

Annual Review of Biophysics and Biomolecular Structure

6310:

Moffitt JR, Chemla YR, Izhaky D, Bustamante C (2006).

4469:

Expanding the beam emitted from the laser to fill the

3360:{\displaystyle P_{0}={\frac {1}{2}}\pi I_{0}w_{0}^{2}} 8639: 6206: 4252: 4135: 4038: 3808: 3564: 3470: 3444: 3418: 3398: 3378: 3305: 3241: 3150: 3002: 2964: 2931: 2905: 2882: 2855: 2835: 2815: 2707: 2410: 2356: 2329: 2309: 2144: 1982: 1615: 1548: 1436: 1417:

In the final steps, two equalities will be used: (1)

1387: 1201: 1174: 1152: 1132: 1103: 745: 693: 667: 631: 511: 297: 175:, would go on to use optical tweezing in his work on 7068:(1994). "Biological Application of Optical Forces". 8633: 8052:, IRC Scotland. Last accessed on September 3, 2006. 7123: 6368: 5511: 4579:. If one end of the optical fiber is molded into a 3464:respectively and equated to the harmonic potential 2686: 6838: 4982: 4980: 4682:Engineering and Physical Sciences Research Council 4344:capable of holding small particles in suspension. 4311: 4228: 4114: 4014: 3787: 3545: 3456: 3430: 3404: 3384: 3359: 3284: 3220: 3129: 2991:. The following formulas define the beam profile: 2983: 2950: 2917: 2888: 2868: 2841: 2821: 2796: 2669: 2390: 2342: 2315: 2295: 2125: 1954: 1590: 1533: 1406: 1368: 1182: 1160: 1138: 1118: 1084: 727:{\displaystyle \mathbf {x} _{1}-\mathbf {x} _{2}.} 726: 675: 653: 608: 327: 8598:Forbes, Kayn A.; Andrews, David L. (2015-05-14). 8554: 7937: 6895: 6788: 5654:Thomas, Jessica; Grondalski, Sonja (2010-01-19). 3861: 3617: 2790: 2778: 9141: 7500:Rodrigo, José A.; Alieva, Tatiana (2015-09-20). 5653: 5084: 5082: 4812: 2829:is the natural line width of the excited state, 1407:{\displaystyle \mathbf {p} =\alpha \mathbf {E} } 479: 6603:Ilic, Ognjen; Atwater, Harry, A. (April 2019). 6500: 6316:Proceedings of the National Academy of Sciences 4986: 4977: 4833:Tweezers combined with other imaging techniques 4549: 4493: 2350:is the index of refraction of the particle and 1126:cancel out. Multiplying through by the charge, 7618: 5399: 5321: 5319: 5050: 4743:The evanescent field can also be used to trap 4617: 4375:have been studied by several research groups. 8818: 8597: 8086: 7499: 6465: 5608: 5606: 5278:Frontiers in Bioengineering and Biotechnology 5219:Frontiers in Bioengineering and Biotechnology 5079: 4570: 4498:The majority of optical tweezers make use of 59:without additional support, it can be called 8331:"Cold-Atom Physics Using Optical Nanofibres" 7338: 7060: 6660:: CS1 maint: multiple names: authors list ( 5497:: CS1 maint: multiple names: authors list ( 5032: 4821:, optical tweezers can be built alongside a 7669: 7303:(2003). Last accessed on September 3, 2006. 7003: 6731: 6602: 6371:"Protein folding and unfolding under force" 5316: 5271: 654:{\displaystyle \mathbf {p} =q\mathbf {d} ,} 8825: 8811: 8600:"Chiral discrimination in optical binding" 8357:"Quantum Networking with Atomic Ensembles" 6898:"Hypothermal opto-thermophoretic tweezers" 5603: 4889: 159: 136:(to study and build materials from single 8718: 8708: 8667: 8484: 8427: 8247: 8177:The Journal of Physical Chemistry Letters 8108: 8002: 7988: 7914: 7849: 7796: 7695: 7654: 7636: 7619:Nemirovsky, Jonathan; Sagi, Yoav (2021). 7563: 7525: 7460: 7352: 7253: 7037: 6980: 6931: 6913: 6872: 6823: 6765: 6700: 6677:"A photophoretic-trap volumetric display" 6555: 6526: 6394: 6345: 6335: 6278: 6221: 6151: 6077: 5979: 5881: 5840:"Atom assembler makes defect-free arrays" 5783: 5710: 5656:"Opening the gate to quantum computation" 5630: 5474: 5425: 5299: 5289: 5240: 5230: 5130: 4952: 4915: 4786:4, 579–580 (01 Aug 2005) News and Views. 425:Ray optics explanation (unfocused laser). 5400:Murugesapillai, D.; et al. (2016). 4621: 4410: 2876:is the frequency of the transition, and 431: 419: 285: 18: 9086:Multiple-prism grating laser oscillator 8394:Linhan Lin, ...; Yuebing Zheng (2018). 7443:A.D. Chandra & A. Banerjee (2020). 7112:"A Practical Guide to Optical Trapping" 4546:and orbital angular momentum of light. 4385: 437:Ray optics explanation (focused laser). 412:using appropriate boundary conditions. 263:Optical tweezers are also used to trap 171:One author of this seminal 1986 paper, 108:(for example to grab and hold a single 9142: 6430: 339: 8806: 8798:Levitating DIAMONDS with a laser beam 7329:. Last accessed on September 3, 2006. 7316:. Last accessed on September 3, 2006. 4603:,1867 (1993), and followed by J.Guck 4324: 328:{\displaystyle -k_{\mathrm {trap} }x} 51:and droplets, in a manner similar to 8363:. California Institute of Technology 8050:"Optical fractionation and sorting." 6734:"Heat-Mediated Optical Manipulation" 6369:Jagannathan, B; Marqusee, S (2013). 4754: 4691: 85:. The trapped particles are usually 7082:10.1146/annurev.bb.23.060194.001335 5936: 360:, the amplitude of the oscillating 13: 8396:"Opto-thermoelectric nanotweezers" 8382:Invention: Soldiers obeying odours 6792:"Opto-thermoelectric nanotweezers" 5449:Witzens, J., Hochberg, M. (2011). 5023:He wrote the book on atom trapping 4803: 3842: 3828: 3598: 3584: 2816: 2745: 2103: 2004: 1886: 1761: 1679: 1650: 1579: 1569: 1549: 1515: 1466: 1450: 1308: 1231: 970: 460:Most optical traps operate with a 316: 313: 310: 307: 224:pioneered the use of optical trap 55:. If the object is held in air or 14: 9201: 8790: 8337:. Vienna University of Technology 4794:The University of Texas at Austin 4771:field gradient, this is known as 4669:(See Physics of optical tweezers) 2849:is the electric dipole coupling, 9124: 9123: 8384:, New Scientist, 8 November 2005 8158:10.1103/PhysRevApplied.18.054041 7656:10.1103/PhysRevResearch.3.013113 7010:Review of Scientific Instruments 6501:Bradshaw DS, Andrews DL (2017). 4587:transverse direction, while the 2787: 2784: 2781: 2775: 2713: 2710: 2687:Harmonic potential approximation 2645: 2511: 2427: 2413: 2280: 2272: 2165: 2157: 2146: 2113: 1984: 1931: 1923: 1849: 1830: 1800: 1778: 1724: 1705: 1686: 1667: 1621: 1573: 1556: 1522: 1503: 1459: 1443: 1400: 1389: 1350: 1331: 1317: 1301: 1273: 1254: 1240: 1224: 1207: 1176: 1154: 1119:{\displaystyle \mathbf {E_{1}} } 1110: 1106: 1066: 1038: 1023: 996: 987: 979: 954: 939: 913: 904: 876: 848: 833: 806: 797: 780: 771: 751: 711: 696: 669: 644: 633: 594: 573: 569: 545: 536: 518: 514: 402: 8735: 8684: 8591: 8548: 8501: 8444: 8387: 8375: 8349: 8323: 8272: 8211: 8164: 8133: 8080: 8055: 8043: 7982: 7931: 7874: 7817: 7755: 7720: 7663: 7612: 7542: 7493: 7436: 7393: 7332: 7319: 7306: 7294:"Structure of Optical Vortices" 7286: 7226: 7176: 7117: 7104: 7054: 6997: 6940: 6889: 6832: 6782: 6725: 6668: 6596: 6535: 6494: 6459: 6424: 6411: 6362: 6303: 6246: 6200: 6126: 6053: 6028: 5955: 5930: 5857: 5832: 5759: 5686: 5647: 5540: 5505: 5442: 5393: 5374: 5265: 5021:Hill, Murray (November 1987). " 4638: 4369:morphology-dependent resonances 97:particles can be trapped, too. 33:single-beam gradient force trap 8995:Amplified spontaneous emission 8301:10.1103/PhysRevLett.100.186804 8021:10.1103/PhysRevLett.104.028302 7670:Hu Z, Wang J, Liang J (2004). 6574:10.1103/PhysRevLett.111.183001 5802:10.1103/PhysRevLett.104.010503 5729:10.1103/PhysRevLett.104.010502 5206: 5147: 5044: 5015: 4924: 4883: 4654:On the other hand, K. Ladavac 4363:required is of the order of 1 3540: 3484: 3160: 3154: 3119: 3113: 3061: 3055: 3018: 3006: 2978: 2965: 2945: 2932: 2912: 2906: 2658: 2649: 2641: 2524: 2515: 2507: 2431: 2423: 2290: 2276: 2268: 2249: 2241: 2222: 2175: 2161: 2117: 2109: 1048: 1018: 1006: 991: 964: 934: 923: 908: 858: 828: 816: 801: 790: 775: 555: 540: 1: 8453:"Opto-Refrigerative Tweezers" 8240:10.1103/PhysRevLett.96.238101 7479:10.1080/09500340.2020.1760954 6841:"Opto-refrigerative tweezers" 5641:10.1103/PhysRevLett.89.097903 4876: 4813:Fluorescence optical tweezers 4464:atomic force microscopy (AFM) 2391:{\displaystyle m=n_{0}/n_{1}} 480:Electric dipole approximation 415: 100:Optical tweezers are used in 77:), depending on the relative 68:attractive or repulsive force 7004:Neuman KC, Block SM (2004). 6488:10.1016/0030-4018(95)00753-9 5176:10.1021/acs.nanolett.5b01366 4550:Multiplexed optical tweezers 4516:Laguerre-Gaussian (LG) beams 4494:Alternative laser beam modes 1183:{\displaystyle \mathbf {p} } 1161:{\displaystyle \mathbf {x} } 676:{\displaystyle \mathbf {d} } 66:The laser light provides an 7: 9051:Chirped pulse amplification 8650:10.1007/978-1-4939-6421-5_8 8534:10.1103/PhysRevLett.63.1233 8189:10.1021/acs.jpclett.3c01679 7789:10.1529/biophysj.104.045476 6750:10.1021/acs.chemrev.1c00626 6507:European Journal of Physics 5025:". Retrieved June 25, 2005. 4844: 4618:Multimode fiber-based traps 4336:transfer. Typically photon 2869:{\displaystyle \omega _{o}} 181:1997 Nobel Prize in Physics 70:(typically on the order of 10: 9206: 8855:List of laser applications 8832: 8627:10.1103/PhysRevA.91.053824 7960:10.1103/PhysRevE.70.010901 7826:"The optical cell rotator" 7212:10.1103/PhysRevLett.75.826 6915:10.1038/s41467-023-40865-y 6232:10.1038/s41586-023-06927-3 6170:10.1038/s41586-021-03585-1 6096:10.1038/s41586-021-03582-4 5115:10.1038/s41467-018-04282-w 4917:10.1103/PhysRevLett.24.156 4571:Single mode optical fibers 2918:{\displaystyle (\lambda )} 1423:Faraday's law of induction 1419:a vector analysis equality 395: 281: 39:that use a highly focused 9119: 9033: 8980: 8868: 8840: 8764:10.1038/s41586-020-1964-y 8710:10.1038/s42004-020-0267-4 8577:10.1080/00268978000101561 8420:10.1038/s41566-018-0134-3 6808:10.1038/s41566-018-0134-3 6632:10.1038/s41566-019-0373-y 5998:10.1038/s41586-018-0450-2 5418:10.1007/s12551-016-0236-4 5232:10.3389/fbioe.2020.580937 4717:total internal reflection 4706:total internal reflection 4406: 152:was lauded with the 2018 89:-sized, or even smaller. 9160:Condensed matter physics 8697:Communications Chemistry 7749:10.1038/nphoton.2007.230 7625:Physical Review Research 7449:Journal of Modern Optics 6528:10.1088/1361-6404/aa6050 5291:10.3389/fbioe.2020.00721 4531:orbital angular momentum 2958:, and power of the beam 2323:is the particle radius, 367:conservation of momentum 8514:Physical Review Letters 8335:Applied quantum physics 8281:Physical Review Letters 8220:Physical Review Letters 8146:Physical Review Applied 7991:Physical Review Letters 7527:10.1364/OPTICA.2.000812 7192:Physical Review Letters 6544:Physical Review Letters 6337:10.1073/pnas.0603342103 5900:10.1126/science.aah3778 5772:Physical Review Letters 5699:Physical Review Letters 5065:10.1126/science.3547653 4896:Physical Review Letters 4823:fluorescence microscope 4561:spatial light modulator 4479:in the sample chamber. 4456:numerical aperture (NA) 2984:{\displaystyle (P_{o})} 2951:{\displaystyle (w_{o})} 2889:{\displaystyle \delta } 2822:{\displaystyle \Gamma } 160:History and development 8845:List of laser articles 8477:10.1126/sciadv.abh1101 8361:Caltech quantum optics 7697:10.1364/OPEX.12.004123 7371:10.1364/OPEX.12.001144 6857:10.1126/sciadv.abh1101 6280:10.1364/OPEX.12.004390 4861:List of laser articles 4627: 4508:Hermite-Gaussian beams 4448:absorption coefficient 4416: 4313: 4230: 4116: 4016: 3789: 3547: 3458: 3432: 3406: 3386: 3361: 3286: 3222: 3131: 2985: 2952: 2919: 2890: 2870: 2843: 2823: 2798: 2671: 2392: 2344: 2317: 2297: 2127: 1956: 1592: 1535: 1408: 1370: 1184: 1162: 1140: 1120: 1086: 728: 677: 655: 610: 441: 429: 336: 329: 185:Claude Cohen-Tannoudji 154:Nobel Prize in Physics 37:scientific instruments 25: 16:Scientific instruments 7887:Nature Communications 7292:Curtis JE, Grier DG, 6902:Nature Communications 6468:Optics Communications 6453:10.1103/PhysRevA.8.14 5382:"Optical Peristalsis" 5095:Nature Communications 4625: 4414: 4314: 4231: 4117: 4017: 3790: 3548: 3459: 3433: 3407: 3387: 3362: 3287: 3223: 3132: 2986: 2953: 2920: 2891: 2871: 2844: 2824: 2799: 2672: 2393: 2345: 2343:{\displaystyle n_{0}} 2318: 2298: 2128: 1957: 1593: 1536: 1409: 1371: 1185: 1168:, into polarization, 1163: 1146:, converts position, 1141: 1121: 1087: 729: 678: 656: 611: 494:electromagnetic field 435: 423: 330: 289: 146:quantum optomechanics 124:, or a molecule like 22: 9020:Population inversion 8119:10.1364/OL.17.000772 7851:10.1364/OE.16.016984 7813:on November 9, 2007. 7582:10.1364/OE.25.011692 7146:10.1364/OL.21.000827 6973:10.1364/OE.14.009786 5680:10.1103/Physics.3.s9 5476:10.1364/OE.19.007034 5272:Berns M. W. (2020). 4963:10.1364/OL.11.000288 4704:that "leaks" during 4645:fluorescence imaging 4425:microscope objective 4386:Optothermal tweezers 4250: 4133: 4036: 3806: 3562: 3468: 3442: 3416: 3396: 3376: 3303: 3239: 3148: 3000: 2962: 2929: 2903: 2880: 2853: 2842:{\displaystyle \mu } 2833: 2813: 2705: 2408: 2354: 2327: 2307: 2142: 1980: 1613: 1546: 1434: 1385: 1199: 1172: 1150: 1130: 1101: 743: 691: 665: 629: 509: 492:in an inhomogeneous 354:microscope objective 295: 269:strongly interacting 204:tobacco mosaic virus 193:Magneto-optical trap 9071:Laser beam profiler 8990:Active laser medium 8930:Free-electron laser 8850:List of laser types 8756:2020Natur.578..317A 8619:2015PhRvA..91e3824F 8569:1980MolPh..40..393T 8526:1989PhRvL..63.1233B 8469:2021SciA....7.1101L 8412:2018NaPho..12..195L 8293:2008PhRvL.100r6804R 8232:2006PhRvL..96w8101V 8101:1992OptL...17..772K 8013:2010PhRvL.104b8302X 7952:2004PhRvE..70a0901L 7899:2014NatCo...5.5481K 7842:2008OExpr..1616984K 7781:2005BpJ....88.3689G 7769:Biophysical Journal 7741:2007NaPho...1..723L 7688:2004OExpr..12.4123H 7647:2021PhRvR...3a3113N 7574:2017OExpr..2511692B 7558:(10): 11692–11700. 7518:2015Optic...2..812R 7471:2020JMOp...67..628C 7363:2004OExpr..12.1144L 7264:1998Natur.394..348F 7204:1995PhRvL..75..826H 7138:1996OptL...21..827G 7022:2004RScI...75.2787N 6965:2006OExpr..14.9786S 6702:10.1038/nature25176 6693:2018Natur.553..486S 6624:2019NaPho..13..289I 6566:2013PhRvL.111r3001G 6519:2017EJPh...38c4008B 6480:1996OptCo.124..529H 6445:1973PhRvA...8...14G 6328:2006PNAS..103.9006M 6271:2004OExpr..12.4390A 6162:2021Natur.595..233S 6088:2021Natur.595..227E 5990:2018Natur.561...79B 5892:2016Sci...354.1021B 5876:(6315): 1021–1023. 5794:2010PhRvL.104a0503I 5721:2010PhRvL.104a0502W 5672:2010PhyOJ...3S...9. 5565:2001Natur.411.1024S 5559:(6841): 1024–1027. 5467:2011OExpr..19.7034W 5406:Biophysical Reviews 5380:Koss BA, Grier DG, 5352:10.1038/nature02144 5344:2003Natur.426..421M 5168:2015NanoL..15.4183R 5107:2018NatCo...9.1882B 5059:(4795): 1517–1520. 5001:2009PhT....62b..26M 4945:1986OptL...11..288A 4908:1970PhRvL..24..156A 4890:Ashkin, A. (1970). 4476:lateral translation 4221: 4107: 4001: 3957: 3774: 3730: 3529: 3501: 3457:{\displaystyle z=0} 3431:{\displaystyle r=0} 3356: 3275: 2767: 2500: 2485: 2201: 486:Rayleigh scattering 340:General description 198:In the late 1980s, 189:William D. Phillips 31:(originally called 9185:1986 introductions 7907:10.1038/ncomms6481 7314:"Optical Spanners" 7299:2006-09-02 at the 7006:"Optical trapping" 5387:2006-09-02 at the 4628: 4417: 4338:radiation pressure 4325:Optical levitation 4309: 4226: 4207: 4112: 4093: 4012: 3987: 3943: 3785: 3760: 3716: 3543: 3515: 3487: 3454: 3428: 3402: 3382: 3357: 3342: 3282: 3261: 3218: 3127: 2981: 2948: 2915: 2886: 2866: 2839: 2819: 2794: 2753: 2667: 2486: 2471: 2388: 2340: 2313: 2293: 2187: 2123: 1952: 1950: 1588: 1531: 1404: 1366: 1364: 1180: 1158: 1136: 1116: 1082: 1080: 724: 673: 651: 606: 455:Newton's third law 442: 430: 398:Radiation pressure 337: 325: 273:quantum simulators 226:force spectroscopy 61:optical levitation 26: 9165:Molecular biology 9137: 9136: 9091:Optical amplifier 8940:Solid-state laser 8750:(7794): 317–320. 8659:978-1-4939-6419-2 8607:Physical Review A 8557:Molecular Physics 8520:(12): 1233–1236. 8510:"Optical binding" 8183:(32): 7306–7312. 7940:Physical Review E 7414:10.1038/nmeth1126 7408:(12): 1031–1036. 7248:(6691): 348–350. 7030:10.1063/1.1785844 6687:(7689): 486–490. 6433:Physical Review A 6387:10.1002/bip.22321 6322:(24): 9006–9011. 6146:(7866): 233–238. 6072:(7866): 227–232. 5526:10.1021/nn305826j 5338:(6965): 421–424. 5009:10.1063/1.3086092 4773:dielectrophoresis 4755:Indirect approach 4749:optical nanofiber 4713:optical waveguide 4692:Evanescent fields 4307: 4285: 4275: 4224: 4223: 4110: 4109: 3982: 3959: 3920: 3856: 3822: 3755: 3732: 3676: 3612: 3578: 3479: 3405:{\displaystyle r} 3385:{\displaystyle z} 3327: 3280: 3216: 3204: 3123: 3065: 2772: 2720: 2661: 2626: 2581: 2527: 2502: 2420: 2316:{\displaystyle a} 2097: 2053: 1999: 1915: 1884: 1843: 1813: 1759: 1718: 1648: 1586: 1482: 1344: 1267: 1139:{\displaystyle q} 1060: 870: 588: 410:Maxwell equations 214:Carlos Bustamante 9197: 9180:Optical trapping 9127: 9126: 9101:Optical isolator 9066:Injection seeder 9046:Beam homogenizer 9025:Ultrashort pulse 9015:Lasing threshold 8827: 8820: 8813: 8804: 8803: 8784: 8783: 8739: 8733: 8732: 8722: 8712: 8688: 8682: 8681: 8671: 8637: 8631: 8630: 8604: 8595: 8589: 8588: 8552: 8546: 8545: 8505: 8499: 8498: 8488: 8463:(26): eabh1101. 8457:Science Advances 8448: 8442: 8441: 8431: 8400:Nature Photonics 8391: 8385: 8379: 8373: 8372: 8370: 8368: 8353: 8347: 8346: 8344: 8342: 8327: 8321: 8320: 8276: 8270: 8269: 8251: 8215: 8209: 8208: 8168: 8162: 8161: 8137: 8131: 8130: 8112: 8084: 8078: 8077: 8075: 8074: 8065:. Archived from 8059: 8053: 8047: 8041: 8040: 8006: 7986: 7980: 7979: 7935: 7929: 7928: 7918: 7878: 7872: 7871: 7853: 7836:(21): 16984–92. 7821: 7815: 7814: 7809:. Archived from 7800: 7775:(5): 3689–3698. 7759: 7753: 7752: 7729:Nature Photonics 7724: 7718: 7717: 7699: 7667: 7661: 7660: 7658: 7640: 7616: 7610: 7609: 7567: 7546: 7540: 7539: 7529: 7497: 7491: 7490: 7464: 7440: 7434: 7433: 7397: 7391: 7390: 7356: 7354:cond-mat/0402634 7336: 7330: 7323: 7317: 7310: 7304: 7290: 7284: 7283: 7257: 7239: 7230: 7224: 7223: 7189: 7180: 7174: 7173: 7121: 7115: 7108: 7102: 7101: 7058: 7052: 7051: 7041: 7001: 6995: 6994: 6984: 6944: 6938: 6937: 6935: 6917: 6893: 6887: 6886: 6876: 6845:Science Advances 6836: 6830: 6829: 6827: 6796:Nature Photonics 6786: 6780: 6779: 6769: 6744:(3): 3122–3179. 6738:Chemical Reviews 6729: 6723: 6722: 6704: 6672: 6666: 6665: 6659: 6651: 6612:Nature Photonics 6609: 6600: 6594: 6593: 6559: 6539: 6533: 6532: 6530: 6498: 6492: 6491: 6474:(5–6): 529–541. 6463: 6457: 6456: 6428: 6422: 6415: 6409: 6408: 6398: 6366: 6360: 6359: 6349: 6339: 6307: 6301: 6300: 6282: 6250: 6244: 6243: 6225: 6204: 6198: 6197: 6155: 6130: 6124: 6123: 6081: 6057: 6051: 6050: 6048: 6047: 6032: 6026: 6025: 5983: 5959: 5953: 5952: 5950: 5949: 5934: 5928: 5927: 5885: 5861: 5855: 5854: 5852: 5851: 5836: 5830: 5829: 5787: 5763: 5757: 5756: 5714: 5690: 5684: 5683: 5651: 5645: 5644: 5634: 5632:quant-ph/0110140 5610: 5601: 5600: 5573:10.1038/35082512 5544: 5538: 5537: 5520:(2): 1725–1730. 5509: 5503: 5502: 5496: 5488: 5478: 5461:(8): 7034–7061. 5446: 5440: 5439: 5429: 5397: 5391: 5378: 5372: 5371: 5323: 5314: 5313: 5303: 5293: 5269: 5263: 5262: 5244: 5234: 5210: 5204: 5203: 5162:(6): 4183–4188. 5151: 5145: 5144: 5134: 5086: 5077: 5076: 5048: 5042: 5036: 5030: 5019: 5013: 5012: 4984: 4975: 4974: 4956: 4928: 4922: 4921: 4919: 4887: 4784:Nature Materials 4698:evanescent field 4609:Phys. Rev. Lett. 4500:conventional TEM 4484:dichroic mirrors 4318: 4316: 4315: 4310: 4308: 4303: 4299: 4298: 4288: 4286: 4281: 4276: 4274: 4273: 4264: 4263: 4254: 4235: 4233: 4232: 4227: 4225: 4222: 4220: 4215: 4203: 4202: 4193: 4192: 4179: 4178: 4177: 4168: 4167: 4151: 4150: 4145: 4144: 4121: 4119: 4118: 4113: 4111: 4108: 4106: 4101: 4086: 4085: 4072: 4071: 4070: 4054: 4053: 4048: 4047: 4021: 4019: 4018: 4013: 4011: 4010: 4000: 3995: 3983: 3975: 3970: 3969: 3960: 3958: 3956: 3951: 3938: 3937: 3936: 3923: 3921: 3919: 3915: 3914: 3898: 3893: 3892: 3883: 3882: 3865: 3864: 3857: 3855: 3854: 3853: 3840: 3836: 3835: 3825: 3823: 3821: 3810: 3794: 3792: 3791: 3786: 3784: 3783: 3773: 3768: 3756: 3748: 3743: 3742: 3733: 3731: 3729: 3724: 3715: 3714: 3704: 3703: 3702: 3693: 3692: 3679: 3677: 3675: 3671: 3670: 3654: 3649: 3648: 3639: 3638: 3621: 3620: 3613: 3611: 3610: 3609: 3596: 3592: 3591: 3581: 3579: 3577: 3566: 3552: 3550: 3549: 3544: 3539: 3538: 3528: 3523: 3511: 3510: 3500: 3495: 3480: 3472: 3463: 3461: 3460: 3455: 3437: 3435: 3434: 3429: 3411: 3409: 3408: 3403: 3391: 3389: 3388: 3383: 3366: 3364: 3363: 3358: 3355: 3350: 3341: 3340: 3328: 3320: 3315: 3314: 3291: 3289: 3288: 3283: 3281: 3276: 3274: 3269: 3256: 3251: 3250: 3227: 3225: 3224: 3219: 3217: 3215: 3214: 3209: 3205: 3203: 3202: 3190: 3177: 3175: 3174: 3136: 3134: 3133: 3128: 3126: 3125: 3124: 3122: 3112: 3111: 3101: 3100: 3099: 3086: 3076: 3075: 3070: 3066: 3064: 3050: 3049: 3040: 3033: 3032: 2990: 2988: 2987: 2982: 2977: 2976: 2957: 2955: 2954: 2949: 2944: 2943: 2925:, minimum waist 2924: 2922: 2921: 2916: 2895: 2893: 2892: 2887: 2875: 2873: 2872: 2867: 2865: 2864: 2848: 2846: 2845: 2840: 2828: 2826: 2825: 2820: 2803: 2801: 2800: 2795: 2793: 2773: 2771: 2766: 2761: 2748: 2744: 2743: 2727: 2722: 2721: 2718: 2716: 2676: 2674: 2673: 2668: 2663: 2662: 2654: 2648: 2637: 2636: 2631: 2627: 2625: 2618: 2617: 2607: 2600: 2599: 2589: 2582: 2580: 2572: 2571: 2570: 2561: 2560: 2551: 2550: 2534: 2529: 2528: 2520: 2514: 2503: 2501: 2499: 2494: 2484: 2479: 2460: 2459: 2458: 2449: 2448: 2438: 2430: 2422: 2421: 2418: 2416: 2397: 2395: 2394: 2389: 2387: 2386: 2377: 2372: 2371: 2349: 2347: 2346: 2341: 2339: 2338: 2322: 2320: 2319: 2314: 2302: 2300: 2299: 2294: 2283: 2275: 2261: 2260: 2248: 2234: 2233: 2221: 2220: 2211: 2210: 2200: 2195: 2168: 2160: 2149: 2132: 2130: 2129: 2124: 2116: 2102: 2098: 2096: 2089: 2088: 2078: 2071: 2070: 2060: 2054: 2049: 2048: 2047: 2038: 2037: 2021: 2016: 2015: 2000: 1992: 1987: 1961: 1959: 1958: 1953: 1951: 1944: 1940: 1939: 1935: 1934: 1926: 1916: 1914: 1903: 1898: 1897: 1885: 1877: 1861: 1857: 1853: 1852: 1844: 1842: 1834: 1833: 1824: 1819: 1815: 1814: 1812: 1804: 1803: 1794: 1781: 1773: 1772: 1760: 1752: 1736: 1732: 1728: 1727: 1719: 1717: 1709: 1708: 1699: 1694: 1690: 1689: 1670: 1662: 1661: 1649: 1641: 1624: 1597: 1595: 1594: 1589: 1587: 1585: 1577: 1576: 1567: 1559: 1540: 1538: 1537: 1532: 1530: 1526: 1525: 1506: 1498: 1494: 1493: 1492: 1483: 1475: 1462: 1457: 1453: 1446: 1413: 1411: 1410: 1405: 1403: 1392: 1375: 1373: 1372: 1367: 1365: 1358: 1354: 1353: 1345: 1343: 1335: 1334: 1325: 1320: 1315: 1311: 1304: 1280: 1276: 1268: 1266: 1258: 1257: 1248: 1243: 1238: 1234: 1227: 1210: 1189: 1187: 1186: 1181: 1179: 1167: 1165: 1164: 1159: 1157: 1145: 1143: 1142: 1137: 1125: 1123: 1122: 1117: 1115: 1114: 1113: 1097:Notice that the 1091: 1089: 1088: 1083: 1081: 1074: 1070: 1069: 1061: 1059: 1051: 1047: 1046: 1041: 1032: 1031: 1026: 1013: 1005: 1004: 999: 990: 982: 977: 973: 963: 962: 957: 948: 947: 942: 922: 921: 916: 907: 888: 884: 880: 879: 871: 869: 861: 857: 856: 851: 842: 841: 836: 823: 815: 814: 809: 800: 789: 788: 783: 774: 754: 733: 731: 730: 725: 720: 719: 714: 705: 704: 699: 682: 680: 679: 674: 672: 660: 658: 657: 652: 647: 636: 615: 613: 612: 607: 602: 598: 597: 589: 587: 579: 578: 577: 576: 562: 554: 553: 548: 539: 523: 522: 521: 334: 332: 331: 326: 321: 320: 319: 230:molecular motors 209:Escherichia coli 83:force of gravity 79:refractive index 29:Optical tweezers 9205: 9204: 9200: 9199: 9198: 9196: 9195: 9194: 9140: 9139: 9138: 9133: 9115: 9029: 9010:Laser linewidth 9000:Continuous wave 8976: 8869:Types of lasers 8864: 8836: 8831: 8793: 8788: 8787: 8740: 8736: 8689: 8685: 8660: 8638: 8634: 8602: 8596: 8592: 8553: 8549: 8506: 8502: 8449: 8445: 8392: 8388: 8380: 8376: 8366: 8364: 8355: 8354: 8350: 8340: 8338: 8329: 8328: 8324: 8277: 8273: 8216: 8212: 8169: 8165: 8138: 8134: 8110:10.1.1.462.4424 8085: 8081: 8072: 8070: 8061: 8060: 8056: 8048: 8044: 7987: 7983: 7936: 7932: 7879: 7875: 7822: 7818: 7760: 7756: 7735:(12): 723–727. 7725: 7721: 7668: 7664: 7617: 7613: 7547: 7543: 7498: 7494: 7441: 7437: 7398: 7394: 7337: 7333: 7324: 7320: 7311: 7307: 7301:Wayback Machine 7291: 7287: 7255:physics/0308113 7237: 7231: 7227: 7187: 7181: 7177: 7132:(11): 827–829. 7122: 7118: 7109: 7105: 7059: 7055: 7016:(9): 2787–809. 7002: 6998: 6959:(21): 9786–93. 6945: 6941: 6894: 6890: 6837: 6833: 6787: 6783: 6730: 6726: 6673: 6669: 6653: 6652: 6607: 6601: 6597: 6540: 6536: 6499: 6495: 6464: 6460: 6429: 6425: 6416: 6412: 6381:(11): 860–869. 6367: 6363: 6308: 6304: 6251: 6247: 6205: 6201: 6131: 6127: 6058: 6054: 6045: 6043: 6034: 6033: 6029: 5974:(7721): 79–82. 5960: 5956: 5947: 5945: 5943:Chemistry World 5937:Extance, Andy. 5935: 5931: 5862: 5858: 5849: 5847: 5838: 5837: 5833: 5764: 5760: 5691: 5687: 5652: 5648: 5619:Phys. Rev. Lett 5611: 5604: 5545: 5541: 5510: 5506: 5490: 5489: 5447: 5443: 5398: 5394: 5389:Wayback Machine 5379: 5375: 5324: 5317: 5270: 5266: 5225:: 580937_1–25. 5211: 5207: 5152: 5148: 5087: 5080: 5049: 5045: 5037: 5033: 5026: 5020: 5016: 4985: 4978: 4954:10.1.1.205.4729 4929: 4925: 4888: 4884: 4879: 4866:Quantum control 4847: 4835: 4815: 4806: 4804:Optical binding 4757: 4694: 4641: 4633:adaptive optics 4620: 4573: 4565:ultracold atoms 4552: 4521: 4513: 4503: 4496: 4409: 4388: 4371:in a spherical 4327: 4294: 4290: 4289: 4287: 4280: 4269: 4265: 4259: 4255: 4253: 4251: 4248: 4247: 4216: 4211: 4198: 4194: 4188: 4184: 4180: 4173: 4169: 4163: 4159: 4152: 4149: 4140: 4136: 4134: 4131: 4130: 4102: 4097: 4081: 4077: 4073: 4066: 4062: 4055: 4052: 4043: 4039: 4037: 4034: 4033: 4006: 4002: 3996: 3991: 3974: 3965: 3961: 3952: 3947: 3939: 3932: 3928: 3924: 3922: 3910: 3906: 3902: 3897: 3888: 3884: 3866: 3860: 3859: 3858: 3849: 3845: 3841: 3831: 3827: 3826: 3824: 3814: 3809: 3807: 3804: 3803: 3779: 3775: 3769: 3764: 3747: 3738: 3734: 3725: 3720: 3710: 3706: 3705: 3698: 3694: 3688: 3684: 3680: 3678: 3666: 3662: 3658: 3653: 3644: 3640: 3622: 3616: 3615: 3614: 3605: 3601: 3597: 3587: 3583: 3582: 3580: 3570: 3565: 3563: 3560: 3559: 3534: 3530: 3524: 3519: 3506: 3502: 3496: 3491: 3471: 3469: 3466: 3465: 3443: 3440: 3439: 3417: 3414: 3413: 3397: 3394: 3393: 3377: 3374: 3373: 3351: 3346: 3336: 3332: 3319: 3310: 3306: 3304: 3301: 3300: 3270: 3265: 3257: 3255: 3246: 3242: 3240: 3237: 3236: 3210: 3198: 3194: 3189: 3185: 3184: 3176: 3170: 3166: 3149: 3146: 3145: 3107: 3103: 3102: 3095: 3091: 3087: 3085: 3081: 3077: 3071: 3051: 3045: 3041: 3039: 3035: 3034: 3028: 3024: 3001: 2998: 2997: 2972: 2968: 2963: 2960: 2959: 2939: 2935: 2930: 2927: 2926: 2904: 2901: 2900: 2881: 2878: 2877: 2860: 2856: 2854: 2851: 2850: 2834: 2831: 2830: 2814: 2811: 2810: 2774: 2762: 2757: 2749: 2739: 2735: 2728: 2726: 2717: 2709: 2708: 2706: 2703: 2702: 2689: 2653: 2652: 2644: 2632: 2613: 2609: 2608: 2595: 2591: 2590: 2588: 2584: 2583: 2573: 2566: 2562: 2556: 2552: 2546: 2542: 2535: 2533: 2519: 2518: 2510: 2495: 2490: 2480: 2475: 2461: 2454: 2450: 2444: 2440: 2439: 2437: 2426: 2417: 2412: 2411: 2409: 2406: 2405: 2382: 2378: 2373: 2367: 2363: 2355: 2352: 2351: 2334: 2330: 2328: 2325: 2324: 2308: 2305: 2304: 2279: 2271: 2256: 2252: 2244: 2229: 2225: 2216: 2212: 2206: 2202: 2196: 2191: 2164: 2156: 2145: 2143: 2140: 2139: 2112: 2084: 2080: 2079: 2066: 2062: 2061: 2059: 2055: 2043: 2039: 2033: 2029: 2022: 2020: 2011: 2007: 1991: 1983: 1981: 1978: 1977: 1969:Poynting vector 1949: 1948: 1930: 1922: 1921: 1917: 1907: 1902: 1893: 1889: 1876: 1875: 1871: 1859: 1858: 1848: 1835: 1829: 1825: 1823: 1805: 1799: 1795: 1793: 1789: 1785: 1777: 1768: 1764: 1751: 1750: 1746: 1734: 1733: 1723: 1710: 1704: 1700: 1698: 1685: 1678: 1674: 1666: 1657: 1653: 1640: 1639: 1635: 1625: 1620: 1616: 1614: 1611: 1610: 1578: 1572: 1568: 1566: 1555: 1547: 1544: 1543: 1521: 1514: 1510: 1502: 1488: 1484: 1474: 1473: 1469: 1458: 1442: 1441: 1437: 1435: 1432: 1431: 1399: 1388: 1386: 1383: 1382: 1363: 1362: 1349: 1336: 1330: 1326: 1324: 1316: 1300: 1299: 1295: 1294: 1290: 1278: 1277: 1272: 1259: 1253: 1249: 1247: 1239: 1223: 1222: 1218: 1211: 1206: 1202: 1200: 1197: 1196: 1175: 1173: 1170: 1169: 1153: 1151: 1148: 1147: 1131: 1128: 1127: 1109: 1105: 1104: 1102: 1099: 1098: 1079: 1078: 1065: 1052: 1042: 1037: 1036: 1027: 1022: 1021: 1014: 1012: 1000: 995: 994: 986: 978: 958: 953: 952: 943: 938: 937: 933: 929: 917: 912: 911: 903: 902: 898: 886: 885: 875: 862: 852: 847: 846: 837: 832: 831: 824: 822: 810: 805: 804: 796: 784: 779: 778: 770: 769: 765: 755: 750: 746: 744: 741: 740: 715: 710: 709: 700: 695: 694: 692: 689: 688: 668: 666: 663: 662: 643: 632: 630: 627: 626: 625:of a dipole is 593: 580: 572: 568: 567: 563: 561: 549: 544: 543: 535: 534: 530: 517: 513: 512: 510: 507: 506: 482: 467: 418: 405: 400: 342: 306: 305: 301: 296: 293: 292: 284: 238:single-molecule 162: 130:nanoengineering 17: 12: 11: 5: 9203: 9193: 9192: 9187: 9182: 9177: 9172: 9167: 9162: 9157: 9152: 9135: 9134: 9132: 9131: 9120: 9117: 9116: 9114: 9113: 9108: 9106:Output coupler 9103: 9098: 9096:Optical cavity 9093: 9088: 9083: 9078: 9073: 9068: 9063: 9058: 9056:Gain-switching 9053: 9048: 9043: 9037: 9035: 9031: 9030: 9028: 9027: 9022: 9017: 9012: 9007: 9005:Laser ablation 9002: 8997: 8992: 8986: 8984: 8978: 8977: 8975: 8974: 8969: 8968: 8967: 8962: 8957: 8952: 8947: 8937: 8932: 8927: 8926: 8925: 8920: 8915: 8910: 8905: 8903:Carbon dioxide 8895: 8894: 8893: 8891:Liquid-crystal 8888: 8878: 8876:Chemical laser 8872: 8870: 8866: 8865: 8863: 8862: 8860:Laser acronyms 8857: 8852: 8847: 8841: 8838: 8837: 8830: 8829: 8822: 8815: 8807: 8801: 8800: 8792: 8791:External links 8789: 8786: 8785: 8734: 8683: 8658: 8632: 8590: 8563:(2): 393–399. 8547: 8500: 8443: 8406:(4): 195–201. 8386: 8374: 8348: 8322: 8287:(18): 186804. 8271: 8226:(23): 238101. 8210: 8163: 8132: 8089:Optics Letters 8079: 8054: 8042: 7981: 7930: 7873: 7830:Optics Express 7816: 7754: 7719: 7682:(17): 4123–8. 7676:Optics Express 7662: 7611: 7552:Optics Express 7541: 7492: 7455:(7): 628–637. 7435: 7402:Nature Methods 7392: 7341:Optics Express 7331: 7327:"Bessel Beams" 7318: 7305: 7285: 7225: 7198:(5): 826–829. 7175: 7126:Optics Letters 7116: 7103: 7053: 6996: 6953:Optics Express 6939: 6888: 6831: 6802:(4): 195–201. 6781: 6724: 6667: 6618:(4): 289–295. 6595: 6550:(18): 183001. 6534: 6493: 6458: 6423: 6417:Lynn Paterson 6410: 6361: 6302: 6265:(19): 4390–8. 6259:Optics Express 6245: 6199: 6125: 6052: 6027: 5954: 5929: 5856: 5831: 5758: 5685: 5646: 5602: 5539: 5504: 5455:Optics Express 5441: 5392: 5373: 5326:MacDonald MP, 5315: 5264: 5205: 5146: 5078: 5043: 5031: 5014: 4976: 4939:(5): 288–290. 4933:Optics Letters 4923: 4902:(4): 156–159. 4881: 4880: 4878: 4875: 4874: 4873: 4871:Quantum optics 4868: 4863: 4858: 4853: 4846: 4843: 4834: 4831: 4814: 4811: 4805: 4802: 4756: 4753: 4693: 4690: 4640: 4637: 4619: 4616: 4572: 4569: 4551: 4548: 4519: 4511: 4504:Gaussian beams 4501: 4495: 4492: 4488:video tracking 4408: 4405: 4403:applications. 4397:photobleaching 4393:thermophoresis 4387: 4384: 4373:optical cavity 4326: 4323: 4322: 4321: 4320: 4319: 4306: 4302: 4297: 4293: 4284: 4279: 4272: 4268: 4262: 4258: 4239: 4238: 4237: 4236: 4219: 4214: 4210: 4206: 4201: 4197: 4191: 4187: 4183: 4176: 4172: 4166: 4162: 4158: 4155: 4148: 4143: 4139: 4125: 4124: 4123: 4122: 4105: 4100: 4096: 4092: 4089: 4084: 4080: 4076: 4069: 4065: 4061: 4058: 4051: 4046: 4042: 4025: 4024: 4023: 4022: 4009: 4005: 3999: 3994: 3990: 3986: 3981: 3978: 3973: 3968: 3964: 3955: 3950: 3946: 3942: 3935: 3931: 3927: 3918: 3913: 3909: 3905: 3901: 3896: 3891: 3887: 3881: 3878: 3875: 3872: 3869: 3863: 3852: 3848: 3844: 3839: 3834: 3830: 3820: 3817: 3813: 3798: 3797: 3796: 3795: 3782: 3778: 3772: 3767: 3763: 3759: 3754: 3751: 3746: 3741: 3737: 3728: 3723: 3719: 3713: 3709: 3701: 3697: 3691: 3687: 3683: 3674: 3669: 3665: 3661: 3657: 3652: 3647: 3643: 3637: 3634: 3631: 3628: 3625: 3619: 3608: 3604: 3600: 3595: 3590: 3586: 3576: 3573: 3569: 3542: 3537: 3533: 3527: 3522: 3518: 3514: 3509: 3505: 3499: 3494: 3490: 3486: 3483: 3478: 3475: 3453: 3450: 3447: 3427: 3424: 3421: 3401: 3381: 3370: 3369: 3368: 3367: 3354: 3349: 3345: 3339: 3335: 3331: 3326: 3323: 3318: 3313: 3309: 3295: 3294: 3293: 3292: 3279: 3273: 3268: 3264: 3260: 3254: 3249: 3245: 3231: 3230: 3229: 3228: 3213: 3208: 3201: 3197: 3193: 3188: 3183: 3180: 3173: 3169: 3165: 3162: 3159: 3156: 3153: 3140: 3139: 3138: 3137: 3121: 3118: 3115: 3110: 3106: 3098: 3094: 3090: 3084: 3080: 3074: 3069: 3063: 3060: 3057: 3054: 3048: 3044: 3038: 3031: 3027: 3023: 3020: 3017: 3014: 3011: 3008: 3005: 2980: 2975: 2971: 2967: 2947: 2942: 2938: 2934: 2914: 2911: 2908: 2885: 2863: 2859: 2838: 2818: 2807: 2806: 2805: 2804: 2792: 2789: 2786: 2783: 2780: 2777: 2770: 2765: 2760: 2756: 2752: 2747: 2742: 2738: 2734: 2731: 2725: 2715: 2712: 2694:AC Stark Shift 2688: 2685: 2680: 2679: 2678: 2677: 2666: 2660: 2657: 2651: 2647: 2643: 2640: 2635: 2630: 2624: 2621: 2616: 2612: 2606: 2603: 2598: 2594: 2587: 2579: 2576: 2569: 2565: 2559: 2555: 2549: 2545: 2541: 2538: 2532: 2526: 2523: 2517: 2513: 2509: 2506: 2498: 2493: 2489: 2483: 2478: 2474: 2470: 2467: 2464: 2457: 2453: 2447: 2443: 2436: 2433: 2429: 2425: 2415: 2385: 2381: 2376: 2370: 2366: 2362: 2359: 2337: 2333: 2312: 2292: 2289: 2286: 2282: 2278: 2274: 2270: 2267: 2264: 2259: 2255: 2251: 2247: 2243: 2240: 2237: 2232: 2228: 2224: 2219: 2215: 2209: 2205: 2199: 2194: 2190: 2186: 2183: 2180: 2177: 2174: 2171: 2167: 2163: 2159: 2155: 2152: 2148: 2136: 2135: 2134: 2133: 2122: 2119: 2115: 2111: 2108: 2105: 2101: 2095: 2092: 2087: 2083: 2077: 2074: 2069: 2065: 2058: 2052: 2046: 2042: 2036: 2032: 2028: 2025: 2019: 2014: 2010: 2006: 2003: 1998: 1995: 1990: 1986: 1965: 1964: 1963: 1962: 1947: 1943: 1938: 1933: 1929: 1925: 1920: 1913: 1910: 1906: 1901: 1896: 1892: 1888: 1883: 1880: 1874: 1870: 1867: 1864: 1862: 1860: 1856: 1851: 1847: 1841: 1838: 1832: 1828: 1822: 1818: 1811: 1808: 1802: 1798: 1792: 1788: 1784: 1780: 1776: 1771: 1767: 1763: 1758: 1755: 1749: 1745: 1742: 1739: 1737: 1735: 1731: 1726: 1722: 1716: 1713: 1707: 1703: 1697: 1693: 1688: 1684: 1681: 1677: 1673: 1669: 1665: 1660: 1656: 1652: 1647: 1644: 1638: 1634: 1631: 1628: 1626: 1623: 1619: 1618: 1601: 1600: 1599: 1598: 1584: 1581: 1575: 1571: 1565: 1562: 1558: 1554: 1551: 1541: 1529: 1524: 1520: 1517: 1513: 1509: 1505: 1501: 1497: 1491: 1487: 1481: 1478: 1472: 1468: 1465: 1461: 1456: 1452: 1449: 1445: 1440: 1402: 1398: 1395: 1391: 1379: 1378: 1377: 1376: 1361: 1357: 1352: 1348: 1342: 1339: 1333: 1329: 1323: 1319: 1314: 1310: 1307: 1303: 1298: 1293: 1289: 1286: 1283: 1281: 1279: 1275: 1271: 1265: 1262: 1256: 1252: 1246: 1242: 1237: 1233: 1230: 1226: 1221: 1217: 1214: 1212: 1209: 1205: 1204: 1178: 1156: 1135: 1112: 1108: 1095: 1094: 1093: 1092: 1077: 1073: 1068: 1064: 1058: 1055: 1050: 1045: 1040: 1035: 1030: 1025: 1020: 1017: 1011: 1008: 1003: 998: 993: 989: 985: 981: 976: 972: 969: 966: 961: 956: 951: 946: 941: 936: 932: 928: 925: 920: 915: 910: 906: 901: 897: 894: 891: 889: 887: 883: 878: 874: 868: 865: 860: 855: 850: 845: 840: 835: 830: 827: 821: 818: 813: 808: 803: 799: 795: 792: 787: 782: 777: 773: 768: 764: 761: 758: 756: 753: 749: 748: 723: 718: 713: 708: 703: 698: 671: 650: 646: 642: 639: 635: 619: 618: 617: 616: 605: 601: 596: 592: 586: 583: 575: 571: 566: 560: 557: 552: 547: 542: 538: 533: 529: 526: 520: 516: 481: 478: 465: 417: 414: 404: 401: 362:electric field 341: 338: 324: 318: 315: 312: 309: 304: 300: 283: 280: 252:properties of 248:, measure the 161: 158: 142:quantum optics 15: 9: 6: 4: 3: 2: 9202: 9191: 9188: 9186: 9183: 9181: 9178: 9176: 9173: 9171: 9168: 9166: 9163: 9161: 9158: 9156: 9153: 9151: 9148: 9147: 9145: 9130: 9122: 9121: 9118: 9112: 9109: 9107: 9104: 9102: 9099: 9097: 9094: 9092: 9089: 9087: 9084: 9082: 9079: 9077: 9074: 9072: 9069: 9067: 9064: 9062: 9061:Gaussian beam 9059: 9057: 9054: 9052: 9049: 9047: 9044: 9042: 9041:Beam expander 9039: 9038: 9036: 9032: 9026: 9023: 9021: 9018: 9016: 9013: 9011: 9008: 9006: 9003: 9001: 8998: 8996: 8993: 8991: 8988: 8987: 8985: 8983: 8982:Laser physics 8979: 8973: 8970: 8966: 8963: 8961: 8958: 8956: 8953: 8951: 8948: 8946: 8943: 8942: 8941: 8938: 8936: 8933: 8931: 8928: 8924: 8921: 8919: 8916: 8914: 8911: 8909: 8906: 8904: 8901: 8900: 8899: 8896: 8892: 8889: 8887: 8884: 8883: 8882: 8879: 8877: 8874: 8873: 8871: 8867: 8861: 8858: 8856: 8853: 8851: 8848: 8846: 8843: 8842: 8839: 8835: 8828: 8823: 8821: 8816: 8814: 8809: 8808: 8805: 8799: 8795: 8794: 8781: 8777: 8773: 8769: 8765: 8761: 8757: 8753: 8749: 8745: 8738: 8730: 8726: 8721: 8716: 8711: 8706: 8702: 8698: 8694: 8687: 8679: 8675: 8670: 8665: 8661: 8655: 8651: 8647: 8643: 8636: 8628: 8624: 8620: 8616: 8613:(5): 053824. 8612: 8608: 8601: 8594: 8586: 8582: 8578: 8574: 8570: 8566: 8562: 8558: 8551: 8543: 8539: 8535: 8531: 8527: 8523: 8519: 8515: 8511: 8504: 8496: 8492: 8487: 8482: 8478: 8474: 8470: 8466: 8462: 8458: 8454: 8447: 8439: 8435: 8430: 8425: 8421: 8417: 8413: 8409: 8405: 8401: 8397: 8390: 8383: 8378: 8367:September 10, 8362: 8358: 8352: 8341:September 10, 8336: 8332: 8326: 8318: 8314: 8310: 8306: 8302: 8298: 8294: 8290: 8286: 8282: 8275: 8267: 8263: 8259: 8255: 8250: 8245: 8241: 8237: 8233: 8229: 8225: 8221: 8214: 8206: 8202: 8198: 8194: 8190: 8186: 8182: 8178: 8174: 8167: 8159: 8155: 8152:(5): 054041. 8151: 8147: 8143: 8136: 8128: 8124: 8120: 8116: 8111: 8106: 8102: 8098: 8095:(11): 772–4. 8094: 8090: 8083: 8069:on 2006-07-21 8068: 8064: 8058: 8051: 8046: 8038: 8034: 8030: 8026: 8022: 8018: 8014: 8010: 8005: 8000: 7997:(2): 028302. 7996: 7992: 7985: 7977: 7973: 7969: 7965: 7961: 7957: 7953: 7949: 7946:(1): 010901. 7945: 7941: 7934: 7926: 7922: 7917: 7912: 7908: 7904: 7900: 7896: 7892: 7888: 7884: 7877: 7869: 7865: 7861: 7857: 7852: 7847: 7843: 7839: 7835: 7831: 7827: 7820: 7812: 7808: 7804: 7799: 7794: 7790: 7786: 7782: 7778: 7774: 7770: 7766: 7758: 7750: 7746: 7742: 7738: 7734: 7730: 7723: 7715: 7711: 7707: 7703: 7698: 7693: 7689: 7685: 7681: 7677: 7673: 7666: 7657: 7652: 7648: 7644: 7639: 7634: 7631:(1): 013113. 7630: 7626: 7622: 7615: 7607: 7603: 7599: 7595: 7591: 7587: 7583: 7579: 7575: 7571: 7566: 7561: 7557: 7553: 7545: 7537: 7533: 7528: 7523: 7519: 7515: 7511: 7507: 7503: 7496: 7488: 7484: 7480: 7476: 7472: 7468: 7463: 7458: 7454: 7450: 7446: 7439: 7431: 7427: 7423: 7419: 7415: 7411: 7407: 7403: 7396: 7388: 7384: 7380: 7376: 7372: 7368: 7364: 7360: 7355: 7350: 7347:(6): 1144–9. 7346: 7342: 7335: 7328: 7322: 7315: 7309: 7302: 7298: 7295: 7289: 7281: 7277: 7273: 7272:10.1038/28566 7269: 7265: 7261: 7256: 7251: 7247: 7243: 7236: 7229: 7221: 7217: 7213: 7209: 7205: 7201: 7197: 7193: 7186: 7179: 7171: 7167: 7163: 7159: 7155: 7151: 7147: 7143: 7139: 7135: 7131: 7127: 7120: 7113: 7110:Shaevitz JW, 7107: 7099: 7095: 7091: 7087: 7083: 7079: 7075: 7071: 7067: 7063: 7057: 7049: 7045: 7040: 7035: 7031: 7027: 7023: 7019: 7015: 7011: 7007: 7000: 6992: 6988: 6983: 6978: 6974: 6970: 6966: 6962: 6958: 6954: 6950: 6943: 6934: 6929: 6925: 6921: 6916: 6911: 6907: 6903: 6899: 6892: 6884: 6880: 6875: 6870: 6866: 6862: 6858: 6854: 6850: 6846: 6842: 6835: 6826: 6821: 6817: 6813: 6809: 6805: 6801: 6797: 6793: 6785: 6777: 6773: 6768: 6763: 6759: 6755: 6751: 6747: 6743: 6739: 6735: 6728: 6720: 6716: 6712: 6708: 6703: 6698: 6694: 6690: 6686: 6682: 6678: 6671: 6663: 6657: 6649: 6645: 6641: 6637: 6633: 6629: 6625: 6621: 6617: 6613: 6606: 6599: 6591: 6587: 6583: 6579: 6575: 6571: 6567: 6563: 6558: 6553: 6549: 6545: 6538: 6529: 6524: 6520: 6516: 6513:(3): 034008. 6512: 6508: 6504: 6497: 6489: 6485: 6481: 6477: 6473: 6469: 6462: 6454: 6450: 6446: 6442: 6438: 6434: 6427: 6420: 6414: 6406: 6402: 6397: 6392: 6388: 6384: 6380: 6376: 6372: 6365: 6357: 6353: 6348: 6343: 6338: 6333: 6329: 6325: 6321: 6317: 6313: 6306: 6298: 6294: 6290: 6286: 6281: 6276: 6272: 6268: 6264: 6260: 6256: 6249: 6241: 6237: 6233: 6229: 6224: 6219: 6215: 6211: 6203: 6195: 6191: 6187: 6183: 6179: 6175: 6171: 6167: 6163: 6159: 6154: 6149: 6145: 6141: 6137: 6129: 6121: 6117: 6113: 6109: 6105: 6101: 6097: 6093: 6089: 6085: 6080: 6075: 6071: 6067: 6063: 6056: 6041: 6040:Physics World 6037: 6031: 6023: 6019: 6015: 6011: 6007: 6003: 5999: 5995: 5991: 5987: 5982: 5977: 5973: 5969: 5965: 5958: 5944: 5940: 5933: 5925: 5921: 5917: 5913: 5909: 5905: 5901: 5897: 5893: 5889: 5884: 5879: 5875: 5871: 5867: 5860: 5845: 5844:Physics World 5841: 5835: 5827: 5823: 5819: 5815: 5811: 5807: 5803: 5799: 5795: 5791: 5786: 5781: 5778:(1): 010503. 5777: 5773: 5769: 5762: 5754: 5750: 5746: 5742: 5738: 5734: 5730: 5726: 5722: 5718: 5713: 5708: 5705:(1): 010502. 5704: 5700: 5696: 5689: 5681: 5677: 5673: 5669: 5665: 5661: 5657: 5650: 5642: 5638: 5633: 5628: 5624: 5620: 5616: 5609: 5607: 5598: 5594: 5590: 5586: 5582: 5578: 5574: 5570: 5566: 5562: 5558: 5554: 5550: 5543: 5535: 5531: 5527: 5523: 5519: 5515: 5508: 5500: 5494: 5486: 5482: 5477: 5472: 5468: 5464: 5460: 5456: 5452: 5445: 5437: 5433: 5428: 5423: 5419: 5415: 5411: 5407: 5403: 5396: 5390: 5386: 5383: 5377: 5369: 5365: 5361: 5357: 5353: 5349: 5345: 5341: 5337: 5333: 5329: 5322: 5320: 5311: 5307: 5302: 5297: 5292: 5287: 5283: 5279: 5275: 5268: 5260: 5256: 5252: 5248: 5243: 5238: 5233: 5228: 5224: 5220: 5216: 5209: 5201: 5197: 5193: 5189: 5185: 5181: 5177: 5173: 5169: 5165: 5161: 5157: 5150: 5142: 5138: 5133: 5128: 5124: 5120: 5116: 5112: 5108: 5104: 5100: 5096: 5092: 5085: 5083: 5074: 5070: 5066: 5062: 5058: 5054: 5047: 5040: 5035: 5029: 5024: 5018: 5010: 5006: 5002: 4998: 4994: 4990: 4989:Physics Today 4983: 4981: 4972: 4968: 4964: 4960: 4955: 4950: 4946: 4942: 4938: 4934: 4927: 4918: 4913: 4909: 4905: 4901: 4897: 4893: 4886: 4882: 4872: 4869: 4867: 4864: 4862: 4859: 4857: 4854: 4852: 4849: 4848: 4842: 4838: 4830: 4826: 4824: 4820: 4810: 4801: 4799: 4798:laser cooling 4795: 4790: 4787: 4785: 4780: 4776: 4774: 4768: 4764: 4762: 4752: 4750: 4746: 4741: 4737: 4733: 4730: 4729:Ronchi Ruling 4726: 4720: 4718: 4714: 4709: 4707: 4703: 4702:optical field 4700:is a residue 4699: 4689: 4687: 4683: 4678: 4674: 4671: 4670: 4665: 4660: 4657: 4652: 4648: 4646: 4636: 4634: 4624: 4615: 4613: 4610: 4606: 4602: 4599: 4595: 4590: 4584: 4582: 4578: 4577:optical fiber 4568: 4566: 4562: 4558: 4547: 4545: 4541: 4540:Micromachines 4537: 4534: 4532: 4527: 4525: 4517: 4509: 4505: 4491: 4489: 4485: 4480: 4477: 4472: 4467: 4465: 4459: 4457: 4453: 4449: 4445: 4440: 4438: 4434: 4430: 4426: 4422: 4413: 4404: 4402: 4401:drug delivery 4398: 4394: 4383: 4380: 4376: 4374: 4370: 4366: 4362: 4358: 4354: 4350: 4345: 4343: 4339: 4335: 4332: 4304: 4300: 4295: 4291: 4282: 4277: 4270: 4266: 4260: 4256: 4246: 4245: 4244: 4243: 4242: 4217: 4212: 4208: 4204: 4199: 4195: 4189: 4185: 4181: 4174: 4170: 4164: 4160: 4156: 4153: 4146: 4141: 4137: 4129: 4128: 4127: 4126: 4103: 4098: 4094: 4090: 4087: 4082: 4078: 4074: 4067: 4063: 4059: 4056: 4049: 4044: 4040: 4032: 4031: 4030: 4029: 4028: 4007: 4003: 3997: 3992: 3988: 3984: 3979: 3976: 3971: 3966: 3962: 3953: 3948: 3944: 3940: 3933: 3929: 3925: 3916: 3911: 3907: 3903: 3899: 3894: 3889: 3885: 3879: 3876: 3873: 3870: 3867: 3850: 3846: 3837: 3832: 3818: 3815: 3811: 3802: 3801: 3800: 3799: 3780: 3776: 3770: 3765: 3761: 3757: 3752: 3749: 3744: 3739: 3735: 3726: 3721: 3717: 3711: 3707: 3699: 3695: 3689: 3685: 3681: 3672: 3667: 3663: 3659: 3655: 3650: 3645: 3641: 3635: 3632: 3629: 3626: 3623: 3606: 3602: 3593: 3588: 3574: 3571: 3567: 3558: 3557: 3556: 3555: 3554: 3535: 3531: 3525: 3520: 3516: 3512: 3507: 3503: 3497: 3492: 3488: 3481: 3476: 3473: 3451: 3448: 3445: 3425: 3422: 3419: 3399: 3379: 3352: 3347: 3343: 3337: 3333: 3329: 3324: 3321: 3316: 3311: 3307: 3299: 3298: 3297: 3296: 3277: 3271: 3266: 3262: 3258: 3252: 3247: 3243: 3235: 3234: 3233: 3232: 3211: 3206: 3199: 3195: 3191: 3186: 3181: 3178: 3171: 3167: 3163: 3157: 3151: 3144: 3143: 3142: 3141: 3116: 3108: 3104: 3096: 3092: 3088: 3082: 3078: 3072: 3067: 3058: 3052: 3046: 3042: 3036: 3029: 3025: 3021: 3015: 3012: 3009: 3003: 2996: 2995: 2994: 2993: 2992: 2973: 2969: 2940: 2936: 2909: 2897: 2883: 2861: 2857: 2836: 2768: 2763: 2758: 2754: 2750: 2740: 2736: 2732: 2729: 2723: 2701: 2700: 2699: 2698: 2697: 2695: 2684: 2664: 2655: 2638: 2633: 2628: 2622: 2619: 2614: 2610: 2604: 2601: 2596: 2592: 2585: 2577: 2574: 2567: 2563: 2557: 2553: 2547: 2543: 2539: 2536: 2530: 2521: 2504: 2496: 2491: 2487: 2481: 2476: 2472: 2468: 2465: 2462: 2455: 2451: 2445: 2441: 2434: 2404: 2403: 2402: 2401: 2400: 2383: 2379: 2374: 2368: 2364: 2360: 2357: 2335: 2331: 2310: 2287: 2284: 2265: 2262: 2257: 2253: 2245: 2238: 2235: 2230: 2226: 2217: 2213: 2207: 2203: 2197: 2192: 2188: 2184: 2181: 2178: 2172: 2169: 2153: 2150: 2120: 2106: 2099: 2093: 2090: 2085: 2081: 2075: 2072: 2067: 2063: 2056: 2050: 2044: 2040: 2034: 2030: 2026: 2023: 2017: 2012: 2008: 2001: 1996: 1993: 1988: 1976: 1975: 1974: 1973: 1972: 1970: 1945: 1941: 1936: 1927: 1918: 1911: 1908: 1904: 1899: 1894: 1890: 1881: 1878: 1872: 1868: 1865: 1863: 1854: 1845: 1839: 1836: 1826: 1820: 1816: 1809: 1806: 1796: 1790: 1786: 1782: 1774: 1769: 1765: 1756: 1753: 1747: 1743: 1740: 1738: 1729: 1720: 1714: 1711: 1701: 1695: 1691: 1682: 1675: 1671: 1663: 1658: 1654: 1645: 1642: 1636: 1632: 1629: 1627: 1609: 1608: 1607: 1606: 1605: 1582: 1563: 1560: 1552: 1542: 1527: 1518: 1511: 1507: 1499: 1495: 1489: 1485: 1479: 1476: 1470: 1463: 1454: 1447: 1438: 1430: 1429: 1428: 1427: 1426: 1424: 1420: 1415: 1396: 1393: 1359: 1355: 1346: 1340: 1337: 1327: 1321: 1312: 1305: 1296: 1291: 1287: 1284: 1282: 1269: 1263: 1260: 1250: 1244: 1235: 1228: 1219: 1215: 1213: 1195: 1194: 1193: 1192: 1191: 1133: 1075: 1071: 1062: 1056: 1053: 1043: 1033: 1028: 1015: 1009: 1001: 983: 974: 967: 959: 949: 944: 930: 926: 918: 899: 895: 892: 890: 881: 872: 866: 863: 853: 843: 838: 825: 819: 811: 793: 785: 766: 762: 759: 757: 739: 738: 737: 736: 735: 721: 716: 706: 701: 686: 685:infinitesimal 648: 640: 637: 624: 603: 599: 590: 584: 581: 564: 558: 550: 531: 527: 524: 505: 504: 503: 502: 501: 499: 498:Lorentz force 495: 491: 487: 477: 474: 470: 463: 462:Gaussian beam 458: 456: 452: 448: 438: 434: 426: 422: 413: 411: 403:Detailed view 399: 394: 392: 386: 384: 380: 376: 370: 368: 363: 359: 355: 351: 347: 322: 302: 298: 288: 279: 276: 274: 270: 266: 261: 259: 258:cell motility 255: 251: 250:visco-elastic 247: 241: 239: 235: 234:biophysicists 231: 227: 223: 219: 218:James Spudich 215: 211: 210: 205: 201: 200:Arthur Ashkin 196: 194: 190: 186: 182: 178: 174: 169: 167: 157: 155: 151: 150:Arthur Ashkin 147: 143: 139: 135: 134:nanochemistry 131: 127: 123: 119: 115: 111: 107: 103: 98: 96: 92: 88: 84: 80: 76: 73: 69: 64: 62: 58: 54: 50: 49:nanoparticles 46: 42: 38: 34: 30: 21: 9190:Force lasers 9170:Cell biology 9081:Mode locking 9034:Laser optics 8747: 8743: 8737: 8700: 8696: 8686: 8641: 8635: 8610: 8606: 8593: 8560: 8556: 8550: 8517: 8513: 8503: 8460: 8456: 8446: 8403: 8399: 8389: 8377: 8365:. Retrieved 8360: 8351: 8339:. Retrieved 8334: 8325: 8284: 8280: 8274: 8223: 8219: 8213: 8180: 8176: 8166: 8149: 8145: 8135: 8092: 8088: 8082: 8071:. Retrieved 8067:the original 8057: 8045: 7994: 7990: 7984: 7943: 7939: 7933: 7890: 7886: 7876: 7833: 7829: 7819: 7811:the original 7772: 7768: 7757: 7732: 7728: 7722: 7679: 7675: 7665: 7628: 7624: 7614: 7555: 7551: 7544: 7509: 7505: 7495: 7452: 7448: 7438: 7405: 7401: 7395: 7344: 7340: 7334: 7321: 7308: 7288: 7245: 7241: 7228: 7195: 7191: 7178: 7129: 7125: 7119: 7106: 7073: 7069: 7056: 7013: 7009: 6999: 6956: 6952: 6942: 6905: 6901: 6891: 6848: 6844: 6834: 6799: 6795: 6784: 6741: 6737: 6727: 6684: 6680: 6670: 6656:cite journal 6615: 6611: 6598: 6547: 6543: 6537: 6510: 6506: 6496: 6471: 6467: 6461: 6439:(1): 14–21. 6436: 6432: 6426: 6413: 6378: 6374: 6364: 6319: 6315: 6305: 6262: 6258: 6248: 6213: 6202: 6143: 6139: 6128: 6069: 6065: 6055: 6044:. Retrieved 6042:. 2021-07-22 6039: 6030: 5971: 5967: 5957: 5946:. Retrieved 5942: 5932: 5873: 5869: 5859: 5848:. Retrieved 5846:. 2016-11-07 5843: 5834: 5775: 5771: 5761: 5702: 5698: 5688: 5663: 5659: 5649: 5622: 5618: 5556: 5552: 5542: 5517: 5513: 5507: 5493:cite journal 5458: 5454: 5444: 5412:(1): 17–40. 5409: 5405: 5395: 5376: 5335: 5331: 5284:: 721_1–16. 5281: 5277: 5267: 5222: 5218: 5208: 5159: 5156:Nano Letters 5155: 5149: 5098: 5094: 5056: 5052: 5046: 5034: 5027: 5017: 4995:(2): 26–28. 4992: 4988: 4936: 4932: 4926: 4899: 4895: 4885: 4839: 4836: 4827: 4819:fluorescence 4816: 4807: 4791: 4788: 4783: 4781: 4777: 4769: 4765: 4758: 4742: 4738: 4734: 4721: 4710: 4695: 4679: 4675: 4668: 4667: 4661: 4655: 4653: 4649: 4642: 4639:Cell sorting 4629: 4611: 4608: 4604: 4600: 4597: 4593: 4585: 4574: 4557:galvanometer 4553: 4538: 4535: 4528: 4524:Bessel beams 4497: 4481: 4475: 4468: 4460: 4444:Nd:YAG laser 4441: 4418: 4389: 4381: 4377: 4349:fused silica 4346: 4342:optical trap 4341: 4328: 4240: 4026: 3371: 2898: 2808: 2690: 2681: 2137: 1966: 1602: 1416: 1380: 1096: 623:polarization 620: 483: 475: 471: 459: 443: 436: 424: 406: 387: 371: 343: 277: 265:laser-cooled 262: 256:, and study 246:cytoskeleton 242: 222:Steven Block 207: 197: 170: 163: 99: 65: 60: 32: 28: 27: 9111:Q-switching 8972:X-ray laser 8965:Ti-sapphire 8935:Laser diode 8913:Helium–neon 8249:11693/53564 7312:Padgett M, 7076:: 247–285. 6908:(1): 5133. 6375:Biopolymers 5328:Spalding GC 5101:(1): 1882. 4851:Atom optics 4761:UC Berkeley 4759:Ming Wu, a 391:Hooke's law 254:biopolymers 183:along with 9175:Biophysics 9150:Levitation 9144:Categories 8703:(1): 1–7. 8073:2005-11-15 7638:2008.09819 7565:1701.08620 7512:(9): 812. 7462:1811.03297 6223:2312.03982 6153:2012.12268 6079:2012.12281 6046:2021-12-04 5981:1712.02727 5948:2021-12-04 5883:1607.03042 5850:2021-12-04 5625:: 097903. 4877:References 4856:Levitation 4745:cold atoms 4715:(multiple 4664:drag force 4598:Opt. Lett. 4452:opticution 4437:CCD camera 4433:photodiode 4353:wavelength 416:Ray optics 373:molecule. 358:beam waist 346:dielectric 173:Steven Chu 122:blood cell 118:sperm cell 91:Dielectric 9155:Photonics 9076:M squared 8898:Gas laser 8881:Dye laser 8780:210949475 8585:0026-8976 8197:1948-7185 8105:CiteSeerX 8004:0912.4754 7590:1094-4087 7536:2334-2536 7487:219646821 7154:1539-4794 7062:Svoboda K 6924:2041-1723 6865:2375-2548 6816:1749-4893 6758:0009-2665 6711:0028-0836 6648:127470391 6640:1749-4893 6557:1307.1175 6240:1476-4687 6194:229363462 6178:0028-0836 6120:229363764 6104:0028-0836 6006:0028-0836 5908:0036-8075 5810:0031-9007 5785:0907.5552 5737:0031-9007 5712:0908.0454 5581:1476-4687 5259:221765039 5200:206726159 5184:1530-6984 5123:2041-1723 4949:CiteSeerX 4725:waveguide 4429:condenser 4357:dye laser 4305:λ 4301:π 4267:ω 4257:ω 4196:ϵ 4186:π 4171:λ 4157:α 4138:ω 4079:ϵ 4075:π 4060:α 4041:ω 3989:ω 3941:π 3908:ϵ 3900:α 3843:∂ 3829:∂ 3762:ω 3708:π 3696:λ 3664:ϵ 3656:α 3599:∂ 3585:∂ 3517:ω 3489:ω 3330:π 3278:λ 3259:π 3083:− 2910:λ 2884:δ 2858:ω 2837:μ 2817:Γ 2769:δ 2755:ω 2746:Γ 2733:π 2711:Δ 2659:^ 2602:− 2540:π 2525:^ 2488:ϵ 2466:π 2452:α 2236:− 2204:ϵ 2185:π 2154:α 2104:∇ 2073:− 2027:π 2005:∇ 2002:α 1928:× 1887:∇ 1869:α 1846:× 1791:− 1783:× 1775:− 1762:∇ 1744:α 1721:× 1683:× 1680:∇ 1672:× 1664:− 1651:∇ 1633:α 1580:∂ 1570:∂ 1564:− 1553:× 1550:∇ 1519:× 1516:∇ 1508:× 1500:− 1467:∇ 1451:∇ 1448:⋅ 1397:α 1347:× 1309:∇ 1306:⋅ 1288:α 1270:× 1232:∇ 1229:⋅ 1063:× 1034:− 984:− 971:∇ 968:⋅ 950:− 873:× 844:− 794:− 707:− 591:× 447:refracted 299:− 166:Bell Labs 138:molecules 110:bacterium 95:absorbing 24:particle. 9129:Category 8923:Nitrogen 8772:31996849 8729:36703465 8678:27844430 8542:10040510 8495:34172454 8438:29785202 8317:38405168 8309:18518404 8266:26221345 8258:16803408 8205:37561048 8127:19794626 8037:21476119 8029:20366628 7976:14608670 7968:15324034 7925:25410595 7893:: 5481. 7868:23912816 7860:18852807 7807:15722433 7714:31640506 7706:19483954 7606:46763848 7598:28788742 7422:17994031 7387:18255607 7379:19474932 7297:Archived 7220:10060128 7162:19876172 7066:Block SM 7048:16878180 6991:19529370 6933:10447564 6883:34172454 6776:34797041 6719:29368704 6590:36954822 6582:24237512 6421:, (2003) 6405:23784721 6356:16751267 6289:19483988 6186:34234335 6112:34234334 6022:52158666 6014:30185955 5924:25496096 5916:27811285 5818:20366355 5753:16384272 5745:20366354 5589:11429597 5534:23311448 5514:ACS Nano 5485:21503017 5436:28303166 5385:Archived 5360:14647376 5310:32850689 5251:33072730 5192:26010468 5141:29760422 4971:19730608 4845:See also 4471:aperture 4359:. 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