Optical tweezers (originally called single-beam gradient force trap) are

scientific instrument A scientific instrument is a device or tool used for scientific purposes, including the study of both natural phenomena and theoretical research. History Historically, the definition of a scientific instrument has varied, based on usage, laws, a ...

s that use a highly focused

laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The ...

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

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...

s, nanoparticles and droplets, in a manner similar to

tweezers Tweezers are small hand tools used for grasping objects too small to be easily handled with the human fingers. Tweezers are thumb-driven forceps most likely derived from tongs used to grab or hold hot objects since the dawn of recorded histo ...

. If the object is held in air or

vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often ...

without additional support, it can be called optical levitation. The laser light provides an attractive or repulsive force (typically on the order of

pico Pico may refer to: Places The Moon * Mons Pico, a lunar mountain in the northern part of the Mare Imbrium basin Portugal * Pico, a civil parish in the municipality of Vila Verde * Pico da Pedra, a civil parish in the municipality of Ribe ...

newtons The newton (symbol: N) is the unit of force in the International System of Units (SI). It is defined as 1 kg⋅m/s, the force which gives a mass of 1 kilogram an acceleration of 1 metre per second per second. It is named after Isaac Newton in r ...

), depending on the relative

refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, ...

between particle and surrounding medium. Levitation is possible if the force of the light counters the force of gravity. The trapped particles are usually

micron The micrometre ( international spelling as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer (American spelling), also commonly known as a micron, is a unit of length in the International System of Un ...

-sized, or even smaller.

Dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the ma ...

and absorbing particles can be trapped, too. Optical tweezers are used in

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...

and

medicine Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pr ...

(for example to grab and hold a single

bacterium Bacteria (; singular: bacterium) are ubiquitous, mostly free-living organisms often consisting of one biological cell. They constitute a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria were am ...

, a cell like a

sperm cell Sperm is the male reproductive cell, or gamete, in anisogamous forms of sexual reproduction (forms in which there is a larger, female reproductive cell and a smaller, male one). Animals produce motile sperm with a tail known as a flagellum, ...

or a

blood cell A blood cell, also called a hematopoietic cell, hemocyte, or hematocyte, is a cell produced through hematopoiesis and found mainly in the blood. Major types of blood cells include red blood cells (erythrocytes), white blood cells (leukocytes) ...

, or a molecule like DNA), nanoengineering and nanochemistry (to study and build materials from single

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...

s), quantum optics and quantum optomechanics (to study the interaction of single particles with light). The development of optical tweezing by

Arthur Ashkin Arthur Ashkin (September 2, 1922 – September 21, 2020) was an American scientist and Nobel laureate who worked at Bell Laboratories and Lucent Technologies. Ashkin has been considered by many as the father of optical tweezers, "LaserFest – t ...

was lauded with the 2018

Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...

History and development

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

Bell Labs Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mul ...

. 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. One of the authors of this seminal 1986 paper,

Steven Chu Steven Chucooling and trapping neutral atoms. This research earned Chu the 1997 Nobel Prize in Physics along with Claude Cohen-Tannoudji and

William D. Phillips William Daniel Phillips (born November 5, 1948) is an American physicist. He shared the Nobel Prize in Physics, in 1997, with Steven Chu and Claude Cohen-Tannoudji. Biography Phillips was born to William Cornelius Phillips of Juniata, Pennsylvan ...

. In an interview, Steven Chu described how Ashkin had first envisioned optical tweezing as a method for trapping atoms."Conversations with History: An Interview with Steven Chu"
(2004), Institute of International Studies, UC Berkeley. Last accessed on September 2, 2006. 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) utilizing resonant laser light and a magnetic gradient trap (cf.

Magneto-optical trap A magneto-optical trap (MOT) is an apparatus which uses laser cooling and a spatially-varying magnetic field to create a trap which can produce samples of cold, trapped, neutral atoms. Temperatures achieved in a MOT can be as low as several microk ...

). In the late 1980s,

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

Escherichia coli ''Escherichia coli'' (),Wells, J. C. (2000) Longman Pronunciation Dictionary. Harlow ngland Pearson Education Ltd. also known as ''E. coli'' (), is a Gram-negative, facultative anaerobic, rod-shaped, coliform bacterium of the genus '' Esc ...

'' bacterium. Throughout the 1990s and afterwards, researchers like Carlos Bustamante, James Spudich, and

Steven Block Steven M. Block (born 1952) is an American biophysicist and Professor at Stanford University with a joint appointment in the departments of Biology and Applied Physics. In addition, he is a member of the scientific advisory group JASON, a senio ...

pioneered the use of optical trap

force spectroscopy Force spectroscopy is a set of techniques for the study of the interactions and the binding forces between individual molecules. These methods can be used to measure the mechanical properties of single polymer molecules or proteins, or individual ...

to characterize molecular-scale biological motors. These

molecular motors Molecular motors are natural (biological) or artificial molecular machines that are the essential agents of movement in living organisms. In general terms, a motor is a device that consumes energy in one form and converts it into motion or mecha ...

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

biophysicists Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. B ...

to observe the forces and dynamics of nanoscale motors at the

single-molecule A single-molecule experiment is an experiment that investigates the properties of individual molecules. Single-molecule studies may be contrasted with measurements on an ensemble or bulk collection of molecules, where the individual behavior of mo ...

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

cytoskeleton The cytoskeleton is a complex, dynamic network of interlinking protein filaments present in the cytoplasm of all cells, including those of bacteria and archaea. In eukaryotes, it extends from the cell nucleus to the cell membrane and is co ...

, measure the visco-elastic properties of biopolymers, and study

cell motility Motility is the ability of an organism to move independently, using metabolic energy. Definitions Motility, the ability of an organism to move independently, using metabolic energy, can be contrasted with sessility, the state of organisms th ...

. 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. Some other achievements have also been trapping a single atom in 2001, trapping of strongly interacting entangled pairs in 2010, great precision in 2-dimensional arrays of atoms in 2016 as well as 3-dimensional assemblings in 2018 and using the technique in quantum simulators to obtain programmable arrays of 196 and 256 atoms in 2021 The Kapitsa–Dirac effect effectively demonstrated during 2001 uses standing waves of light to affect a beam of particles. Researchers have also worked to convert optical tweezers from large, complex instruments to smaller, simpler ones, for use by those with smaller research budgets. The main challenge is t
correlate
the force measurements and fluorescent/imaging data in combination with the fluidics to capture the objects and or manipulate the conditions.

Physics

General description

Optical tweezers are capable of manipulating nanometer and micron-sized

dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the ma ...

particles by exerting extremely small forces via a highly focused

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

microscope objective In optical engineering, the objective is the optical element that gathers light from the object being observed and focuses the light rays to produce a real image. Objectives can be a single lens or mirror, or combinations of several optical elem ...

. The narrowest point of the focused beam, known as the beam waist, contains a very strong

electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field ...

gradient. 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 conservation of momentum: 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. 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 molecule. DNA and the

proteins Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...

and

enzymes Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. ...

that interact with it are commonly studied in this way. 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 the displacement is small. In this way, an optical trap can be compared to a simple spring, which follows

Hooke's law In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring by some distance () scales linearly with respect to that distance—that is, where is a constant factor characteristic of t ...

Detailed view

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 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

Maxwell equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. Th ...

using appropriate boundary conditions.

Ray optics

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 refracted 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

momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...

associated with it, this change in direction indicates that its momentum has changed. Due to Newton's third law, there should be an equal and opposite momentum change on the particle. Most optical traps operate with a Gaussian beam (TEM₀₀ 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 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. 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 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. The standard tweezers works with the trapping laser propagated in the direction of gravity and the inverted tweezers works against gravity.

Electric dipole approximation

In cases where the diameter of a trapped particle is significantly smaller than the wavelength of light, the conditions for Rayleigh scattering are satisfied and the particle can be treated as a point dipole in an inhomogeneous

electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...

. The force applied on a single charge in an electromagnetic field is known as the

Lorentz force In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...

, ::

\mathbf=q\left(\mathbf(\mathbf_1)+\frac\times\mathbf\right).

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 polarization of a dipole is

\mathbf=q\mathbf,

where

\mathbf

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

infinitesimal In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally re ...

\mathbf_1-\mathbf_2.

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

\begin
 \mathbf & = q\left(\mathbf(\mathbf_1)-\mathbf(\mathbf_2)+\frac\times\mathbf\right) \\
 & = q\left(\mathbf(\mathbf_1)+\left((\mathbf_1-\mathbf_2)\cdot\nabla\right)\mathbf-\mathbf(\mathbf_1)+\frac\times\mathbf\right). \\
\end

Notice that the

\mathbf

cancel out. Multiplying through by the charge,

q

, converts position,

\mathbf

, into polarization,

\mathbf

, ::

\\ \end

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

\mathbf=\alpha\mathbf

). In the final steps, two equalities will be used: (1) A Vector Analysis Equality, (2)

Faraday's law of induction Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf)—a phenomenon known as electromagnetic in ...

. :#

\left(\mathbf\cdot\nabla\right)\mathbf=\nabla\left(\fracE^2\right)-\mathbf\times\left(\nabla\times\mathbf\right)

\nabla\times\mathbf=-\frac

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. ::

\\ \end

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

Poynting vector In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area per unit time) or ''power flow'' of an electromagnetic field. The SI unit of the Poynting vector is the watt p ...

, 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 ~10¹⁴ Hz, the derivative of this term averages to zero and the force can be written as ::

\mathbf=\frac\alpha\nabla E^2 = \frac\left(\frac\right) \nabla I(\mathbf),

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

\mathbf = \alpha \mathbf(\mathbf,t) = 4 \pi n_1^2 \epsilon_0 a^3 (m^2 - 1)/(m^2 + 2) \mathbf(\mathbf,t)

, where

a

is the particle radius,

n_0

is the index of refraction of the particle and

m = n_0/n_1

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 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 ::

\mathbf_(\mathbf) = \frac I(\mathbf) \hat = \frac \left(\frac\right)^2 I(\mathbf) \hat.

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 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.

Harmonic potential approximation

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 AC Stark Shift, ::

\mathbf_ = \frac \mathbf

where

\Gamma

is the natural line width of the excited state,

\mu

is the electric dipole coupling,

\omega_o

is the frequency of the transition, and

\delta

is the detuning or difference between the laser frequency and the transition frequency. The intensity of a gaussian beam profile is characterized by the wavelength

(\lambda)

, minimum waist

(w_o)

, and power of the beam

(P_o)

. The following formulas define the beam profile: ::

I(r,z)=I_0 \left (\frac\right ) ^2 e^

w(z)=w_0 \sqrt

z_R = \frac

P_0 = \frac \pi I_0 w_0^2

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

z

and

r

for

r=0

and

z=0

respectively and equated to the harmonic potential

\fracm(\omega_z^2 z^2 + \omega_r^2 r^2)

. These expansions are evaluated assuming fixed power. ::

\frac\frac \Biggr, _z^2=\frac z^2=\frac12 m \omega_z^2 z^2

\frac\frac \Biggr, _r^2=\frac r^2=\frac12 m \omega_r^2 r^2

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

\omega_r = \sqrt

\omega_z = \sqrt

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

\frac=\sqrt\frac

Optical levitation

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

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...

transfer. Typically photon radiation pressure 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 ''optical trap'' capable of holding small particles in suspension. Micrometer sized (from several to 50 micrometers in diameter) transparent

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

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...

such as that of an argon ion laser or that of a tunable dye laser. Laser power required is of the order of 1

Watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James ...

focused to a spot size of several tens of micrometers. Phenomena related to morphology-dependent resonances in a spherical

optical cavity An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors or other optical elements that forms a cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and prov ...

have been studied by several research groups. 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. Materials that have been successfully levitated include Black liquor, aluminum oxide, tungsten, and nickel.

Setups

The most basic optical tweezer setup will likely include the following components: a laser (usually Nd:YAG), a beam expander, some optics used to steer the beam location in the sample plane, a

and condenser to create the trap in the sample plane, a position detector (e.g. quadrant photodiode) to measure beam displacements and a microscope illumination source coupled to a CCD camera. An Nd:YAG laser (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 absorption coefficient at this wavelength. A low absorption is advisable so as to minimise damage to the biological material, sometimes referred to as opticution. 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 numerical aperture (NA) of the objective, be greater than the scattering force. Suitable objectives typically have an NA between 1.2 and 1.4. 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 atomic force microscopy (AFM). Expanding the beam emitted from the laser to fill the

aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An ...

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 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 ''lateral translation'' 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 end result of which is an axially displaced position of the beam waist in the sample chamber. 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 dichroic mirrors. 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 video tracking.

Alternative laser beam modes

The majority of optical tweezers make use of conventional TEM₀₀ Gaussian beams. However a number of other beam types have been used to trap particles, including high order laser beams i.e. Hermite-Gaussian beams (TEM_xy), Laguerre-Gaussian (LG) beams (TEM_pl) and Bessel beams. 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 orbital angular momentum that can rotate particles. This is accomplished without external mechanical or electrical steering of the beam. 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. Micromachines can be driven by these unique optical beams due to their intrinsic rotating mechanism due to the

spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally ...

and orbital angular momentum of light.

Multiplexed optical tweezers

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 tweezers, or by diffractively splitting the beam into multiple traps. With acousto-optic deflectors or galvanometer-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 spatial light modulator, 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 ultracold atoms. Ultracold atoms could also be used for realization of quantum computers.

Single mode optical fibers

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

optical fiber An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass ( silica) or plastic to a diameter slightly thicker than that of a human hair Hair is a protein filament that grows ...

. If one end of the optical fiber is molded into a lens-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. 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 transverse direction, while the

axial Axial may refer to: * one of the anatomical directions describing relationships in an animal body * In geometry: :* a geometric term of location :* an axis of rotation * In chemistry, referring to an axial bond * a type of modal frame, in music * ...

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 ''et al.'', ''Opt. Lett.'' 18,1867 (1993), and followed by J.Guck ''et al.'', ''Phys. Rev. Lett.'' 84, 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.

Multimode fiber-based traps

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 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 adaptive optics, allowing to dynamically reconfigure the optical trap during operation and adapt it to the sample.

Cell sorting

One of the more common cell-sorting systems makes use of flow cytometry through fluorescence imaging. 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. 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 optical lattice can be created using diffractive optics and optical elements. On the other hand, K. Ladavac ''et al.'' 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. 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

drag force In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...

that is competing directly with the optical gradient force ''(See Physics of optical tweezers)'' 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, 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. 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. Scientists at the University of St. Andrews have received considerable funding from the UK

Engineering and Physical Sciences Research Council The Engineering and Physical Sciences Research Council (EPSRC) is a British Research Council that provides government funding for grants to undertake research and postgraduate degrees in engineering and the physical sciences, mainly to univers ...

( EPSRC) for an optical sorting machine. This new technology could rival the conventional fluorescence-activated cell sorting.

Evanescent fields

An evanescent field is a residue optical field that "leaks" during

total internal reflection Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflect ...

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

). 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. 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 waveguide. It is termed as Lensless Optical Trapping ("LOT"). The orderly movement of the particles is aided by the introduction of Ronchi Ruling 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. 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 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. The evanescent field can also be used to trap cold atoms and molecules near the surface of an optical waveguide or optical nanofiber.

Indirect approach

Ming Wu, a

UC Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant uni ...

Professor of electrical engineering and computer sciences invented the new optoelectronic tweezers. 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 optical projection, this method allows a high flexibility of switching different optical landscapes. 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 field gradient, this is known as dielectrophoresis. 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. See comments by Professor Kishan Dholakia on this new technique, K. Dholakia, ''Nature Materials'' 4, 579–580 (01 Aug 2005) News and Views. "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 irectoptical tweezers".

Optical binding

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 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.

Fluorescence optical tweezers

In order to simultaneously manipulate and image samples that exhibit

fluorescence Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, tha ...

, optical tweezers can be built alongside a fluorescence microscope or as an integrated solution such a
C-trap^®
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. 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.

Tweezers combined with other imaging techniques

Other than 'standard' fluorescence optical tweezers are now being build with multiple color Confocal, Widefield, STED, FRET, TIRF or IRM. This allows applications such as measuring: protein/DNA localization binding, protein folding, motor protein force generation, visualization of cytoskeletal filaments and motor dynamics, microtubule dynamics, manipulating liquid droplet (rheology) or fusion. These are being built in non correlated 'academic' setups and fully integrated solutions such a
Lumicks's C-trap ^®.

References

External links

* Video
Levitating DIAMONDS with a laser beam
{{Lasers Levitation Photonics Condensed matter physics Molecular biology Cell biology Biophysics Optical trapping 1986 introductions Force lasers