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What is optical manipulation?

Optical tweezers are a tool that can be used for trapping and manipulation of small transparent objects, such as cells and bacteria. This is possible since light carries momentum and thus can exert forces, or radiation pressure, on matter. The transfer of momentum from light to matter is also part of the reason why the tail of a comet always points away from the sun. Johannes Kepler attributed this to the radiation from the sun already in the 17th century. However, it was not until the advent of the laser that it became possible to exert sufficiently large forces to displace microscopic or nanoscale objects in the laboratory.

Arthur Ashkin did pioneering work in the 1970's regarding the effects of radiation pressure, and in 1986 he experimentally demonstrated stable trapping of 25 nm - 10 um dielectric particles, using a single strongly focused laser beam (the single-beam gradient force optical trap), usually referred to as optical tweezers. A year later Ashkin also demonstrated trapping of viruses, bacteria and eukaryotic cells, as well as the manipulation of organelles within cells. By using infrared laser light for trapping, absorption and optical damage could be reduced, allowing cells to reproduce within the optical trap.
Apart from the laser providing the light for optical trapping, a key component in the optical setup is a powerful lens, able to strongly focus the light to enable stable three dimensional trapping. This is possible with a high numerical aperture microscope objective. Thus, optical trapping can preferably be performed with the same microscope objective as is used for imaging of the sample. Optical tweezers have been combined with most modern optical imaging techniques, such as epi-fluorescence, confocal and multiphoton microscopy. Optical tweezers can therefore successfully be introduced to microscopy based single cell studies.

Traditionally there are two main theories that explain the trapping mechanisms in optical tweezers. When the trapped object is much smaller than the wavelength of the trapping laser beam, trapping can be explained by treating the object as an induced point dipole effected by an electromagnetic field. The time-averaged trapping force arises from the interaction of the induced dipole with the gradient of the field. This theory, using wave optics, is referred to as the Rayleigh approximation. In the other extreme, the conditions for Mie scattering are fulfilled, and the optical forces can be described using ray optics. This theory uses Snell's law of refraction and Fresnel's equations for reflection and transmission. When the trapped object has a size comparable to the wavelength, which is often the case in our research group working with biological objects, neither of the two theories is strictly valid to describe the optical trapping forces. Instead, more complete electromagnetic theories must be used.

An illustration of the trapping forces in the ray-optics regime is shown in the figure below.

In the figure a laser beam of increasing intensity from left to right is incident on a transparent sphere with a refractive index higher than the surrounding medium. The beam can be considered as a collection of rays, but for simplicity only two rays are shown, indicated by 1 and 2, where the ray from the more intense part of the beam, 1, is represented by a thicker line. Neglecting surface reflection and absorption, the rays are purely refracted in the surface of the sphere according to Snell's law. The refraction results in a different direction of the ray when leaving the bead, compared to the initial direction. Since photons carry momentum, the momentum of the ray has therefore changed, as illustrated for ray 1 in the vector diagram, by the amount dp.

According to Newton's third law, the sphere must therefore have gained an equal amount of momentum but of the opposite sign. The force on the sphere is thus given by the rate of momentum change, which is directly proportional to the light intensity. Thus, the ray denoted by 1 exerts a larger force, F1, than the weaker ray 2 exerting the force F2. The resulting net force will therefore be mainly directed towards the right in the, i.e. in the direction of the spatial intensity gradient (there is also a small component of the resulting force pointing in the direction of the incoming rays). The resulting force is usually divided into a scattering force, pointing in the direction of the incoming ray, and a gradient force acting in the perpendicular direction, i.e in the direction of the spatial intensity gradient. It is the gradient force that can be used for trapping, while the scattering force has the effect of pushing the particle in the direction of the ray. In the case illustrated in the figure above, the net force still has a component in the direction of light propagation (F1 and F2 have small components in the direction of the incoming rays), and stable trapping in three dimensions cannot occur. To achieve stable trapping, the light must be focused strongly, producing a three dimensional intensity gradient, as in b). In the illustrated case the intensity distribution is radial, which is the case for Gaussian laser beams.

Tracing two rays through the bead, the resulting forces points backward towards the laser focus, i.e., the forces in the axial direction resulting from the intensity gradient in the axial direction are larger than the forces trying to push the bead away. The consequence is that if the sphere is displaced from the equilibrium position near the laser focus, the optical forces will counteract the movement and push it back towards the equilibrium position. Thus, it is possible to trap objects in three dimensions by using a single strongly focused laser beam.

Basic optical tweezers setup

The basic optical and optomechanical elements needed for an optical tweezers setup are a laser, beam expansion optics, steering optics, a high NA objective, a holder for the sample and some means of observing the trapped objects. Conventional optical tweezers use a Gaussian TEM00 mode laser beam with good pointing stability and low power fluctuations. The optical tweezers are preferably configured around an inverted optical microscope, which can then also be used to image the sample. In addition, the microscope can be used to provide focus functions and means to control movements of the microscope table.

The use of an inverted microscope keeps the laser beam path close to the optical table, which is good both for safety reasons and for mechanical stability. An inverted microscope also facilitates the introduction of the laser beam into the optical path of the microscope before the objective. The laser beam can be introduced via a dichroic mirror that reflects the wavelength of the trapping laser light but transmits the wavelengths used for imaging the sample. Several microscope designs allow the laser beam to be introduced via a dichroic mirror positioned at a 45 degree angle between the microscope objective and the filter cube cassette.

This configuration allows the filter cubes for imaging to be changed without affecting the optical trapping, which is important when imaging multiple fluorescent probes with a monochrome camera. For trapping of biological samples, infrared laser light should be used to minimize optical damage. This is convenient also for the design of the dichroic mirror, which can be constructed to transmit light in the entire visible wavelength range used for imaging. An alternative approach would be to use the same dichroic mirror for the reflection of both the fluorescence excitation wavelengths and the wavelength of the trapping laser beam. Multi-band dichroic mirrors and filters must then be used in the filter cube to allow multicolor imaging, since the filter cube cannot be changed without releasing the trapped object.

The strong focusing of the laser light needed for stable three dimensional trapping can be achieved using a microscope objective with a high NA. Thus, immersion objectives are normally used to obtain a NA above 1. The external optics are usually arranged so that the plane where objects are trapped coincides with the imaging plane. This allows the same microscope objective to be used simultaneously for both optical trapping and imaging. The fact that the optical trapping plane coincides with the imaging plane also improves the quality of the trap, since microscope objectives are designed to minimize aberrations near the image plane. For infinity corrected objectives this implies that the laser beam should be collimated when entering the objective. Optimum trapping performance is obtained when the laser beam is expanded so that the 1/e2 intensity overfills the objective back aperture by around 10%, depending on the exact experimental conditions.

The optical trap can be moved within the sample using a number of different approaches. For xy movement of a single trap the easiest method is to move the microscope table. This is also the only way to move the trap over large distances (larger than the field of view). The trap is in this case kept at a fixed position, on the optical axis, relative to the objective. The direction of the laser beam must be changed to move the trap within the field of view. This can be achieved by moving one of the lenses external to the microscope, or by changing the direction of the laser beam using a gimbal mounted galvanometric or piezoelectric scanning mirror, an acousto-optic modulator (AOM) or a spatial light modulator (SLM). The two last approaches can also be used to split the laser light into several optical traps, which can be steered individually in two dimensions (AOM) or three dimensions (SLM). The trap can be moved in the axial (z) direction relative to the coverslip, by moving the microscope objective or the sample up and down. In both cases the trapped object remains in the image plane of the objective, while the object is moved with respect to the surrounding medium. The optical trap can also be moved relative to the image plane by changing the divergence of the laser beam. This can be realized by moving one of the external lenses in the axial direction, or by using an SLM. An example of an optical setup that can be used to realize optical trapping is shown in the figure below.

In this setup the laser beam is first expanded by an afocal telescope containing lenses L1 and L2. The laser light is then reflected in a gimbal mounted mirror (GMM) that is imaged onto the back aperture of the microscope objective by a second afocal telescope (lenses L3 and L4) in a 4-f configuration. The total transverse magnification of the two telescopes should be chosen such that the appropriate degree of overfilling of the objective back aperture is obtained. A gimbal mount allows the mirror to be tilted around its center position without any translation of the mirror. Thus, if the laser beam is centered on the mirror and the mirror is imaged onto the back aperture of the microscope objective, tilting the mirror only results in a change of the angle of the laser beam entering the microscope objective, without affecting the degree of overfilling. In other words, the laser beam will pivot around the back aperture of the microscope objective. Tilting the GMM thus results in an xy movement of the optical trap.

Since the angles needed for steering of the optical tweezers are usually small, the angle of the laser beam entering the objective is thus a factor of f3/f4 larger than the angle formed with the optical axis at the GMM. The tilting of the laser beam when entering the objective is converted to a transverse translation in the trapping plane.

A movement of the trap in the axial direction, that simultaneously keeps the degree of overfilling of the objective, can be achieved by moving lens L1 along the optical axis. This requires that the lens L2 is placed at focal length distance from the GMM. An alternative way of achieving movement in the axial direction is by moving lens L3 in the axial direction, which results in movement of the optical trap. This keeps the degree of overfilling at the back aperture if the optical trap is not simultaneously moved in the x or y direction through tilting of the GMM. However, even when combined with xy movements the change in degree of overfilling of the back aperture is small, since only the position of the beam at the back aperture, not the size, is affected by the tilting of the GMM when L3 has been moved.

More information

Read more about optical manipulation in Martin Persson's doctoral thesis

Page Manager: Måns Henningson|Last update: 5/4/2016

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