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Three-Dimensional Optical Trap
According to the force analysis in the previous section, gradient force mainly affects the particle in the transverse direction, which will eventually balance at the extremes of light intensity and form a two-dimensional optical trap. Generally a Gaussian beam can easily form a two-dimensional optical trap, where particles are confined to the direction of light propagation by gradient force. However, due to the presence of scattering force, the direction of movement still maintains along the beam propagation. People have tried many methods to capture particles such as binding particle using a vertically upward laser beam, so that the force of gravity along the axial direction balances gradient force. However, these methods do not really solve the problem of the axial direction of the scattering force. In 1986 A. Ashkin proposed a single-beam optical trap to realize the three-dimensional optical trap .
In the three-dimensional optical trap particles in the force is divided into three scenarios: the focus of the beam is located directly on the center of the sphere, below and to the right, shown in Fig. 3.2. When a laser beam interacts with a dielectric particle, light rays will suffer a change in momentum in both horizontal and vertical directions. In Fig. 3.2a the center of dielectric particle O is located below the focus,
Fig. 3.2 Force diagrams of small bead in a laser beam when light rays a and b refract twice upon exiting the particle, angle between ray and the optical axis becomes small, namely longitudinal momentum of the light rays have increased. By momentum conservation the particle receives a force generated by the momentum change, means that the force will push the particle toward the beam focus. Similarly, when the focus of the beam is located above the center of the particle, as shown in Fig. 3.2b, and to the right of the particle, as shown in Fig.3.2c, gradient force will move the particle back to the beam focus. In addition, in beam propagation direction (Z-axis), the lateral forces will have a gradient in the Z-axis, tending to pull the particle close to beam focus too. Eventually, the dielectric particle confined by three-dimensional gradient force is stabilized bound in a potential well- the focal point of the beam.
A popular method for optical cell trapping in bio-engineering is to use either a microscope objective or optical fiber to deliver a focused laser beam onto a cell. The optical trapping process is illustrated step by step here using microscopic figures taken from video clips recorded in authors’ laboratory. Figure 3.3a-e display effect of optical force acting on a yeast cell. On the left side is an optical fiber axicon, a cone-shaped lens, which focuses laser beam into a narrow beam of width 2-3 ц-m, with a focus depth of 100 ^m at laser wavelength of 680nm. The yeast cells used in the test have a diameter of 3-5 m. A tightly focused beam is produced by a fiber axicon (a conical lens fabricated on fiber tip, which will be elaborated in the following sections). Once a cell falls into the light field, it is immediately being trapped by the beam and pushed toward right along the direction of laser propagation. It is very interesting to notice that the cell was not being bounced off the beam path, instead the tiny focused beam behaves as a grabber, first capturing the cell and then pushing the cell along beam path with a speed about 10mm/s at a laser power of 5mW. Oftentimes a cell can be trapped and affixed onto a microfluidic sidewall if it faces a
Fig. 3.3 Microscopic views of effect of optical force acting on a yeast cell: a, b a free-fall yeast cell moving downward, close to apex of a fiber axicon, c-e the yeast cell was pushed toward to the right by focused laser beam coming from fiber axicon, moving rightward along the beam pathway
Fig. 3.4 Two laser beams from fiber axicons are aligned collinear, forming a line-shaped cell trapping zone in three-dimensional space: a, b two cells passing through this zone are trapped along the beam path; c One more cell is trapped in a row, along with previously trapped two cells; d when laser is powered off, the three cells dissociate and move freely
focused laser beam. Figure 3.4a-d show a three-dimensional trap that can be used to catch a row of cells between two fiber tips. When two axicons are precisely aligned face-to-face, both laser beams coming from two axicons constitute a line-shaped cell trapping zone in three-dimensional space: it can trap multiple cells passing through this zone. Figure 3.4a display that two cells are moving toward the trap zone, and Fig.3.4b, c show trapping of two and three yeast cells trapped in the line shaped zone, lined up in a row in the zone. When the laser is powered off, the three cells dissociate immediately and move toward different directions freely, as shown in Fig. 3.4d.
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