The Science Of Optical Trapping Arryx, Inc. July, 2002 The Light ...
The Science of Optical Trapping
Arryx, Inc.
July, 2002
The basic physical principles that make optical traps possible are not very complex. Understanding how and why
optical trapping works will help you to better control your experiments and the BioRyx® 200 system. This
document covers the basic physical concepts behind optical trapping and explains how the BioRyx® 200 system
works. Using this background, we then discuss techniques you can use for various types of samples and
applications. This document covers the following topics:
I. The Light Wave
II. Dielectrics
III. Trapping Matter with Light
IV. Absorption, Scattering and Transmission of Light
V. Laser Basics
VI. Further Thinking About Optical Traps
VII. Optical Trapping Techniques
I. The Light Wave
Light and Electromagnetic Fields
A fundamental property of light is that it consists of
oscil ating electric and magnetic fields. These fields carry the
light’s energy and are responsible for the interaction of the
light with material. The fields are transverse (perpendicular)
to the direction in which the light is traveling, as shown to the
right. In the figure on the right, the light ray is traveling to the
right. As the light travels, the electric field (E) oscil ates along
the vertical direction while the magnetic field (B) oscil ates in
and out of the page.
Wavelength and Color
The wavelength, λ, of light is the distance the light must travel for its electric field to oscil ate from its maximum
value to its minimum value and back to its maximum value. Thus, Figure 1 shows the fields over about 1.5
wavelengths of travel. The wavelength of light is what we perceive as color. Table 1 shows the wavelengths
corresponding to various colors of light.
Table 1—Wavelength of Light
Color
Approx. Wavelength (nm)
Approx Frequency (tera Hertz)
Ultraviolet
10-350
30000-857
Blue
475
632
Green
530
566
Yellow
590
508
Orange
610
492
Red
700
429
Infrared
780-700,000
385-0.4.29
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Light and Energy
The energy of light is inversely proportional to its wavelength. For example, blue light has more energy than red
light, since red corresponds to a longer wavelength. Another way to describe this relation is in terms of
frequency. The frequency of light, i.e. the rate at which the electric field oscil ates, is inversely proportional to the
wavelength. The energy of light is therefore proportional to its frequency.
The intensity of light describes the amount of energy that passes through an area in a given amount of time. To
increase the intensity, one typical y increases the output of the light source or else focuses the light into a
smal er region.
II. Dielectrics
A Close Look At Matter
The atoms and molecules which comprise a material are typical y electrically neutral. Although the material
consists of a large number of positively charged protons and negatively charged electrons, the net electric
charge is zero. Furthermore, the positive and negative charges within the material are uniformly distributed. If
one thinks of a single atom, this corresponds to the negative electrons being symmetrically distributed around
the positive nuclear charge.
Polarization of a Dielectric
The strength of the polarization increases with the strength of the applied electric field. The stronger the applied
field, the more charge is drawn to the ends of the atom or molecule. The quantity that indicates the degree of
charge separation is known as the electric dipole moment. When the external electric field is turned off, the
charges return to their former symmetric and uniform distribution. Materials which behave this way are cal ed
non-polar dielectrics.
Some molecules, such as water, have intrinsic dipole moments due to their atomic structure. These materials
are referred to as polar dielectrics. When a polar dielectric is placed in an electric field, the field tends to orient
the molecules such that their dipole moments align in the electric field. Thermal motion of the molecules tends to
randomize their orientation. Thus, the amount of alignment varies with temperature.
The Dielectric Constant
When a material is polarized by an external field, the many aligned dipoles within the material produce an
internal electric field that opposes the external y applied field.
The strength of the internal field depends upon the material properties and the strength and frequency of the
external y applied field. The material properties are captured in a single parameter cal ed the dielectric constant,
k. A vacuum has a dielectric constant of k=1, since it has no atoms to shield the external y applied field. In
general, as the frequency of the applied field is increased, the dielectric constant decreases because the
molecules have a harder time "keeping up" with the rapid field oscil ations. Polar substances, such as water,
tend to have high dielectric constants at low frequencies. For our purposes, the important parameter is the
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dielectric constant of the material at optical frequencies. The dielectric constants of some common materials are
given in Table 2. Values are shown both for a static applied field (DC) and for a field at optical frequencies. It
should be noted that the dielectric constant for a material is often given via a related quantity, the index of
refraction. The index of refraction is the square root of the dielectric constant at optical frequencies.
Table 2--Dielectric Constants of Common Materials
Material
Dielectric Constant k (DC)
Dielectric Constant k (Optical)
Vacuum
1
1
Air
1.0005
1.00005
Mineral Oil
2.24
2.22
Polystyrene
2.6
2.4
Pyrex
4.7
2.17
Ethanol
2.5
1.85
Water (25 °C)
78.5
1.78
Water (20 °C)
80.4
1.78
Silica
3.8
2.1
III. Trapping Matter with Light
Interaction of a Dipole with an External Electric Field
An electric dipole experiences an alignment force when placed in an external electric field. Additional y, the
entire dipole experiences a force in the direction of increasing electric field strength. The magnitude of the force
is determined by how quickly the electric field changes in space. If nothing prevents the motion of the dipole, it
wil move to the region of maximum electric field strength.
Optical Traps for High Dielectric Objects
In most cases, the object one may want to manipulate with an optical trap has a higher dielectric constant than
its environment. An example of this would be a polystyrene (k=2.4) sphere in water (k=1.78). To trap the sphere,
we need to create a smal region with very high electric field strength which fal s off quickly at the edges. One
way to do this is to focus a beam of light into a very narrow and intense spot by using a high-power lens like a
microscope objective lens.
In this case, the electric field used to trap the object is the electric fields associated with the beam of light. We
refer to this localized region of very high light intensity as an optical trap. Any object that has a higher dielectric
constant than the surrounding material--such as the polystyrene sphere in the example above—and that enters
the optical trap, wil become trapped.
Optical Trap Strength
The ability of an optical trap to hold an object in place or move it around depends on the strength of the trap. The
fol owing properties determine the trapping force:
• Dielectric constant: For most materials, the larger the difference between the object’s dielectric
constant and the dielectric constant of its environment, the stronger the trap will be. For very large
dielectric constants, radiation pressure begins to dominate and the traps begin to weaken. Good
trapping is usual y possible for objects that have a dielectric constant that is between 1.1 to 2.25 times
higher than the dielectric constant of the surrounding medium.
• Trap intensity: Higher-intensity light in the trap wil create a stronger trap.
• Trap gradient: The gradient is the rate of change in light intensity as one goes away from the center of
the trap. If the light intensity drops off very quickly with distance from the center of the trap, the trap wil
be much stronger.
If a trap is not strong enough, the trapped object may escape from the trap due to random thermal motion
(Brownian motion) or external forces such as drag force from flow of the surrounding medium, or gravity.
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IV. Absorption, Scattering, and Transmission of Light
Absorption and Heating
Some of the light in the optical trap is absorbed by the material in the trap. The exact amount of absorption
depends upon the material in the trap and the intensity of the trap. The absorbed light may heat up the object in
the trap dramatical y because the intensity of the light inside the light is extremely high. For example, because of
the low absorption of visible light by silica, heating effects are unimportant for most trapping purposes.
Transmission
If the sample is transparent, most of the light from the optical trap is transmitted through the sample. Trapping is
possible as long as the light is refracted by the sample. This occurs as long as the dipole moment of the medium
is sufficiently different from the dipole moment of the sample to be trapped.
Scattering
The term "scattering" refers to a number of different processes whereby light interacts with material and changes
direction. In some cases, other properties of the light such as its wavelength or polarization will also be changed.
In general, light may be scattered in any direction from the sample.
V. Laser Basics
What Is a Laser?
Lasers today are very commonplace and come in many varieties. However, al lasers share some common
characteristics. Central to the operation of a laser is the notion of light amplification. Lasers take a little bit of
"seed" light and amplify the light greatly by converting some external energy source, such as electricity, into
additional light. Another important feature of lasers is that the light coming out is highly collimated. Most
commonplace sources of light emit radiation uniformly in al directions. Col ecting al of this light and focusing it
into a narrow beam increases the intensity of light enormously (a factor of one mil ion at a distance of one
meter).
Using Lasers For Optical Traps
Both amplification and col imation result in a high-intensity source of light, which is a critical feature for creating
optical traps. Most realizations of optical traps achieve even higher field intensities by focusing the laser through
the objective lens of a microscope. This implementation creates a high-intensity spot in the viewing plane of the
microscope. Typical intensities are around 106 W/m2.
Another feature of lasers which is important for Arryx’s holographic optical trapping (HOT) technology is beam
coherence. The amplification mechanism for most lasers results in a beam whose constituent light waves are al
moving together in phase. This is critical for the process of using holograms to control optical traps.
Holographic Optical Traps
The BioRyx® 200 system employs a spatial light modulator to sculpt the light from the laser into as many as 200
independently controllable optical traps. The spatial light modulator consists of a liquid crystal display element
which modifies the phase of the coherent laser beam in order to create user-defined, three-dimensional patterns
of optical traps. The ability to sculpt the beam in this manner also al ows the user to create traps which have
non-standard beam profiles, allowing for stronger, more numerous, and more versatile traps than are available
with traditional optical trapping systems.
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VI. Further Thinking About Optical Trapping
Light and Momentum
In the description above, light was treated as a wave. Light can also be thought
of as a stream of photons which carry both energy and momentum. Photons
striking the surface of an object transfer some of their momentum to that object.
This effect, known as radiation pressure, is much like the force exerted by the
stream of water from a fire hose pointed at an object. However, radiation
pressure is a much weaker force and is usual y unnoticeable on macroscopic
objects.
Conserving Momentum of Scattered Light
The previous explanation for the trapping effect of an optical trap relies on
consideration of the change in energy of the light beam as a dielectric particle
enters the beam. It is also possible to understand trapping from a momentum
point of view. As a spherical particle is displaced from its central position in the
trap, it bends light, much as a lens does, as il ustrated in Figure 3. The bending
of the light means that a momentum component away from the trap has been
introduced into the light beam. In order to conserve momentum, the sphere
must therefore be deflected back into the focal point of the trap, and it is clear
again that the focused beam of light wil serve to contain the particle.
VII. Optical Trapping Techniques
Simple Optical Trap
The most straightforward optical trapping method involves using highly focused beams of light to grab particles
or cel s. Each beam grabs and manipulates a single object.
Using Boundaries
The ability to create multiple traps allows for unique trap implementations. For example, a tightly spaced circle of
traps can be generated in order to serve as a corral for containing particles. Optical traps in the corral can be
turned on and off briefly to serve as doors to the corral for introducing or removing particles.
Optical Trap Nets
Grabbing biological specimens with optical traps carries a risk for injury to the specimen resulting from heating
by the highly focused beam of light. Trap nets enable a "bed of nails" approach, in which a number of weaker
traps are combined to work together in manipulating objects. Trap nets also al ow motile objects to be captured
by distributing a large number of traps and increasing the likelihood that the object wanders into one or more of
the traps. Trap nets also make possible adroit manipulations of objects because the multiple traps can rotate as
wel as translate objects.
Trapping Materials with a Small Dielectric Constant
One of the disadvantages of standard optical traps is that the trapping mechanism relies on the fact that the
dielectric constant of the trapped particle is higher than that of the surrounding medium. Particles that have a
dielectric constant lower than the surrounding medium are repelled from the focused light. The BioRyx® 200
system implements a form of trap called an optical vortex, which is basical y a hollow shel of light, which forms a
container for the particle. The particle is repelled from the wal s of the light container, trapping the particle.
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Three-Dimensional Optical Trapping
The BioRyx® 200 system enables translation of trapped objects in the third dimension in addition to motion in
the imaging plane. Since many objects of interest have higher density than their surrounding medium,
sedimentation is common. Three-dimensional control al ows trapped objects to be lifted over sedimented
neighbors.
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