A Brief History: The physics behind the relatively young technique of optical tweezing has been known for centuries. In the seventeenth century, Johannes Kepler theorized that solar irradiance caused the tail of a comet to point away from the sun, and in 1873, James Clerk Maxwell proved theoretically that light can exert a force on matter (commonly know as radiation pressure, the "light force"). Sixty years later, Otto R. Frisch was able to deflet a beam of sodium atoms by bombarding the beam with light from a sodium lamp. In 1975, Hansch and Schalow proposed the idea of using lasers to trap atoms; a decade later, Steven Chu of Bell Laboratories was able to achieve three dimensional cooling in a technique nicknamed "optical molasses" (he would go on to win the Nobel Prize in Physics for the laser cooling and trapping of atoms with William Phillips and Claude Cohen-Tannoudji). These earlier techniques were all either optical two-beam traps or required an external force to be supplied by gravity or an electric field (these external forces provided trap stability). This paved the way for a single-beam gradient trap now known as optical tweezers . A year after Vladilen S. Letokov's proposal of atmoic trapping by light beams, Arthur Ashkin at Bell Laboratories accelerated transparent latex shpheres suspended in water using a laser beam (1986). By 1987, Arthur Ashkin of Bell Laboratories was able to trap living biological objects with a single laser, bringing the technique of optical tweezers, or optical trapping, to the scientific world.

Optical Trapping Theory: There are three general schemes for describing the physics behind optical tweezing. Generally, the particles trapped are dielectric (a substance with a conductivity less than a millionth of a siemens) spheres of polystyrene silica or silica and are polarized when subjected to an applied electric field. The ratio of sphere diameter to the wavelength of trapping length (d/lambda) is referred to as Z. In general, the less refractile or the smaller the particle, the less trapping force there is per watt.

• Rayleigh Regime, Z << 1 Trapping is described through electromagnetic theory (sphere dimensions are neglected; it is treated as an induced point dipole, since electromagnetic radiation incident on a dipole causes a force which naturally divides itself into two components, the gradient force and the scattering force). The focus is pictured as a diffraction limited region whose overall dimensions are approximately equal to the wavelength of the light. Trapping foces are calculated from the electromagnetic interaction between the laser field and the induced dipole (which decomposes into two components, the scattering and gradient forces). The gradient force points in the direction of the intensity gradient of the light, while the scattering force points in the direction of incident light. The condition of stability of the dipole in the field is that that ratio of the gradient force to the scattering force to be greater than unity (the restoring foce is greater than the force pushing the dipole out of the field). With Rayleigh particles, the direction of the force is independent of the particle shape, and only the magnitude varies with direction. (note: photo-refractive effect: light changes the index of refraction of piezoelectric crystals {piezoelectric effect: The generation of electricity or of electric polarity in dielectric crystals subjected to mechanical stress, or the generation of stress in such crystals subjected to an applied voltage}; discovered by Ashkin @ Bell Laboratories)
• Complex Region, Z = 1 Requires a complex approach to describe trapping; in this case, the dimensions of the focus cannot be negledted so ray optics cannot be used and the problem is usually solved by using electromagnetic theory. To derive trapping forces, we take into account the vector character of the laser's electromagnetic field (partial fields: incident, scattered and internal fields) and solve Maxwell's equations for the appropriate boundary value problem.
• Mie or Ray Optics Regmie, Z >> 1 In this region, the effects of diffraction are neglected and trapping is described using ray optics. The sphere is assumed to have a certain refractive index and the focus is assumed to be a point (the converging cone-shaped laser beam rays meet at the apex). Trapping forces are calculated considering the relection and refraction of rays at the surface of the sphere. More specifically, the radiation pressure is a force per unit area on an object due to the change in momentum of light. Since the force on a dielectric object is given by the change in momentum of light induced due to refraction of the light by the object, the total force on the object is the difference between the momentum flux entering the object and that leaving the object. The obejct is pushed by the reflection of light from its surface while radiation forces due to refraction can be used to pull a transparent object. When trapping Mie particles, both the magnigude and the direction of the forces depend on the particle shape. Within these constrictions, trapping in generally restricted to spheres and ellipsoids.

• Laser Scapel
• Kinetic Studies of DNA and other Nucleic Acids
• DNA Injection and/or incorporation
• Controlled Cell Fusion
• Microsurgery and manipulation of cells in vivo
• Studies of in vitro Fertilization
• Force measurements of Kinesin and other molecular motors
• Mechanical Studies of Bacterial Flagella
• Chromosome Dissection
• Chromosome Manipulation during Mitosis
• Gravity Perception in Plants
• Manipulation of Organelles & other subcellular structures
• Measure forces associated with cellular transport and adhesion
• DNA Stretching

Construction:the principles that govern an ideal optical trap cannot accurately reflect the the experimental setup due to the physical limitations of the laser (its divergent nature and Gaussian profile). Consequently, there is an intensive process of alignment of numerous optical components. For the current setup, the materials for the trap include:

• Sharp LT024 780nm (near-infrared) diode laser
• 50X90cm Optical Breadboard by Vere Inc. Thorlab Standard Optical Mounts/Posts
• Cylindrical Lenses (a pair with L1 + L2 = 31 cm)
• 2 Aluminum Coated first surface mirrors to redirect beam in x and y directions
• Spherical Lenses (a pair to resize the beam to completely fill the microscope objective)
• Periscope redirects beam in z-direction (and alllows beam to remain close to optical table)
• Dichroic Mirror
• Commercial Quality 1000X oil-immersion microscope
• CCD Camera and Filter

• Phosphor Infrared Viewing Card
• Yeast Cells
• Post-it Notes
• Microscope Slides
• Coverslips
• Parafilm
• Immersion Oil
• Scotch Tape

Research: Much attention has been given to optimization of trapping capabilities. The Numerical Aperture Quandary (NAQ) is the 'real life' trade-off between numerical aperture, trapping efficiency and trapping depth. The difficulty in many of these procedures has been the formulation of an effective measurement of trapping force. Past examples of quantifying the trapping power include the treatment of a trap as a spring with a stiffness value k. A dielectric particle at some position x from the focus of the laser beam experiences an attractive force towards the focus, and this restoring foce is proportional to the distance between the center of the sphere and the focus of the laser. The force is commonly calibrated through the application of a known force, such as gravity or viscous drag (related to sphere radius r, velocity v, liquid viscosity n and viscous drag coefficient y, F _vis = yv = 6ónrv). Additional indirect methods are employed, including the subjection of a trapped particle to a certain stress trap or vigorous osciallation at constant frequency and amplitude.

Abstract:A Study of Trapping Efficiency in Optical Tweezers as a Function of Beam Profile Yiyi Deng, Ward Melville High School, East Setauket, NY; Harold Metcalf and John No�, Laser Teaching Center, Department of Physics and Astronomy, Stony Brook University.

Optical tweezers are an important application of James Clerk Maxwell's 1873 abstraction of radiation pressure, or the ability of light to exert a force. More than a century was to pass before Arthur Ashkin of Bell Laboratories became the first to exploit the theory of radiation pressure by demonstrating optical confinement of transparent latex spheres suspended in aqueous media. Optical tweezers are capable of non-invasive trapping and manipulation of a variety of dielectric nanoparticles and have many interesting applications, especially in biomedical fields. These include chromosome dissection, kinetic studies of DNA and other nucleic acids, DNA injection, controlled cell fusion, microsurgery and manipulation of cells in vivo, in vitro fertilization and finally force measurements of kinesin, organelles, and other sub cellular structures associated with cellular transport and adhesion.

Tweezing theory depends on the ratio of the diameter of the sphere being trapped to the wavelength of the laser light. The ratio of the yeast cell diameter to the wavelength is approximately 5; consequently, the principles of ray optics are used to describe trapping. In this region (known as Mie), the effects of diffraction are neglected and trapping forces are calculated considering the momentum impulse of light due to the reflection and refraction of rays at the surface of the sphere. Since the force on a dielectric object is given by the change in momentum of light induced due to refraction of the light by the object, the total force on the object is the difference between the momentum flux entering the object and that leaving the object. The object is pushed by the reflection of light from its surface while radiation forces due to refraction can be used to pull a transparent object.

In this study, a compact optical tweezers setup has been constructed on a 50x90 cm optical breadboard; the setup consists of a Sharp LT024 780 nm (near-infrared) diode laser, cylindrical and spherical lenses, various first-surface mirrors, and a commercial-quality 1000x oil-immersion microscope. Safety precautions have been taken into consideration in the design of the setup. There are many practical obstacles (mis-alignment of optical elements, laser beam distortions, etc) to achieving the theoretically predicted performance. Optimizing the trap efficiency is especially crucial when working with a relatively low power laser beam. Our setup uses a 20 mW laser (which is not much stronger than a laser pointer), while other research tweezers use lasers 10 - 100 times more powerful. For an optical trap to be stable, the beam must be symmetric about the direction of propagation; this is achieved by careful positioning of the telescoping lens systems and adjustment of the mirrors that lead to the microscope so the beam passes directly through the middle of each lens. Mounting the components as close as possible to the surface of the rigid optical breadboard minimizes changes in alignment due to vibration.

In a past study in this laboratory, modifying the laser beam profile has been shown to increase trapping efficiency, in spite of some loss of beam intensity. I hope to formulate a mathematical model for the dependence of trapping efficiency on beam intensity distribution, and to test this model with appropriate experiments; the light can be redistributed by simply blocking out portions of the beam, or by using an aspheric lens system or a diffractive element. Difficulties already encountered stem from the lack of a mature theoretical explanation of trapping in the complex-Mie region as well as the absence of a universal and effective method for quantifying trapping power.

This research was supported by the Simons Foundation and NSF Grant PHY 00-98044.

Challenges:

• The beam must be symmetric about the direction of propagation in order for the optical trap to be stable. This is achieved throgh careful adjustment of the mirrors that lead to the microscope so the beam passes directly through the middle of each lens.
• Vibrations of the optical components must be minimized. The setup is atop a pre-drilled optical table and the introduction of a periscope (a vertical mirror configuration) allows the majority of the beam path to be kept close to the optical table.
• The formulation of a practical theoretical model for trapping in the "complex region" that agrees with experimental results has yet to be developed. At this time, most researchers resort to the ray optics regime for theory which has projected trapping efficiency significantly deviant from observed trapping.
• Beam collimation and reshaping are necessary for optimal trapping conditions. A near-infrared diode laser is too divergent for use without alteration. Spherical lenses correct the beam diameter while cylindrical lenses correct for the elliptical nature of the emerging beam. The beam diameter deviation due to spherical aberration has been calculated and does not present a noticeable effect at this stage.
• Attempts to modify the Gaussian nature of the emergent laser have been numerous. This has been accomplished with diffractive optics as well as an aspheric lens system. Both systems are scientifically sound methods for molding a Gaussian profile beam into a "flat top" or "top hat" profile, though not without significant intensity losses. The patented aspheric beam flattener has the advantage of operation over a wide range of wavelengths.

Procedures: Electronic Setup

• Power Boxes:

  

• Two Power Boxes:

  

• Research operational amplifiers ("op amps") for integrated circuits and floating output
• There are three basic assumptions made about op amps : infinite voltage gain, infinite input resistance (or zero input current), and zero output resistance (infinite output current capability).

Procedures: Turning on the sharp LT024 laser

• Turn down laser current on large box
• Turn on small boxes and set voltage to 15V, 15V
• Turn on voltmeter and set to 2 decimal points
• Turn on larfe box and flip switch labelled laser current
• SLOWLY use coarse and fine adjustment to get voltmeter to read 5.00V (2.50 is threshold for beam)
• A not on turning the contraption off: slowly reduce the laser current (both coarse and fine adjustments to zero) and retrace all steps

Procedures: "Un-ellipticalizing" the Emergent Laser Beam

• The diode laser's characteristic elliptical profile must be corrected for maximum use of laser power
• To preserve the collimated nature of the laser (from the collimating lens), place two lenses at the sum of their focal lengths
• Since the beam needs to be rezised in one direction ("horizontal" or "x"), cylindrical lenses should be used
• Based on the thin lens assumptions, the lenses can be placed at any distance from the laser beam (as long as their relative positions are f1 +f2)
• The lens configuration created should resemble a telescoping (or reverse telescoping) system
• Use the infrared phosphor viewer to make sure the beam appears round (even after extended propagation)
• Remember the Cylindrical Lens Study and the study to measure focal lengths (and "Vodka effect")

Procedures: Redirection of the the Laser Beam with Al coated first surface mirrors

• Mirrors will reduce the length of the setup; use mirrors of the highest possible quality (preferable gold)
• Be sure the beam is not hitting the edge of a mirror at all times
• All beam redirections should not resize the beam in any way (resultant beams are of uniform quality along the path of propagation)
• The spot should maintain the same height (this is ensured by comparing the reflected beam to a mark on a beam block)
• Because of the pre-drilled optical breadboard, the laser is directed along a selected array of dots in this experiment

Procedures: Resizing the Laser Beam

• Optimal trapping has been shown to require the filling of the microscope objective (or slight overfilling)
• A generally accepted method for calculating the size of the pupil of the objective: d(pupil)= 500 * Numerical aperture / Magnification
• For this setup, NA = 1.25, M = 100 so the beam size should be 6.25mm to create the maximum intensity gradient
• Various measurements of the laser beam diameter were taken (see "data"); results projected a 2X beam expansion
• Beam expansion is done with spherical lenses; to retain collimation, they are placed at the sum of the focal lengths
• The ratio of f1 to f2 should be 1:2; the beam should travel through the lens with the shorter focal length first (see thin lens equations)
• The actual focal lengths used depend on the amount of available space for the setup (shorter focal lengths magnify error but save space)
• The beam leaves the second Al mirror and travels through BPX060 (f1=50mm) and 150mm later, BPX070 (f2=100mm)
• At this point, the beam is ready for use in the tweezers device.

Procedures: Redirection of the Laser Beam (Periscope)

• Special precautions have been taken to minimize alignment and trapping difficulties due to vibrations (inculding the use of an optical breadboard, the laboratory location and the use of low posts to keep the setup low).
• To use the laser beam for trapping, it must be directed up into the microscope (periscope)
• Be sure the beam does not hit mirror edges and adjust heignt of periscope enter microscope
• The dichroic mirror (which reflects 80% of infrared radiation) should be on separate posts from the CCD and the filter for ease of edjustment

Procedures: Verticalization and Horizontalization of Beam

• The basic Goal of this procedure is to use optical tricks to get a reflected image superimposed on the incident beam
• The beam must run parallel to a plumb bob dropped from the dichroic mirror so that the reflected laser light can be seen
• Avoid looking directly into the beam; a neutral density filter may be used to attenuate the beam to prevent injury
• To verticalize, use a flat mirror on the surface of the optical breadboard and an infrared viewing card with a small aperture
• Adjust the dichroic mirror carefully; small angluar shifts modify beam position significantly
• When the reflection of the infrared dot coincides with the incident beam, verticalization has been achieved
• This is a tedious process; the use of a hollow column to hold the infrared viewer may help reduce strain
• When this is complete, use the infrared aperture between the top periscope mirror and dichroic; repeat process of aligning incident and reflected beams

Figure 1: Correct Dichroic Mirror Angle

Figure 2: Incorrect Dichroic Mirror Tilt

Figure 3: Incorrect Dichroic Mirror Tilt

Figure 4: Dichroic Mirror Tilt Adjustment

Procedures: Rose Chamber Construction

• Cut a square of parafilm approximately the size of a no. 0 coverslip
• Make parafilm doughnut and remove film in the middle
• Place parafilm doughnut flat on the slide and warm with heat gun
• Dilute particles with water and place a small drop inside parafilm doughnut
• Be sure not to let aqueous sample touch inside edges of parafilm doughnut
• If trapping yeast cells, use warm water (not hot)
• Using proper technique, put coverslip on parafilm (avoid air bubbles); make sure airtight seal is created
• Drop immersion oil on top of coverslip and place slide under microscope
• Note parafilm wax film thickness ~ 0.11mm (chamber thickness ~0.11mm)

Procedures: Measurement of Fine Adjustment Vertical Displacement :: Angular Degree Displacement Ratio

• Turn both fine and coarse adjustment knobs of microscope to either the highest or lowest setting
• Note that on this setup, CW rotation (from power side) = +y; ccw rotation (from power side) = -y
• Lay a ROUND pen flat on the stage of the microscope so its point extends beyond the edge of the stage
• Position a beam block with a post-it attached so that the tip of the pen is centered on the post-it
• Make a mark on the post-it by rolling the pen flat along the stage of the microscope
• Attach a tapered triangle needle to the fine adjustment knob (FAK) by using tapered 0.05" double sided foam adhesive and a stiff wire
• Position the wire to point to any of the compass directions, and then turn the FAK the maximum number of times possible
• The final rotation may not be complete; use a plum-bob angle finder to ascertain the rotation fraction
• Roll the pen flat on the stage again to make another mark on the post-it (thus he relative height is accurate)
• Measure the y dispancement marked on the post-it with a caliper, noting to measure consistently from ink top to ink top (width of line)
• Calculate the VD:ADD ratio by dividing the measured value of vertical dispacement by the number of (fractional) rotations or degrees
• The large number of rotations of the FAK is to maximize accuracy...think repeated trials in sequence
• Trial 1
• Data: 0.1079 in VD; 13 full rotations + 330deg
• Calculations: (0.1078in * 25.4mm/in)/(13rot + 11/12rot) = 0.196751137725mm VD/360rot
• Conversions: (0.196751137725mm VD/360rot) = .000546530938124mm/deg
• Trial 2
• Data: 0.1125 in VD; 13 full rotations + 330deg
• Calculations: (0.1125in * 25.4mm/in)/(13rot + 11/12rot) = 0.205329341317mm VD/360rot
• Conversions: (0.205329341317mm VD/360rot) = 0.000570359281437mm/deg
• Trial 3
• Data: 0.1167 in VD; 13 full rotations + 330deg
• Calculations: (0.1167in * 25.4mm/in)/(13rot + 11/12rot) = 0.29949700621mm VD/360rot
• Conversions: (0.196751137725mm VD/360rot) = 0.000591652694611mm/deg

Figure 1: Microscope Setup

Figure 2: Degree Finder

Procedures: Viewing the Laser Beam

• The laser will be visible only when it travels between materials of different indicides of refraction (n)
• Consequently, when the fine adjustment of the laser is tuned to the coverslip-sample interface or the sample-slide interface, the laser will be in focus
• The microscope is infinity corrected while the focus of the CCD is behind the actual camera. This allows for viewing on the TV screen

Procedures: Approximation of the Thickness of Melted Parafilm Wax

• As stated in the previous procedure for viewing the beam, the focused laser is the result of the positioning of the stage focus at the exact interfaces between the glass and aqueous media (rose chamber)
• The (y) distance between the two places where the laser is focused is equal to y(rose chamber) = y(melted parafilm)
• In another procedure, there is a method for determining the y(stage) as a function of fine adjustment knob degrees
• Find one laser focus. Attach a tapered triangular degree finder to the FAK at one of the cardinal directions
• Count the amount of full and fractional rotations (using the plum-bob angle finder) of the FAK as the stage moves from one laser focus to another
• The total number of degrees can be multipied by the VD::ADD ratio to find the y(focii of laser) = y(rose chamber) = y(melted parafilm)
• Setup 1 Calculations: 0.000546530938124mm/deg * 340deg = 0.185820618962mm
• Setup 2 Calculations: 0.000570359281437mm/deg * 340deg = 0.193922155689mm
• Setup 3 Calculations: 0.000591652694611mm/deg * 340deg = 0.201161916168mm
• Is it reasonable? Using a caliper, the unmelted unstretched parafilm wax thickness was determined to be (.0042in * 25.4cm/in) = .10668mm
• It was expected that stretched and melted parafilm would be be thinner...
• Note that stretched parafilm tends to "bunch", so it may measure up to (0.0053in * 25.4cm/in) = 0.13462mm
• Note that melted parafilm wax tends to (bubble? oxygen infused?) and measures approximately 0. ___mm
• Additionally, rose chamber thicknesses in this tweezer setup varies due to the use of double parafilm layers for greater sample volumes
• This investigation will be continued...

DATA:

• Measurements of Beam Diameter (after collimation and before expansion):
  5.00V = 2.9718mm ~ 2.63652mm ~ 2.62128mm ~ 2.63652mm ~ 2.65430mm ~ 3.42392mm
  5.01V = 2.9972mm ~ 3.13944mm ~ 3.21310mm ~ 3.13944mm ~ 2.95910mm
  5.02V = 3.0226mm ~ 3.31470mm ~ 3.68046mm ~ 3.31470mm ~ 3.67792mm
  5.10V = 4.30022mm
  5.20V = 7.19836mm
• All measurements are made in the dark with the caliper by the same person; still, there seem to be fluctuations in beam diameter, approximately ___%

New Developments:

• The problem with a beam traversing many optical elements (mirrors, lenses, etc) is noticable when the laser is of low power. At 10mW, this is certainly the case. A new design has been suggested that combines the tasks of beam circularization and expansion: the use of the cylindrical lenses NOT to minimize the beam (making the beam as wide as it was tall), but to maximize it (making it as tall as it is wide). The result is the elimination of two optical elements and trapping has been observed with this configuration.
• A new procedure for Rose Chamber construction involves heat gun application time and order. Also used mounting adhesive instead of parafilm wax to make a very thick chamber.

Paper:

• Introduction
• Trapping Theory
• Description of Setup (components, sample chamber, beam profile, field of view measurements)
• Trapping Force
• Hollow Beam Creation
• Perfomance Issues
• Conclusions
• Acknowledgements

• Introduction
• Theory
• Construction and Procedure
• Results and Discussion

Did You...

• Turn off the Laser Current
• Turn off the Laser
• Turn off the Laser Power Box
• Turn down both supply boxes
• Shut off the Multimeter
• Turn off the light source (box)
• Turn off the CCD Screen
• Dump out the yeast samples
• Store all slides properly
• Throw away all "experimental debris"

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