Optical Tweezers

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Optical Tweezers

Optical Tweezers Web Page


Scattering Basics - Incident Plane Wave (from Michigan Tech)

Plane wave scattering theory may be used to illustrate gross optical trapping behavior via momentum transfer between the light field and the particle (total momentum is conserved). However, the optical waves employed to trap a particle in a typical optical-tweezers setup are most definitely not planar. For a full description of the scattering process see "Theory of trapping forces in optical tweezers", A. Mazolli, P. A. Maia Neto and H. M. Nussenzveig, Proc. R. Soc. Lond., A 8 December 2003 vol. 459 no. 2040 3021-3041.

When the size parameter \beta=\frac{2\pi a n}{\lambda_{0}}\gg 1, where a is the particle radius, n is the index of the medium surrounding the particle and \lambda_{0} is the vacuum wavelength of the trapping light, the results from a geometrical optics treatment holds.

For a geometrical optics treatment see, "Optical tweezers for undergraduates: Theoretical analysis and experiments", M. S. Rocha, Am. J. Phys. 77, 704 (2009).

Example: For a trapping laser of wavelength 635nm and a 2 micron particle in a surrounding medium of water, \beta\approx14 so the geometrical optics treatment holds and Mie scattering is the dominant trapping process.

More simply, there are two forces in action on a trapped particle, one of which will be more dominant depending on the size of the particle, the wavelength, etc. One of these forces is the transference of momentum by photons, the other force is the attractive force of the electric field gradient. The first acts somewhat like a strong current of water, the second draws the particle up to the highest point of the gradient, the center of the laser.



Making Diluted Solutions of MicroSpheres

  • Summer 2014 Powerpoint[1]
  • [2] Directions on how to use a QPD in an optical tweezer setup.
  • [3] Here are some slide prepping instructions from Berkeley.

Our own setup

  • Slide Setup
  • Microscope Slide Mount
  • Stokes' Setup
    • Spring 2013 Method (ramped) [4]
    • Summer 2014 Method (sinusoidal) [5]
      • Stoke's Force Calibration Video (sinusoidal)[6]

    Using NI Vision Assistant

    • [7] Image Acquisition/Saving Images. The UI for this program is rather difficult. To exit from video capture mode after capturing images there is a button that says close near the bottom left, underneath the camera options window.
    • [8] How to track the microspheres in NI Vision Assistant using pattern matching.
      • To get an actual video, you need to run the pictures through another video editing program. There is one on the computer, but there is no video option in NI Vision Assistant itself.
      • We actually tried both using pattern matching and brute force point and click methods. Neither worked very well, so we recommend using the QPD to get position measurements. You don't need an actual video for this.
      • The pattern matching does work quite well for the purposes of tracking brownian motion. You need to create a pattern matching script and then run it through batch processing.
    • Calibration

      • Calibrating the laser so that it points directly at the slide is very important. There are two steps.
      • First remove the slide so that you have only the objective, then position a pair of pinholes straight above the objective, and adjust the objective and mirrors until the laser can shoot through both pinholes. That's the rough calibration.
      • Next, put the slide on and and adjust the focus until you can see the interference patterns the laser makes on the slide. Then adjust the mirrors until the interference patterns are are round. Then the laser should be pointed straight at the slide.

    Our calculations using Brownian Motion

    • 2.56 micrometer spheres
      • Spring 2014- 4.6 mW Beam [9]
      • Summer 2014- 637nm and 980nm lasers [10]

    Calculating Trap Forces Using Stokes' Drag Force

    • [11] iPython Calculations
    • Beam Power (mW) Escape Velocity (microns/second) Trap Force (pN)
      5.5 20.57 0.44
      8.5 33.49 0.72
      11.7 40.00 0.86
      15.3 62.60 1.34
      19.0 84.71 1.82
      23.0 110.77 2.38
      Trap force graph stokes 1.png
    • A simple calculation would say that I need a 10 billion watt laser to achieve a 1 Newton trapping force. We should totally do that. The spheres would be so incredibly trapped.

    Trapping Video


    Performing Biological Measurements