# Difference between revisions of "Optical Tweezers"

## Optical Tweezers

### Background

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 1 micron particle in a surrounding medium of water, $\beta\approx7$ so the geometrical optics treatment holds and Mie scattering is the dominant trapping process.

### Resources

• 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
• [8] How to track the microspheres in NI Vision Assistant using pattern matching.
• 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

### 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
• 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.

### Performing Biological Measurements

• Installing Infared Laser
• Preparing bacteria to Analyze
• Current Progress and Issues