Ideas for Summer Project

At this point, I definitely want to work with optical tweezers, because the more I read about them the more fascinating they get (as well as more complicated). Dr. Noé showed me an old project that incorrectly determined the optimal overfilling of the objective aperture, and suggested that I could do a similar experiment correctly, which seemed like a good start.

When I read some recent studies that actually acquired results that suggested that underfilling is better, I thought that this disproved the old ray-optics calculations; however, as I read further I realized that the parameters of this experiment were specifically for microspheres sized close to the wavelength of light (0.5-2μmeters), and there are some differences in trap strength depending on whether the particle is significantly smaller than the wavelength of light, the same size, or significantly larger. At the moment there are two different models of tweezers: the dipole approach and the ray-optics approach. The problem is that neither theory works for particles between the two size ranges used (Rayleigh and Mie, respectively).

Since optical tweezers are primarily utilized in the biological sciences, the majority of samples that are optically tweezed are in this size range that has not been widely studied. So although I was originally thinking about doing a project that compared the trap force depending on over and underfilling the microscopic objective's aperture, I realized that there were two problems with this; (1) it's impractical (if not impossible in the given situation) to tweeze something that is significantly smaller than the wavelength of light and (2) there's really not a lot of practical application to measuring the forces on particles that aren't generally optically tweezed, especially since there are already two established, straightforward models for them. Although there is a generalized Lorenz-Mie theory that can quantify the in-between forces, it's a lot more complicated.

As for ideas, what I'm thinking at the moment is creating an inverted optical tweezers setup and doing one of several things with this:

1. The idea that I like the most right now is using spiral phase plates (or possibly a computer-generated phase mask, if possible?) to create optical vortices of varying topological charges in order to optimize the trapping force. I could look at this on an axial and/or lateral dimension, compare the intensity lost to the phase plate to the trap strength to see if there is a net gain in trap efficiency, analyze the size of the vortex vs the size of the particle and how this affects the trap strength (perhaps with slightly varying sized particles?), etc.
2. I just came up with a new idea after Dr. Noé sent me an article about a summary of optical tweezers that included a reference to a different article that talked about using optical vortices to trap particles with a lower IOR than the surrounding medium (which could be useful in drug delivery). I could therefore do an experiment that tests LG modes of different topological charges to trap a hollow glass sphere (or UCA) to see which produces the strongest trap, and/or test the overfilling that is best for these beams. I could also compare these forces to a regular TEM₀₀ beam's trap, for particles with a higher IOR.
3. I could also continue with Dr. Noé's original idea of recalculating the optimal overfilling/underfilling of the aperture of the microscopic objective. The problem with this is I'd either have to do it with large, Mie sized particles (at least 20x larger than the wavelength of the light) or I'd run into the issue of an experiment having already been done on the topic. The problem with this is that you have to create a new beam expander with different lenses every time you want to change the overfilling ratio.
4. If I created a fully steerable setup, then I could compare the optical trapping force for varying angles of input light and see if there's any difference depending on the angle of incidence upon the aperture of the microscopic objective (which it seems like there should be, despite no change in trap location, but I can't find any information on it.)

The easiest way to measure the optical trapping force on any of these three setups would be to calculate the drag force on the particle when it escapes the trap using the Stokes Theorem, or the equipartition theorem (which would use a high frame-rate ~200Hz camera). I think that it would be a lot cooler (as well as possibly more accurate) though to use some sort of motion detector (QPD, or higher frame-rate camera) to map the Brownian motion of the particle and analyze the power spectrum density to find the force of the trap. I've been reading a bit about Brownian motion and how to quantify it in this way, and even though it seems really complicated, I don't think that it would be impossible.

On that note, another possible project idea is to actually discover a way to quantify Brownian motion in the axial direction, as this has never been done before. Perhaps this could be done either using some sort of Doppler shift analysis, or having a photodiode (not quadrant) that's set at a certain distance from the trap and can tell how far the particle is by measuring the power and analyzing the displacement from this.

There are definitely other ideas out there (some more complex like using SLMs to create HOTs) but I think I have some ideas that would work, so I'll ask Dr. Noé about the feasibility of the ones that I have here, as well as the equipment that we have available.

Mini Project Ideas

These are ideas for experiments I might want to do with any time that I have left or as side projects, not directly related to optical tweezers.