# Project Overview

## Topological singularities in light beams

### Department(s)

Physics and Astronomy

### Abstract

The goal of this project is to study optical beams that carry singular points or lines. These are beams where the mathematical wave description of the light involves the appearance points points where a parameter of the beam is multivalued. Optical vortices are an example where the phase of the wave circulates about a point. At the singular point, where the vortex lies, the intensity is zero. Situations involving singular points are not necessarily intuitive, revealing interesting and novel behavior when studied. Upon propagation the vortices may move or even form knots in 3-dimensions. Similar situations appear when we add polarization if light into the mix. These situations are interesting because they are physical manifestations of wave nature and their mathematical structure. They are of fundamental interest in topology but also have important information in biomedical imaging, remote sensing and communications, where singularities are the features that convey information.

The work will involve analyzing the theoretical aspects of the problem with Matlab or Mathematica, and in the lab, recreating the situations that we model. All of our projects involve novel ideas and seek new scientific results, so they will appear in publications when the work is completed. The actual lab work involves working with laser beams, optical hardware and programing beam-encoding devices, known as spatial light modulators. With them we can encode beams with a single vortex, or in a superposition of vortices that form a singular wavepacket, a new situation that we wish to investigate. We also use digital cameras to image the light. Further analysis is done with Matlab. The student will work independently on this project.

### Student Qualifications

Physics student. Preference is sophomore or upper-level.

### Number of Student Researchers

1 student

### Project Length

8 weeks