# Ideas Page

In general, I am very interested in the operation of lasers. I have a decent basic understanding of laser operation, but would like to explore this topic more through my project for the summer. I am particularly interested in transverse laser modes. I have been doing research into previous experiments and papers regarding laser modes, and several ideas look promising as potential project topics. Here is a list of my ideas:

### Using Longitudinal Modes to Determine the Speed of Light:

In exploring my interest in laser modes, I came across a paper describing an experimental setup to determine the speed of light by analyzing the longitudinal modes in a laser. It involves measuring the beat frequency between different longitudinal modes for several lengths of the laser cavity. Using knowledge of the frequency separation of longitudinal modes and the change in length, the speed of light can be obtained from a graph of the data. This experiment seems feasible with the materials on hand, and provides an interesting application of the topic of laser modes. A copy of the paper can be found here.

### Producing LG Modes with an End-Pumped Laser:

I came across a paper describing the experimental observation of Ince-Gaussian modes (see next idea). The experimental setup of this paper was centered around an end-pumped laser. The cavity would operate in higher order Laguerre-Gaussian modes, but by breaking the symmetry Ince-Gaussian modes were produced. Creating an end-pumped laser setup that produces Laguerre-Gaussian modes may prove to be a reasonably complex and worthwile project by itself. I found a paper describing such a setup in greater detail.

### Ince-Gaussian Modes:

In addition to the well known Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) laser modes, there are also Ince-Gaussian (IG) modes. These display elliptical symmetry, as opposed to spherical or Cartesian (as in LG and HG modes). I find it very interesting that HG and LG modes can be thought of as extreme cases of IG modes where the ellipticity is infinity and 0, respectively. Doing a project that explores this relationship would be very interesting to me. I found a paper on the experimental production of IG modes, which can be found here. This may serve as a starting point for a project.

### Fractal Laser Modes:

I found a paper discussing the production of fractal laser modes, which looks very interesting. Fractals are a fascinating topic, and I am also very interested in laser modes, so this paper intrigued me. The experimental setup in the paper seems relatively complicated, but perhaps I can conduct a simpler version here at the LTC. Fractal modes are achieved using an unstable cavity. According to the paper, this can be attributed to the following: unstable cavities have round-trip magnification of M > 1, but a given mode must be the same when it completes a round-trip around the cavity, thus giving rise to the self-similar attribute of the fractal mode. Again, I'm not sure I have the means to replicate their experiment exactly, but it may be possible to make some simplifications. The paper can be found here.

### Creating Optical Vortex Modes with a Single Cylinder Lens:

This idea is directly from a previous project at the LTC by Hamsa Sridhar which I learned about through the paper. The project makes use of several different laser topics, including the form of the Gaussian beam and different types of laser modes. Although this project was already done here, perhaps I can do something similar or explore the original project from a different angle.

 Vince Gregoric June - 2010 Laser Teaching Center Stony Brook University