## Wednesday, June 30, 2010

### Measuring the Speed of Light Using Beating Longitudinal Modes in an Open-Cavity HeNe Laser

I love these kinds of experiments. They can be done in an undergraduate setting, the equipment isn't too expensive or complicated, and you get very accurate results. In this case, they measured the speed of light in air, and the experiment is accurate enough to distinguish that measured speed with the speed of light in vacuum.

Abstract: We describe an undergraduate laboratory that combines an accurate measurement of the speed of light, a fundamental investigation of a basic laser system, and a nontrivial use of statistical analysis. Students grapple with the existence of longitudinal modes in a laser cavity as they change the cavity length of an adjustable-cavity HeNe laser and tune the cavity to produce lasing in the TEM$_{00}$ mode. For appropriate laser cavity lengths, the laser gain curve of a HeNe laser allows simultaneous operation of multiple longitudinal modes. The difference frequency between the modes is measured using a self-heterodyne detection with a diode photodetector and a radio frequency spectrum analyzer. Asymmetric effects due to frequency pushing and frequency pulling, as well as transverse modes, are minimized by simultaneously monitoring and adjusting the mode structure as viewed with a Fabry-Perot interferometer. The frequency spacing of longitudinal modes is proportional to the inverse of the cavity length with a proportionality constant equal to half the speed of light. By changing the length of the cavity, without changing the path length within the HeNe gas, the speed of light in air can be measured to be ($2.9972 \pm0.0002) \times 10^{8}$ m/s, which is to high enough precision to distinguish between the speed of light in air and that in a vacuum.

But I think, equally as important, is the skill that the students could gather out of something like this.

This experiment exposes students to a variety of experimental and mathematical techniques, demonstrates the importance of uncertainty in measurement, provides a meaningful context for using weighted regression, and familiarizes the student with three ubiquitous instruments: the laser, the Fabry-Perot interferometer, and the RF spectrum analyzer.

Those are skills that can't be taught, but rather, acquired.

Zz.