Measuring the speed of light using beating longitudinal modes in an open-cavity HeNe laser

TL;DR

This undergraduate experiment measures the speed of light using beating longitudinal modes in an open-cavity HeNe laser, combining laser physics, statistical analysis, and precise measurement techniques.

Contribution

It introduces a practical method for measuring the speed of light with undergraduate laboratory equipment by analyzing longitudinal mode spacing in a HeNe laser.

Findings

Measured the speed of light as (2.9972 ± 0.0002) × 10^8 m/s

Demonstrated the relationship between mode spacing and cavity length

Minimized effects of frequency pushing and pulling

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.