A precise measurement of the speed of light in air from the frequency separation of longitudinal modes in an open-cavity HeNe laser

Vince Gregoric, Mount Union College
Marty Cohen, Sam Goldwasser and John Noe,
Department of Physics and Astronomy,
Stony Brook University

    This project was motivated by an interest in the longitudinal modes of laser cavities, which are similar to standing wave harmonics on a string fixed on both ends in that the allowed modes are those in which an integer number of half-wavelengths exactly 'fit' within the laser cavity. From this condition, the frequencies of adjacent longitudinal modes are ideally separated by c/2nL where c is the speed of light, n is the refractive index of the medium in the cavity, and L is the cavity length. Thus by measuring the beat frequency between two adjacent longitudinal modes and the cavity length, one can in principle determine the speed of light.
    D'Orazio et al. [1] have recently described an experiment which uses this general concept to determine the speed of light with enough precision to differentiate between its value in air and in vacuum. The key feature of their method is to use an open-cavity laser with a movable output coupler (OC) mirror. It is then sufficient to determine the intermode beat frequency as a function of the precise mirror position relative to some fixed reference point, rather than the absolute total cavity length. The light velocity obtained in the analysis depends on the index of refraction of the ambient air but not that of the laser gain medium and Brewster window within the laser cavity. Finally, as discussed in Ref. [1], the exact separation between two adjacent longitudinal modes can be effected by frequency "pulling" and "pushing." These effects can be minimized by using a scanning Fabry-Perot interferometer to monitor and then adjust both the absolute and relative intensities of the longitudinal modes.
    Our experimental setup was similar to that described in Ref. [1]. The main modification was taking length measurements closely spaced over approximately 2 cm as opposed to the larger range of 16 cm used in Ref. [1]. We also determined distances from the micrometer driving the translation stage on which the OC mirror was mounted, rather than by using a separate caliper. The beam from our open cavity HeNe laser (λ = 632.8 nm) was directed by a beam splitter into both a photodiode connected to an RF spectrum analyzer (HP model 8566A) and a scanning Fabry-Perot interferometer connected to an oscilloscope. The spectrum analyzer was used to measure the precise beat frequency between adjacent modes, while the Fabry-Perot was used to monitor the mode intensities. Two complete sets of data were taken, one with and one without using the Fabry-Perot to minimize frequency pulling/pushing effects. It was apparent from the results that frequency pulling and pushing does in fact have a significant effect on the observed beat frequency for a given cavity length. Our final result for the speed of light in air was 2.9973 x108 m/s. This result is comparable to that obtained in Ref. [1]. The accepted value of the speed of light is 2.9979 x108 m/s in vacuum and 2.9971 x108 m/s in air at standard temperature and pressure. We are currently seeking to determine the error in our final result by analyzing the uncertainties in the length and frequency measurements.

This research was supported by a grant from the National Science Foundation (PHY-0851594).

[1] D. J. D'Orazio et al., Am. J. Phys. 78, pgs 524-528 (May 2010).