Faraday rotation resulting from negative absorption

It is shown that `negative' Faraday rotation can be induced in a gas laser as a consequence of optical gain and is of opposite sign to that resulting from an absorbing transition. The magnitude of this rotation in the vicinity of a Gaussian gain line is derived theoretically and compared with measurements on two He-Ne laser tubes at a wavelength of 339 μm. The results offer a means of measuring Doppler linewidths and give rise to values of 380 MHz and 470 MHz for tubes of length 33 cm and 14 cm, respectively. These figures correspond to temperatures of 760 °K and 1140 °K, which are considerably higher values than have been quoted for larger laser tubes.