SOVIET PHYSICS JETP VOLUME 22, NUMBER 4 APRIL, 1966 ON THE THEORY OF THE GAS LASER IN A WEAK LONGITUDINAL MAGNETIC FIELD M. I. D'YAKONOV A. F. Ioffe Physico-technical Institute, Academy of Sciences, U.S.S.R. Submitted to JETP editor April 17, 1965 J. Exptl. Theoret. Phys. (U.S.S.R.) 49, 116!:1-1179 (October, 1965) The emission from a gas laser in a longitudinal magnetic field is treated assuming that the Zeeman splitting is much smaller than the Doppler line width. The frequency of the resonator is assumed to be the same as the atomic frequency in the absence of a magnetic field. The polarizability of the gas in a magnetic field is evaluated with an accuracy to terms quadratic in the electric field strength. The threshold regime is investigated for the case that the Q 's for oscillations polarized along the x axis and along the y axis are different. It is shown that as long as the magnetic field strength is smaller than some critical value H 0 the radiation is linearly polarized and the frequency is constant. The polarization direction rotates in the magnetic field from 0 to 45°. In magnetic field strengths exceeding the critical value two modes with different frequencies arise and are right and left elliptically polarized. The de- pendence of the critical field, rotation of direction of polarization and frequency shifts on excitation above the threshold value are investigated qualitatively. For sufficiently intense excitation the beat frequency for H > H 0 depends nonmonotonically on the magnetic field strength and a second region of linear polarization appears. The results of the theory agree with experiment. 1. INTRODUCTION and for a magnetic field H 1 of the order of 10 Oe I became zero again. Beginning at this point there N recent experiments Culshaw and Kannelaud [_t , 2 ] was a new narrow region of linearly polarized observed a number of interesting effects occurring emission at the frequency w. Rotation of the polar- when a He-Ne gas laser (A. = 1.153 11) was placed ization direction was also observed in this region. in a weak magnetic field. In particular, in a longi- With further increase in field beats were again tudinal magnetic field when the cavity frequency w observed between circularly polarized modes. The coincided with the center of the atomic resonance beat frequency increased monotonically. line w 0 the following was observed. In the absence The existence of beats between circularly of a magnetic field the laser emission was linearly polarized modes in a magnetic field had been ob- polarized in a definite direction (the x axis). When served previously [ 3 ] and was explained by the fact the magnetic field was increased from zero to a that due to the Zeeman splitting of the working certain critical value, H 0 , of the order of some tens levels in a magnetic field the gain coefficients for of oersteds the emission remained linearly polar- right and left circularly polarized modes differ by ized but the direction of polarization was rotated an amount 2fl 2JL 0 H jti, where llo is the Bohr 45° from the x axis. The laser frequency did not magneton. Because of the well known laser fre- change when this occurred but remained equal to quency pulling towards the maximum gain coeffi- w. The rate of rotation of the direction of polari- cient [ 4 ] the frequencies of the left and right polar- zation as a function of magnetic field and the criti- ized modes were shifted in opposite directions cal value H 0 depended strongly on the excitation. from the frequency w by an amount "'(Aw/ku)fl Larger excitation corresponded to greater rotation where Aw is the cavity bandwidth and ku is the rates. In a magnetic field larger than the critical Doppler line width. value low frequency beats were observed between The nonmonotonic nature of the beat frequency two left and right circularly polarized modes at variation is of special interest; the existence of different frequencies. The dependence of the beat regions where beats are not observed but where frequency on the magnetic field was distinctive. the direction of polarization of the emission at the With increasing magnetic field the beat frequency unshifted frequency w rotates with increasing mag- increased linearly at first, then attained a maximum, netic field are of particular interest. Culshaw and 812