Use of the beat frequency between two modes for frequency stabilization of internal-mirror lasers

We present a simple method of frequency stabilization of a laser with two orthogonal modes that uses the effects of anomalous dispersion at the active line. The result of this effect is that the frequency difference between oscillation modes varies during the frequency tuning along the Doppler line of the transition and has its minimum or maximum when the modes are symmetrically placed around the central part of the gain curve. We applied the semiclassical approach to describe the laser, and we established the rules for laser parameters to obtain the most convenient conditions for stabilization. We stabilized the thermally compensated experimental laser tube and reached frequency stabilities of 3 × 10(-9) and 3 × 10(-10) for integrating times of 1 and 134 s, respectively.