Recoil-induced effects in a bidirectional ring laser

We present a theoretical study of a bidirectional ring laser in which the active medium is a cold atomic vapor. A novel feature of our analysis is the self-consistent description of the atomic motion due to recoil. It is shown that the evolution of the two count er-propagating fields within the cavity can be very different from that when recoil is neglected. We present an analytical study of the stationary unidirectional and bidirectional emission solutions and an analysis of their stability for a given average atomic velocity and Gaussian atomic velocity distribution. It is shown that the unidirectional emission solution is unstable if either the average velocity or the velocity distribution width is larger than a specific threshold value. If the mode frequency is resonant with the atoms. the symmetric bidirectional emission solution is stable. If the mode frequency is blue-detuned, the laser emits, unidirectional pulses alternately in opposite directions. An initially inhomogeneously broadened medium in a blue-detuned ring laser experiences a continuous self-cooling process. which may reduce the atomic temperature down to the Doppler cooling limit. A simple analytical model interpreting the effect is presented.