Multimode instabilities in the transit-multistable ring cavity

The transmission of a ring resonator, whose nonlinear medium is a beam of resonant two-level atoms with transit time shorter than their spontaneous lifetime, exhibits multistability. The stability of multiple longitudinal modes in such a system is analyzed for cavities tuned both to resonance and midway between resonances, with atoms injected in an eigenstate or in superposition states. Regions of instability are identified and are usually found to be locally associated with the multiple Ž . segments of the transmission function state equation that have negative slope. However, in some cases, the transmission is found to be globally unstable; the instability region covers a large continuous range of input field. This is because, in contrast to the usual multimode instability, the imaginary part of the field contributes even when atoms and cavity are both resonant with the driving laser. q 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 42.65.Sf; 42.65.Pc; 42.50.Gy