Multi-longitudinal mode emission in a bidirectional laser model

We are studying what can be considered as an intermediate situation between the unidirectional and the Fabry-Perot cavity configurations: the bidirectional ring laser. In it some spatial hole-burning appears because of the interference between the two counter propagating fields, which creates a shallow spatial modulation of the population inversion. Multimode emission in such systems has been investigated recently with a full Maxwell-Bloch model in which the uniform field approximation is not applied. With such a model only a few analytical results can be derived and the study of is thus mainly numeric. We address the analytical study of a mean-field bidirectional laser model that includes the possibility of backscattering.