Distributed feedback modes in a partially filled ring cavity

We have studied the threshold longitudinal modes of a structure composed of a ring cavity partially filled with a distributed feedback (DFB) medium. An eigenvalue equation and dispersion relation for the propagation constant, threshold gain, and mode location are derived and numerically solved for a number of cases. We show that the incommensurate nature of the unfilled ring cavity eigenfrequencies and DFB eigenfrequencies can lead to an enhancement of the frequency selectivity of the distributed feedback laser. The analysis is extended to consider finite linewidth and dispersion.