Oscillations conditions in a gain grating in the Bragg diffraction regime

Coupled-wave analysis is applied to the determination of an oscillation threshold in thick periodic grating with gain (distributed-feedback oscillator). Pure phase (refractive index modulation), amplitude (gain modulation) and mixed-type gratings are considered. The origin of oscillation modes and their position on the diffraction efficiency contour is analyzed. The threshold conditions are determined on a basis of analytical expressions.