Theory of optical-waveguide distributed feedback lasers: A Green´s functions approach

The total scattered electric field of a periodic dielectric optical waveguide is derived in terms of the Green´s functions of the unperturbed structure. A condition for self-excitation that takes into account the coupling between radiation and guided modes is obtained in a very general manner and, therefore, is valid for arbitrary periods of the grating structure. Results show that the effect of the coupling between the oscillating guided field and radiation modes is to change the dependence of the threshold gain on the amplitude of the periodic perturbation: increasing the depth of the grating beyond an optimum value causes an increase in threshold due to larger coupling to radiation modes.